# 有限流網路基礎 · 脈衝 R07

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261015-advance-20261113-r07-finite-flow-network-foundations · 2026-10-15 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s0","a0","t0","u0"],"edges":[["s0","a0"],["a0","s0"],["a0","t0"],["t0","a0"]],"source":"s0","sink":"t0","capacities":[5,5,5,5],"flows":[4,2,3,1]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a0, s0, t0, u0], s0, t0, [[[a0, s0], 5, 2], [[a0, t0], 5, 3], [[s0, a0], 5, 4], [[t0, a0], 5, 1]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a0, s0, t0, u0], s0, t0, [[[a0, s0], 5, 2], [[a0, t0], 5, 3], [[s0, a0], 5, 4], [[t0, a0], 5, 1]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0001/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 2. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s1","a1","t1","u1"],"edges":[["s1","a1"],["a1","s1"],["a1","t1"],["t1","a1"]],"source":"s1","sink":"t1","capacities":[10,10,10,10],"flows":[8,4,6,2]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a1, s1, t1, u1], s1, t1, [[[a1, s1], 10, 4], [[a1, t1], 10, 6], [[s1, a1], 10, 8], [[t1, a1], 10, 2]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a1, s1, t1, u1], s1, t1, [[[a1, s1], 10, 4], [[a1, t1], 10, 6], [[s1, a1], 10, 8], [[t1, a1], 10, 2]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0002/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 3. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s2","a2","t2","u2"],"edges":[["s2","a2"],["a2","s2"],["a2","t2"],["t2","a2"]],"source":"s2","sink":"t2","capacities":[15,15,15,15],"flows":[12,6,9,3]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a2, s2, t2, u2], s2, t2, [[[a2, s2], 15, 6], [[a2, t2], 15, 9], [[s2, a2], 15, 12], [[t2, a2], 15, 3]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a2, s2, t2, u2], s2, t2, [[[a2, s2], 15, 6], [[a2, t2], 15, 9], [[s2, a2], 15, 12], [[t2, a2], 15, 3]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0003/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 4. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s3","a3","t3","u3"],"edges":[["s3","a3"],["a3","s3"],["a3","t3"],["t3","a3"]],"source":"s3","sink":"t3","capacities":[20,20,20,20],"flows":[16,8,12,4]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a3, s3, t3, u3], s3, t3, [[[a3, s3], 20, 8], [[a3, t3], 20, 12], [[s3, a3], 20, 16], [[t3, a3], 20, 4]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a3, s3, t3, u3], s3, t3, [[[a3, s3], 20, 8], [[a3, t3], 20, 12], [[s3, a3], 20, 16], [[t3, a3], 20, 4]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0004/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 5. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s4","a4","t4","u4"],"edges":[["s4","a4"],["a4","s4"],["a4","t4"],["t4","a4"]],"source":"s4","sink":"t4","capacities":[25,25,25,25],"flows":[20,10,15,5]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a4, s4, t4, u4], s4, t4, [[[a4, s4], 25, 10], [[a4, t4], 25, 15], [[s4, a4], 25, 20], [[t4, a4], 25, 5]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a4, s4, t4, u4], s4, t4, [[[a4, s4], 25, 10], [[a4, t4], 25, 15], [[s4, a4], 25, 20], [[t4, a4], 25, 5]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0005/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 6. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s5","a5","t5","u5"],"edges":[["s5","a5"],["a5","s5"],["a5","t5"],["t5","a5"]],"source":"s5","sink":"t5","capacities":[30,30,30,30],"flows":[24,12,18,6]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a5, s5, t5, u5], s5, t5, [[[a5, s5], 30, 12], [[a5, t5], 30, 18], [[s5, a5], 30, 24], [[t5, a5], 30, 6]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a5, s5, t5, u5], s5, t5, [[[a5, s5], 30, 12], [[a5, t5], 30, 18], [[s5, a5], 30, 24], [[t5, a5], 30, 6]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0006/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 7. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s6","a6","t6","u6"],"edges":[["s6","a6"],["a6","s6"],["a6","t6"],["t6","a6"]],"source":"s6","sink":"t6","capacities":[35,35,35,35],"flows":[28,14,21,7]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a6, s6, t6, u6], s6, t6, [[[a6, s6], 35, 14], [[a6, t6], 35, 21], [[s6, a6], 35, 28], [[t6, a6], 35, 7]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a6, s6, t6, u6], s6, t6, [[[a6, s6], 35, 14], [[a6, t6], 35, 21], [[s6, a6], 35, 28], [[t6, a6], 35, 7]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0007/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 8. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s7","a7","t7","u7"],"edges":[["s7","a7"],["a7","s7"],["a7","t7"],["t7","a7"]],"source":"s7","sink":"t7","capacities":[40,40,40,40],"flows":[32,16,24,8]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a7, s7, t7, u7], s7, t7, [[[a7, s7], 40, 16], [[a7, t7], 40, 24], [[s7, a7], 40, 32], [[t7, a7], 40, 8]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a7, s7, t7, u7], s7, t7, [[[a7, s7], 40, 16], [[a7, t7], 40, 24], [[s7, a7], 40, 32], [[t7, a7], 40, 8]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0008/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 9. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s8","a8","t8","u8"],"edges":[["s8","a8"],["a8","s8"],["a8","t8"],["t8","a8"]],"source":"s8","sink":"t8","capacities":[45,45,45,45],"flows":[36,18,27,9]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a8, s8, t8, u8], s8, t8, [[[a8, s8], 45, 18], [[a8, t8], 45, 27], [[s8, a8], 45, 36], [[t8, a8], 45, 9]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a8, s8, t8, u8], s8, t8, [[[a8, s8], 45, 18], [[a8, t8], 45, 27], [[s8, a8], 45, 36], [[t8, a8], 45, 9]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0009/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 10. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s9","a9","t9","u9"],"edges":[["s9","a9"],["a9","s9"],["a9","t9"],["t9","a9"]],"source":"s9","sink":"t9","capacities":[50,50,50,50],"flows":[40,20,30,10]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a9, s9, t9, u9], s9, t9, [[[a9, s9], 50, 20], [[a9, t9], 50, 30], [[s9, a9], 50, 40], [[t9, a9], 50, 10]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a9, s9, t9, u9], s9, t9, [[[a9, s9], 50, 20], [[a9, t9], 50, 30], [[s9, a9], 50, 40], [[t9, a9], 50, 10]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0010/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 11. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s10","a10","t10","u10"],"edges":[["s10","a10"],["a10","s10"],["a10","t10"],["t10","a10"]],"source":"s10","sink":"t10","capacities":[55,55,55,55],"flows":[44,22,33,11]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a10, s10, t10, u10], s10, t10, [[[a10, s10], 55, 22], [[a10, t10], 55, 33], [[s10, a10], 55, 44], [[t10, a10], 55, 11]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a10, s10, t10, u10], s10, t10, [[[a10, s10], 55, 22], [[a10, t10], 55, 33], [[s10, a10], 55, 44], [[t10, a10], 55, 11]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0011/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 12. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s11","a11","t11","u11"],"edges":[["s11","a11"],["a11","s11"],["a11","t11"],["t11","a11"]],"source":"s11","sink":"t11","capacities":[60,60,60,60],"flows":[48,24,36,12]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a11, s11, t11, u11], s11, t11, [[[a11, s11], 60, 24], [[a11, t11], 60, 36], [[s11, a11], 60, 48], [[t11, a11], 60, 12]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a11, s11, t11, u11], s11, t11, [[[a11, s11], 60, 24], [[a11, t11], 60, 36], [[s11, a11], 60, 48], [[t11, a11], 60, 12]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0012/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 13. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s12","a12","t12","u12"],"edges":[["s12","a12"],["a12","s12"],["a12","t12"],["t12","a12"]],"source":"s12","sink":"t12","capacities":[65,65,65,65],"flows":[52,26,39,13]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a12, s12, t12, u12], s12, t12, [[[a12, s12], 65, 26], [[a12, t12], 65, 39], [[s12, a12], 65, 52], [[t12, a12], 65, 13]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a12, s12, t12, u12], s12, t12, [[[a12, s12], 65, 26], [[a12, t12], 65, 39], [[s12, a12], 65, 52], [[t12, a12], 65, 13]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0013/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 14. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s13","a13","t13","u13"],"edges":[["s13","a13"],["a13","s13"],["a13","t13"],["t13","a13"]],"source":"s13","sink":"t13","capacities":[70,70,70,70],"flows":[56,28,42,14]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a13, s13, t13, u13], s13, t13, [[[a13, s13], 70, 28], [[a13, t13], 70, 42], [[s13, a13], 70, 56], [[t13, a13], 70, 14]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a13, s13, t13, u13], s13, t13, [[[a13, s13], 70, 28], [[a13, t13], 70, 42], [[s13, a13], 70, 56], [[t13, a13], 70, 14]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0014/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 15. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s14","a14","t14","u14"],"edges":[["s14","a14"],["a14","s14"],["a14","t14"],["t14","a14"]],"source":"s14","sink":"t14","capacities":[75,75,75,75],"flows":[60,30,45,15]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a14, s14, t14, u14], s14, t14, [[[a14, s14], 75, 30], [[a14, t14], 75, 45], [[s14, a14], 75, 60], [[t14, a14], 75, 15]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a14, s14, t14, u14], s14, t14, [[[a14, s14], 75, 30], [[a14, t14], 75, 45], [[s14, a14], 75, 60], [[t14, a14], 75, 15]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0015/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 16. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s15","a15","t15","u15"],"edges":[["s15","a15"],["a15","s15"],["a15","t15"],["t15","a15"]],"source":"s15","sink":"t15","capacities":[80,80,80,80],"flows":[64,32,48,16]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a15, s15, t15, u15], s15, t15, [[[a15, s15], 80, 32], [[a15, t15], 80, 48], [[s15, a15], 80, 64], [[t15, a15], 80, 16]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a15, s15, t15, u15], s15, t15, [[[a15, s15], 80, 32], [[a15, t15], 80, 48], [[s15, a15], 80, 64], [[t15, a15], 80, 16]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0016/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 17. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s16","a16","t16","u16"],"edges":[["s16","a16"],["a16","s16"],["a16","t16"],["t16","a16"]],"source":"s16","sink":"t16","capacities":[85,85,85,85],"flows":[68,34,51,17]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a16, s16, t16, u16], s16, t16, [[[a16, s16], 85, 34], [[a16, t16], 85, 51], [[s16, a16], 85, 68], [[t16, a16], 85, 17]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a16, s16, t16, u16], s16, t16, [[[a16, s16], 85, 34], [[a16, t16], 85, 51], [[s16, a16], 85, 68], [[t16, a16], 85, 17]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0017/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 18. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s17","a17","t17","u17"],"edges":[["s17","a17"],["a17","s17"],["a17","t17"],["t17","a17"]],"source":"s17","sink":"t17","capacities":[90,90,90,90],"flows":[72,36,54,18]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a17, s17, t17, u17], s17, t17, [[[a17, s17], 90, 36], [[a17, t17], 90, 54], [[s17, a17], 90, 72], [[t17, a17], 90, 18]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a17, s17, t17, u17], s17, t17, [[[a17, s17], 90, 36], [[a17, t17], 90, 54], [[s17, a17], 90, 72], [[t17, a17], 90, 18]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0018/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 19. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s18","a18","t18","u18"],"edges":[["s18","a18"],["a18","s18"],["a18","t18"],["t18","a18"]],"source":"s18","sink":"t18","capacities":[95,95,95,95],"flows":[76,38,57,19]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a18, s18, t18, u18], s18, t18, [[[a18, s18], 95, 38], [[a18, t18], 95, 57], [[s18, a18], 95, 76], [[t18, a18], 95, 19]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a18, s18, t18, u18], s18, t18, [[[a18, s18], 95, 38], [[a18, t18], 95, 57], [[s18, a18], 95, 76], [[t18, a18], 95, 19]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0019/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 20. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s19","a19","t19","u19"],"edges":[["s19","a19"],["a19","s19"],["a19","t19"],["t19","a19"]],"source":"s19","sink":"t19","capacities":[100,100,100,100],"flows":[80,40,60,20]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a19, s19, t19, u19], s19, t19, [[[a19, s19], 100, 40], [[a19, t19], 100, 60], [[s19, a19], 100, 80], [[t19, a19], 100, 20]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a19, s19, t19, u19], s19, t19, [[[a19, s19], 100, 40], [[a19, t19], 100, 60], [[s19, a19], 100, 80], [[t19, a19], 100, 20]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0020/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 21. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s20","a20","t20","u20"],"edges":[["s20","a20"],["a20","s20"],["a20","t20"],["t20","a20"]],"source":"s20","sink":"t20","capacities":[105,105,105,105],"flows":[84,42,63,21]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a20, s20, t20, u20], s20, t20, [[[a20, s20], 105, 42], [[a20, t20], 105, 63], [[s20, a20], 105, 84], [[t20, a20], 105, 21]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a20, s20, t20, u20], s20, t20, [[[a20, s20], 105, 42], [[a20, t20], 105, 63], [[s20, a20], 105, 84], [[t20, a20], 105, 21]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0021/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 22. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s21","a21","t21","u21"],"edges":[["s21","a21"],["a21","s21"],["a21","t21"],["t21","a21"]],"source":"s21","sink":"t21","capacities":[110,110,110,110],"flows":[88,44,66,22]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a21, s21, t21, u21], s21, t21, [[[a21, s21], 110, 44], [[a21, t21], 110, 66], [[s21, a21], 110, 88], [[t21, a21], 110, 22]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a21, s21, t21, u21], s21, t21, [[[a21, s21], 110, 44], [[a21, t21], 110, 66], [[s21, a21], 110, 88], [[t21, a21], 110, 22]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0022/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 23. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s22","a22","t22","u22"],"edges":[["s22","a22"],["a22","s22"],["a22","t22"],["t22","a22"]],"source":"s22","sink":"t22","capacities":[115,115,115,115],"flows":[92,46,69,23]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a22, s22, t22, u22], s22, t22, [[[a22, s22], 115, 46], [[a22, t22], 115, 69], [[s22, a22], 115, 92], [[t22, a22], 115, 23]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a22, s22, t22, u22], s22, t22, [[[a22, s22], 115, 46], [[a22, t22], 115, 69], [[s22, a22], 115, 92], [[t22, a22], 115, 23]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0023/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 24. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s23","a23","t23","u23"],"edges":[["s23","a23"],["a23","s23"],["a23","t23"],["t23","a23"]],"source":"s23","sink":"t23","capacities":[120,120,120,120],"flows":[96,48,72,24]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a23, s23, t23, u23], s23, t23, [[[a23, s23], 120, 48], [[a23, t23], 120, 72], [[s23, a23], 120, 96], [[t23, a23], 120, 24]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a23, s23, t23, u23], s23, t23, [[[a23, s23], 120, 48], [[a23, t23], 120, 72], [[s23, a23], 120, 96], [[t23, a23], 120, 24]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0024/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 25. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s24","a24","t24","u24"],"edges":[["s24","a24"],["a24","s24"],["a24","t24"],["t24","a24"]],"source":"s24","sink":"t24","capacities":[125,125,125,125],"flows":[100,50,75,25]}。請依 [vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention] 欄序回答。

查看答案與解釋([a24, s24, t24, u24], s24, t24, [[[a24, s24], 125, 50], [[a24, t24], 125, 75], [[s24, a24], 125, 100], [[t24, a24], 125, 25]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

Wave6第七層核對=([a24, s24, t24, u24], s24, t24, [[[a24, s24], 125, 50], [[a24, t24], 125, 75], [[s24, a24], 125, 100], [[t24, a24], 125, 25]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0025/)

有限流網路 · qf-mod44-flow-network-qualification · candidate





## 26. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s0","a0","t0","u0"],"edges":[["s0","a0"],["a0","s0"],["a0","t0"],["t0","a0"]],"source":"s0","sink":"t0","capacities":[5,5,5,5],"flows":[-1,2,3,1]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s0, t0, [[[a0, s0], 5, 2], [[a0, t0], 5, 3], [[s0, a0], 5, -1], [[t0, a0], 5, 1]], [[[a0, s0], 2, 5, 是], [[a0, t0], 3, 5, 是], [[s0, a0], -1, 5, 否], [[t0, a0], 1, 5, 是]], 否, [[s0, a0], -1, 5, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s0, t0, [[[a0, s0], 5, 2], [[a0, t0], 5, 3], [[s0, a0], 5, -1], [[t0, a0], 5, 1]], [[[a0, s0], 2, 5, 是], [[a0, t0], 3, 5, 是], [[s0, a0], -1, 5, 否], [[t0, a0], 1, 5, 是]], 否, [[s0, a0], -1, 5, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0026/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 27. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s1","a1","t1","u1"],"edges":[["s1","a1"],["a1","s1"],["a1","t1"],["t1","a1"]],"source":"s1","sink":"t1","capacities":[10,10,10,10],"flows":[12,4,6,2]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s1, t1, [[[a1, s1], 10, 4], [[a1, t1], 10, 6], [[s1, a1], 10, 12], [[t1, a1], 10, 2]], [[[a1, s1], 4, 10, 是], [[a1, t1], 6, 10, 是], [[s1, a1], 12, 10, 否], [[t1, a1], 2, 10, 是]], 否, [[s1, a1], 12, 10, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s1, t1, [[[a1, s1], 10, 4], [[a1, t1], 10, 6], [[s1, a1], 10, 12], [[t1, a1], 10, 2]], [[[a1, s1], 4, 10, 是], [[a1, t1], 6, 10, 是], [[s1, a1], 12, 10, 否], [[t1, a1], 2, 10, 是]], 否, [[s1, a1], 12, 10, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0027/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 28. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s2","a2","t2","u2"],"edges":[["s2","a2"],["a2","s2"],["a2","t2"],["t2","a2"]],"source":"s2","sink":"t2","capacities":[15,15,15,15],"flows":[12,6,9,3]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s2, t2, [[[a2, s2], 15, 6], [[a2, t2], 15, 9], [[s2, a2], 15, 12], [[t2, a2], 15, 3]], [[[a2, s2], 6, 15, 是], [[a2, t2], 9, 15, 是], [[s2, a2], 12, 15, 是], [[t2, a2], 3, 15, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s2, t2, [[[a2, s2], 15, 6], [[a2, t2], 15, 9], [[s2, a2], 15, 12], [[t2, a2], 15, 3]], [[[a2, s2], 6, 15, 是], [[a2, t2], 9, 15, 是], [[s2, a2], 12, 15, 是], [[t2, a2], 3, 15, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0028/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 29. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s3","a3","t3","u3"],"edges":[["s3","a3"],["a3","s3"],["a3","t3"],["t3","a3"]],"source":"s3","sink":"t3","capacities":[20,20,20,20],"flows":[-4,8,12,4]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s3, t3, [[[a3, s3], 20, 8], [[a3, t3], 20, 12], [[s3, a3], 20, -4], [[t3, a3], 20, 4]], [[[a3, s3], 8, 20, 是], [[a3, t3], 12, 20, 是], [[s3, a3], -4, 20, 否], [[t3, a3], 4, 20, 是]], 否, [[s3, a3], -4, 20, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s3, t3, [[[a3, s3], 20, 8], [[a3, t3], 20, 12], [[s3, a3], 20, -4], [[t3, a3], 20, 4]], [[[a3, s3], 8, 20, 是], [[a3, t3], 12, 20, 是], [[s3, a3], -4, 20, 否], [[t3, a3], 4, 20, 是]], 否, [[s3, a3], -4, 20, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0029/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 30. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s4","a4","t4","u4"],"edges":[["s4","a4"],["a4","s4"],["a4","t4"],["t4","a4"]],"source":"s4","sink":"t4","capacities":[25,25,25,25],"flows":[30,10,15,5]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s4, t4, [[[a4, s4], 25, 10], [[a4, t4], 25, 15], [[s4, a4], 25, 30], [[t4, a4], 25, 5]], [[[a4, s4], 10, 25, 是], [[a4, t4], 15, 25, 是], [[s4, a4], 30, 25, 否], [[t4, a4], 5, 25, 是]], 否, [[s4, a4], 30, 25, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s4, t4, [[[a4, s4], 25, 10], [[a4, t4], 25, 15], [[s4, a4], 25, 30], [[t4, a4], 25, 5]], [[[a4, s4], 10, 25, 是], [[a4, t4], 15, 25, 是], [[s4, a4], 30, 25, 否], [[t4, a4], 5, 25, 是]], 否, [[s4, a4], 30, 25, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0030/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 31. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s5","a5","t5","u5"],"edges":[["s5","a5"],["a5","s5"],["a5","t5"],["t5","a5"]],"source":"s5","sink":"t5","capacities":[30,30,30,30],"flows":[24,12,18,6]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s5, t5, [[[a5, s5], 30, 12], [[a5, t5], 30, 18], [[s5, a5], 30, 24], [[t5, a5], 30, 6]], [[[a5, s5], 12, 30, 是], [[a5, t5], 18, 30, 是], [[s5, a5], 24, 30, 是], [[t5, a5], 6, 30, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s5, t5, [[[a5, s5], 30, 12], [[a5, t5], 30, 18], [[s5, a5], 30, 24], [[t5, a5], 30, 6]], [[[a5, s5], 12, 30, 是], [[a5, t5], 18, 30, 是], [[s5, a5], 24, 30, 是], [[t5, a5], 6, 30, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0031/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 32. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s6","a6","t6","u6"],"edges":[["s6","a6"],["a6","s6"],["a6","t6"],["t6","a6"]],"source":"s6","sink":"t6","capacities":[35,35,35,35],"flows":[-7,14,21,7]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s6, t6, [[[a6, s6], 35, 14], [[a6, t6], 35, 21], [[s6, a6], 35, -7], [[t6, a6], 35, 7]], [[[a6, s6], 14, 35, 是], [[a6, t6], 21, 35, 是], [[s6, a6], -7, 35, 否], [[t6, a6], 7, 35, 是]], 否, [[s6, a6], -7, 35, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s6, t6, [[[a6, s6], 35, 14], [[a6, t6], 35, 21], [[s6, a6], 35, -7], [[t6, a6], 35, 7]], [[[a6, s6], 14, 35, 是], [[a6, t6], 21, 35, 是], [[s6, a6], -7, 35, 否], [[t6, a6], 7, 35, 是]], 否, [[s6, a6], -7, 35, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0032/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 33. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s7","a7","t7","u7"],"edges":[["s7","a7"],["a7","s7"],["a7","t7"],["t7","a7"]],"source":"s7","sink":"t7","capacities":[40,40,40,40],"flows":[48,16,24,8]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s7, t7, [[[a7, s7], 40, 16], [[a7, t7], 40, 24], [[s7, a7], 40, 48], [[t7, a7], 40, 8]], [[[a7, s7], 16, 40, 是], [[a7, t7], 24, 40, 是], [[s7, a7], 48, 40, 否], [[t7, a7], 8, 40, 是]], 否, [[s7, a7], 48, 40, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s7, t7, [[[a7, s7], 40, 16], [[a7, t7], 40, 24], [[s7, a7], 40, 48], [[t7, a7], 40, 8]], [[[a7, s7], 16, 40, 是], [[a7, t7], 24, 40, 是], [[s7, a7], 48, 40, 否], [[t7, a7], 8, 40, 是]], 否, [[s7, a7], 48, 40, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0033/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 34. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s8","a8","t8","u8"],"edges":[["s8","a8"],["a8","s8"],["a8","t8"],["t8","a8"]],"source":"s8","sink":"t8","capacities":[45,45,45,45],"flows":[36,18,27,9]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s8, t8, [[[a8, s8], 45, 18], [[a8, t8], 45, 27], [[s8, a8], 45, 36], [[t8, a8], 45, 9]], [[[a8, s8], 18, 45, 是], [[a8, t8], 27, 45, 是], [[s8, a8], 36, 45, 是], [[t8, a8], 9, 45, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s8, t8, [[[a8, s8], 45, 18], [[a8, t8], 45, 27], [[s8, a8], 45, 36], [[t8, a8], 45, 9]], [[[a8, s8], 18, 45, 是], [[a8, t8], 27, 45, 是], [[s8, a8], 36, 45, 是], [[t8, a8], 9, 45, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0034/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 35. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s9","a9","t9","u9"],"edges":[["s9","a9"],["a9","s9"],["a9","t9"],["t9","a9"]],"source":"s9","sink":"t9","capacities":[50,50,50,50],"flows":[-10,20,30,10]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s9, t9, [[[a9, s9], 50, 20], [[a9, t9], 50, 30], [[s9, a9], 50, -10], [[t9, a9], 50, 10]], [[[a9, s9], 20, 50, 是], [[a9, t9], 30, 50, 是], [[s9, a9], -10, 50, 否], [[t9, a9], 10, 50, 是]], 否, [[s9, a9], -10, 50, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s9, t9, [[[a9, s9], 50, 20], [[a9, t9], 50, 30], [[s9, a9], 50, -10], [[t9, a9], 50, 10]], [[[a9, s9], 20, 50, 是], [[a9, t9], 30, 50, 是], [[s9, a9], -10, 50, 否], [[t9, a9], 10, 50, 是]], 否, [[s9, a9], -10, 50, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0035/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 36. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s10","a10","t10","u10"],"edges":[["s10","a10"],["a10","s10"],["a10","t10"],["t10","a10"]],"source":"s10","sink":"t10","capacities":[55,55,55,55],"flows":[66,22,33,11]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s10, t10, [[[a10, s10], 55, 22], [[a10, t10], 55, 33], [[s10, a10], 55, 66], [[t10, a10], 55, 11]], [[[a10, s10], 22, 55, 是], [[a10, t10], 33, 55, 是], [[s10, a10], 66, 55, 否], [[t10, a10], 11, 55, 是]], 否, [[s10, a10], 66, 55, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s10, t10, [[[a10, s10], 55, 22], [[a10, t10], 55, 33], [[s10, a10], 55, 66], [[t10, a10], 55, 11]], [[[a10, s10], 22, 55, 是], [[a10, t10], 33, 55, 是], [[s10, a10], 66, 55, 否], [[t10, a10], 11, 55, 是]], 否, [[s10, a10], 66, 55, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0036/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 37. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s11","a11","t11","u11"],"edges":[["s11","a11"],["a11","s11"],["a11","t11"],["t11","a11"]],"source":"s11","sink":"t11","capacities":[60,60,60,60],"flows":[48,24,36,12]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s11, t11, [[[a11, s11], 60, 24], [[a11, t11], 60, 36], [[s11, a11], 60, 48], [[t11, a11], 60, 12]], [[[a11, s11], 24, 60, 是], [[a11, t11], 36, 60, 是], [[s11, a11], 48, 60, 是], [[t11, a11], 12, 60, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s11, t11, [[[a11, s11], 60, 24], [[a11, t11], 60, 36], [[s11, a11], 60, 48], [[t11, a11], 60, 12]], [[[a11, s11], 24, 60, 是], [[a11, t11], 36, 60, 是], [[s11, a11], 48, 60, 是], [[t11, a11], 12, 60, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0037/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 38. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s12","a12","t12","u12"],"edges":[["s12","a12"],["a12","s12"],["a12","t12"],["t12","a12"]],"source":"s12","sink":"t12","capacities":[65,65,65,65],"flows":[-13,26,39,13]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s12, t12, [[[a12, s12], 65, 26], [[a12, t12], 65, 39], [[s12, a12], 65, -13], [[t12, a12], 65, 13]], [[[a12, s12], 26, 65, 是], [[a12, t12], 39, 65, 是], [[s12, a12], -13, 65, 否], [[t12, a12], 13, 65, 是]], 否, [[s12, a12], -13, 65, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s12, t12, [[[a12, s12], 65, 26], [[a12, t12], 65, 39], [[s12, a12], 65, -13], [[t12, a12], 65, 13]], [[[a12, s12], 26, 65, 是], [[a12, t12], 39, 65, 是], [[s12, a12], -13, 65, 否], [[t12, a12], 13, 65, 是]], 否, [[s12, a12], -13, 65, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0038/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 39. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s13","a13","t13","u13"],"edges":[["s13","a13"],["a13","s13"],["a13","t13"],["t13","a13"]],"source":"s13","sink":"t13","capacities":[70,70,70,70],"flows":[84,28,42,14]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s13, t13, [[[a13, s13], 70, 28], [[a13, t13], 70, 42], [[s13, a13], 70, 84], [[t13, a13], 70, 14]], [[[a13, s13], 28, 70, 是], [[a13, t13], 42, 70, 是], [[s13, a13], 84, 70, 否], [[t13, a13], 14, 70, 是]], 否, [[s13, a13], 84, 70, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s13, t13, [[[a13, s13], 70, 28], [[a13, t13], 70, 42], [[s13, a13], 70, 84], [[t13, a13], 70, 14]], [[[a13, s13], 28, 70, 是], [[a13, t13], 42, 70, 是], [[s13, a13], 84, 70, 否], [[t13, a13], 14, 70, 是]], 否, [[s13, a13], 84, 70, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0039/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 40. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s14","a14","t14","u14"],"edges":[["s14","a14"],["a14","s14"],["a14","t14"],["t14","a14"]],"source":"s14","sink":"t14","capacities":[75,75,75,75],"flows":[60,30,45,15]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s14, t14, [[[a14, s14], 75, 30], [[a14, t14], 75, 45], [[s14, a14], 75, 60], [[t14, a14], 75, 15]], [[[a14, s14], 30, 75, 是], [[a14, t14], 45, 75, 是], [[s14, a14], 60, 75, 是], [[t14, a14], 15, 75, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s14, t14, [[[a14, s14], 75, 30], [[a14, t14], 75, 45], [[s14, a14], 75, 60], [[t14, a14], 75, 15]], [[[a14, s14], 30, 75, 是], [[a14, t14], 45, 75, 是], [[s14, a14], 60, 75, 是], [[t14, a14], 15, 75, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0040/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 41. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s15","a15","t15","u15"],"edges":[["s15","a15"],["a15","s15"],["a15","t15"],["t15","a15"]],"source":"s15","sink":"t15","capacities":[80,80,80,80],"flows":[-16,32,48,16]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s15, t15, [[[a15, s15], 80, 32], [[a15, t15], 80, 48], [[s15, a15], 80, -16], [[t15, a15], 80, 16]], [[[a15, s15], 32, 80, 是], [[a15, t15], 48, 80, 是], [[s15, a15], -16, 80, 否], [[t15, a15], 16, 80, 是]], 否, [[s15, a15], -16, 80, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s15, t15, [[[a15, s15], 80, 32], [[a15, t15], 80, 48], [[s15, a15], 80, -16], [[t15, a15], 80, 16]], [[[a15, s15], 32, 80, 是], [[a15, t15], 48, 80, 是], [[s15, a15], -16, 80, 否], [[t15, a15], 16, 80, 是]], 否, [[s15, a15], -16, 80, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0041/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 42. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s16","a16","t16","u16"],"edges":[["s16","a16"],["a16","s16"],["a16","t16"],["t16","a16"]],"source":"s16","sink":"t16","capacities":[85,85,85,85],"flows":[102,34,51,17]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s16, t16, [[[a16, s16], 85, 34], [[a16, t16], 85, 51], [[s16, a16], 85, 102], [[t16, a16], 85, 17]], [[[a16, s16], 34, 85, 是], [[a16, t16], 51, 85, 是], [[s16, a16], 102, 85, 否], [[t16, a16], 17, 85, 是]], 否, [[s16, a16], 102, 85, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s16, t16, [[[a16, s16], 85, 34], [[a16, t16], 85, 51], [[s16, a16], 85, 102], [[t16, a16], 85, 17]], [[[a16, s16], 34, 85, 是], [[a16, t16], 51, 85, 是], [[s16, a16], 102, 85, 否], [[t16, a16], 17, 85, 是]], 否, [[s16, a16], 102, 85, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0042/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 43. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s17","a17","t17","u17"],"edges":[["s17","a17"],["a17","s17"],["a17","t17"],["t17","a17"]],"source":"s17","sink":"t17","capacities":[90,90,90,90],"flows":[72,36,54,18]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s17, t17, [[[a17, s17], 90, 36], [[a17, t17], 90, 54], [[s17, a17], 90, 72], [[t17, a17], 90, 18]], [[[a17, s17], 36, 90, 是], [[a17, t17], 54, 90, 是], [[s17, a17], 72, 90, 是], [[t17, a17], 18, 90, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s17, t17, [[[a17, s17], 90, 36], [[a17, t17], 90, 54], [[s17, a17], 90, 72], [[t17, a17], 90, 18]], [[[a17, s17], 36, 90, 是], [[a17, t17], 54, 90, 是], [[s17, a17], 72, 90, 是], [[t17, a17], 18, 90, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0043/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 44. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s18","a18","t18","u18"],"edges":[["s18","a18"],["a18","s18"],["a18","t18"],["t18","a18"]],"source":"s18","sink":"t18","capacities":[95,95,95,95],"flows":[-19,38,57,19]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s18, t18, [[[a18, s18], 95, 38], [[a18, t18], 95, 57], [[s18, a18], 95, -19], [[t18, a18], 95, 19]], [[[a18, s18], 38, 95, 是], [[a18, t18], 57, 95, 是], [[s18, a18], -19, 95, 否], [[t18, a18], 19, 95, 是]], 否, [[s18, a18], -19, 95, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s18, t18, [[[a18, s18], 95, 38], [[a18, t18], 95, 57], [[s18, a18], 95, -19], [[t18, a18], 95, 19]], [[[a18, s18], 38, 95, 是], [[a18, t18], 57, 95, 是], [[s18, a18], -19, 95, 否], [[t18, a18], 19, 95, 是]], 否, [[s18, a18], -19, 95, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0044/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 45. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s19","a19","t19","u19"],"edges":[["s19","a19"],["a19","s19"],["a19","t19"],["t19","a19"]],"source":"s19","sink":"t19","capacities":[100,100,100,100],"flows":[120,40,60,20]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s19, t19, [[[a19, s19], 100, 40], [[a19, t19], 100, 60], [[s19, a19], 100, 120], [[t19, a19], 100, 20]], [[[a19, s19], 40, 100, 是], [[a19, t19], 60, 100, 是], [[s19, a19], 120, 100, 否], [[t19, a19], 20, 100, 是]], 否, [[s19, a19], 120, 100, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s19, t19, [[[a19, s19], 100, 40], [[a19, t19], 100, 60], [[s19, a19], 100, 120], [[t19, a19], 100, 20]], [[[a19, s19], 40, 100, 是], [[a19, t19], 60, 100, 是], [[s19, a19], 120, 100, 否], [[t19, a19], 20, 100, 是]], 否, [[s19, a19], 120, 100, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0045/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 46. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s20","a20","t20","u20"],"edges":[["s20","a20"],["a20","s20"],["a20","t20"],["t20","a20"]],"source":"s20","sink":"t20","capacities":[105,105,105,105],"flows":[84,42,63,21]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s20, t20, [[[a20, s20], 105, 42], [[a20, t20], 105, 63], [[s20, a20], 105, 84], [[t20, a20], 105, 21]], [[[a20, s20], 42, 105, 是], [[a20, t20], 63, 105, 是], [[s20, a20], 84, 105, 是], [[t20, a20], 21, 105, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s20, t20, [[[a20, s20], 105, 42], [[a20, t20], 105, 63], [[s20, a20], 105, 84], [[t20, a20], 105, 21]], [[[a20, s20], 42, 105, 是], [[a20, t20], 63, 105, 是], [[s20, a20], 84, 105, 是], [[t20, a20], 21, 105, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0046/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 47. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s21","a21","t21","u21"],"edges":[["s21","a21"],["a21","s21"],["a21","t21"],["t21","a21"]],"source":"s21","sink":"t21","capacities":[110,110,110,110],"flows":[-22,44,66,22]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s21, t21, [[[a21, s21], 110, 44], [[a21, t21], 110, 66], [[s21, a21], 110, -22], [[t21, a21], 110, 22]], [[[a21, s21], 44, 110, 是], [[a21, t21], 66, 110, 是], [[s21, a21], -22, 110, 否], [[t21, a21], 22, 110, 是]], 否, [[s21, a21], -22, 110, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s21, t21, [[[a21, s21], 110, 44], [[a21, t21], 110, 66], [[s21, a21], 110, -22], [[t21, a21], 110, 22]], [[[a21, s21], 44, 110, 是], [[a21, t21], 66, 110, 是], [[s21, a21], -22, 110, 否], [[t21, a21], 22, 110, 是]], 否, [[s21, a21], -22, 110, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0047/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 48. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s22","a22","t22","u22"],"edges":[["s22","a22"],["a22","s22"],["a22","t22"],["t22","a22"]],"source":"s22","sink":"t22","capacities":[115,115,115,115],"flows":[138,46,69,23]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s22, t22, [[[a22, s22], 115, 46], [[a22, t22], 115, 69], [[s22, a22], 115, 138], [[t22, a22], 115, 23]], [[[a22, s22], 46, 115, 是], [[a22, t22], 69, 115, 是], [[s22, a22], 138, 115, 否], [[t22, a22], 23, 115, 是]], 否, [[s22, a22], 138, 115, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s22, t22, [[[a22, s22], 115, 46], [[a22, t22], 115, 69], [[s22, a22], 115, 138], [[t22, a22], 115, 23]], [[[a22, s22], 46, 115, 是], [[a22, t22], 69, 115, 是], [[s22, a22], 138, 115, 否], [[t22, a22], 23, 115, 是]], 否, [[s22, a22], 138, 115, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0048/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 49. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s23","a23","t23","u23"],"edges":[["s23","a23"],["a23","s23"],["a23","t23"],["t23","a23"]],"source":"s23","sink":"t23","capacities":[120,120,120,120],"flows":[96,48,72,24]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s23, t23, [[[a23, s23], 120, 48], [[a23, t23], 120, 72], [[s23, a23], 120, 96], [[t23, a23], 120, 24]], [[[a23, s23], 48, 120, 是], [[a23, t23], 72, 120, 是], [[s23, a23], 96, 120, 是], [[t23, a23], 24, 120, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s23, t23, [[[a23, s23], 120, 48], [[a23, t23], 120, 72], [[s23, a23], 120, 96], [[t23, a23], 120, 24]], [[[a23, s23], 48, 120, 是], [[a23, t23], 72, 120, 是], [[s23, a23], 96, 120, 是], [[t23, a23], 24, 120, 是]], 是, null, every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0049/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 50. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-capacity-audit；資料={"vertices":["s24","a24","t24","u24"],"edges":[["s24","a24"],["a24","s24"],["a24","t24"],["t24","a24"]],"source":"s24","sink":"t24","capacities":[125,125,125,125],"flows":[-25,50,75,25]}。請依 [source, sink, edge_capacity_flow_rows, capacity_rows, capacity_feasible, first_failed_edge_or_null, certificate] 欄序回答。

edge_capacity_flow_rows是[edge,capacity,candidate flow]，capacity_rows是[edge,flow,capacity,pass]；候選flow原值保留，負值須在此判失敗而非被改掉。

查看答案與解釋(s24, t24, [[[a24, s24], 125, 50], [[a24, t24], 125, 75], [[s24, a24], 125, -25], [[t24, a24], 125, 25]], [[[a24, s24], 50, 125, 是], [[a24, t24], 75, 125, 是], [[s24, a24], -25, 125, 否], [[t24, a24], 25, 125, 是]], 否, [[s24, a24], -25, 125, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)

Wave6第七層核對=(s24, t24, [[[a24, s24], 125, 50], [[a24, t24], 125, 75], [[s24, a24], 125, -25], [[t24, a24], 125, 25]], [[[a24, s24], 50, 125, 是], [[a24, t24], 75, 125, 是], [[s24, a24], -25, 125, 否], [[t24, a24], 25, 125, 是]], 否, [[s24, a24], -25, 125, 否], every_edge_requires_zero_less_equal_flow_less_equal_capacity)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0050/)

有限流網路 · qf-mod44-flow-capacity-audit · candidate





## 51. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s0","a0","t0","u0"],"edges":[["s0","a0"],["a0","s0"],["a0","t0"],["t0","a0"]],"source":"s0","sink":"t0","capacities":[5,5,5,5],"flows":[4,2,3,1]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s0, t0, [[[a0, s0], 5, 2], [[a0, t0], 5, 3], [[s0, a0], 5, 4], [[t0, a0], 5, 1]], [[a0, 5, 5, 是], [u0, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s0, t0, [[[a0, s0], 5, 2], [[a0, t0], 5, 3], [[s0, a0], 5, 4], [[t0, a0], 5, 1]], [[a0, 5, 5, 是], [u0, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0051/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 52. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s1","a1","t1","u1"],"edges":[["s1","a1"],["a1","s1"],["a1","t1"],["t1","a1"]],"source":"s1","sink":"t1","capacities":[10,10,10,10],"flows":[8,4,4,2]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s1, t1, [[[a1, s1], 10, 4], [[a1, t1], 10, 4], [[s1, a1], 10, 8], [[t1, a1], 10, 2]], [[a1, 10, 8, 否], [u1, 0, 0, 是]], 否, [a1, 10, 8, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s1, t1, [[[a1, s1], 10, 4], [[a1, t1], 10, 4], [[s1, a1], 10, 8], [[t1, a1], 10, 2]], [[a1, 10, 8, 否], [u1, 0, 0, 是]], 否, [a1, 10, 8, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0052/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 53. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s2","a2","t2","u2"],"edges":[["s2","a2"],["a2","s2"],["a2","t2"],["t2","a2"]],"source":"s2","sink":"t2","capacities":[15,15,15,15],"flows":[12,6,9,3]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s2, t2, [[[a2, s2], 15, 6], [[a2, t2], 15, 9], [[s2, a2], 15, 12], [[t2, a2], 15, 3]], [[a2, 15, 15, 是], [u2, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s2, t2, [[[a2, s2], 15, 6], [[a2, t2], 15, 9], [[s2, a2], 15, 12], [[t2, a2], 15, 3]], [[a2, 15, 15, 是], [u2, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0053/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 54. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s3","a3","t3","u3"],"edges":[["s3","a3"],["a3","s3"],["a3","t3"],["t3","a3"]],"source":"s3","sink":"t3","capacities":[20,20,20,20],"flows":[16,8,8,4]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s3, t3, [[[a3, s3], 20, 8], [[a3, t3], 20, 8], [[s3, a3], 20, 16], [[t3, a3], 20, 4]], [[a3, 20, 16, 否], [u3, 0, 0, 是]], 否, [a3, 20, 16, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s3, t3, [[[a3, s3], 20, 8], [[a3, t3], 20, 8], [[s3, a3], 20, 16], [[t3, a3], 20, 4]], [[a3, 20, 16, 否], [u3, 0, 0, 是]], 否, [a3, 20, 16, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0054/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 55. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s4","a4","t4","u4"],"edges":[["s4","a4"],["a4","s4"],["a4","t4"],["t4","a4"]],"source":"s4","sink":"t4","capacities":[25,25,25,25],"flows":[20,10,15,5]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s4, t4, [[[a4, s4], 25, 10], [[a4, t4], 25, 15], [[s4, a4], 25, 20], [[t4, a4], 25, 5]], [[a4, 25, 25, 是], [u4, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s4, t4, [[[a4, s4], 25, 10], [[a4, t4], 25, 15], [[s4, a4], 25, 20], [[t4, a4], 25, 5]], [[a4, 25, 25, 是], [u4, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0055/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 56. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s5","a5","t5","u5"],"edges":[["s5","a5"],["a5","s5"],["a5","t5"],["t5","a5"]],"source":"s5","sink":"t5","capacities":[30,30,30,30],"flows":[24,12,12,6]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s5, t5, [[[a5, s5], 30, 12], [[a5, t5], 30, 12], [[s5, a5], 30, 24], [[t5, a5], 30, 6]], [[a5, 30, 24, 否], [u5, 0, 0, 是]], 否, [a5, 30, 24, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s5, t5, [[[a5, s5], 30, 12], [[a5, t5], 30, 12], [[s5, a5], 30, 24], [[t5, a5], 30, 6]], [[a5, 30, 24, 否], [u5, 0, 0, 是]], 否, [a5, 30, 24, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0056/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 57. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s6","a6","t6","u6"],"edges":[["s6","a6"],["a6","s6"],["a6","t6"],["t6","a6"]],"source":"s6","sink":"t6","capacities":[35,35,35,35],"flows":[28,14,21,7]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s6, t6, [[[a6, s6], 35, 14], [[a6, t6], 35, 21], [[s6, a6], 35, 28], [[t6, a6], 35, 7]], [[a6, 35, 35, 是], [u6, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s6, t6, [[[a6, s6], 35, 14], [[a6, t6], 35, 21], [[s6, a6], 35, 28], [[t6, a6], 35, 7]], [[a6, 35, 35, 是], [u6, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0057/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 58. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s7","a7","t7","u7"],"edges":[["s7","a7"],["a7","s7"],["a7","t7"],["t7","a7"]],"source":"s7","sink":"t7","capacities":[40,40,40,40],"flows":[32,16,16,8]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s7, t7, [[[a7, s7], 40, 16], [[a7, t7], 40, 16], [[s7, a7], 40, 32], [[t7, a7], 40, 8]], [[a7, 40, 32, 否], [u7, 0, 0, 是]], 否, [a7, 40, 32, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s7, t7, [[[a7, s7], 40, 16], [[a7, t7], 40, 16], [[s7, a7], 40, 32], [[t7, a7], 40, 8]], [[a7, 40, 32, 否], [u7, 0, 0, 是]], 否, [a7, 40, 32, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0058/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 59. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s8","a8","t8","u8"],"edges":[["s8","a8"],["a8","s8"],["a8","t8"],["t8","a8"]],"source":"s8","sink":"t8","capacities":[45,45,45,45],"flows":[36,18,27,9]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s8, t8, [[[a8, s8], 45, 18], [[a8, t8], 45, 27], [[s8, a8], 45, 36], [[t8, a8], 45, 9]], [[a8, 45, 45, 是], [u8, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s8, t8, [[[a8, s8], 45, 18], [[a8, t8], 45, 27], [[s8, a8], 45, 36], [[t8, a8], 45, 9]], [[a8, 45, 45, 是], [u8, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0059/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 60. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s9","a9","t9","u9"],"edges":[["s9","a9"],["a9","s9"],["a9","t9"],["t9","a9"]],"source":"s9","sink":"t9","capacities":[50,50,50,50],"flows":[40,20,20,10]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s9, t9, [[[a9, s9], 50, 20], [[a9, t9], 50, 20], [[s9, a9], 50, 40], [[t9, a9], 50, 10]], [[a9, 50, 40, 否], [u9, 0, 0, 是]], 否, [a9, 50, 40, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s9, t9, [[[a9, s9], 50, 20], [[a9, t9], 50, 20], [[s9, a9], 50, 40], [[t9, a9], 50, 10]], [[a9, 50, 40, 否], [u9, 0, 0, 是]], 否, [a9, 50, 40, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0060/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 61. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s10","a10","t10","u10"],"edges":[["s10","a10"],["a10","s10"],["a10","t10"],["t10","a10"]],"source":"s10","sink":"t10","capacities":[55,55,55,55],"flows":[44,22,33,11]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s10, t10, [[[a10, s10], 55, 22], [[a10, t10], 55, 33], [[s10, a10], 55, 44], [[t10, a10], 55, 11]], [[a10, 55, 55, 是], [u10, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s10, t10, [[[a10, s10], 55, 22], [[a10, t10], 55, 33], [[s10, a10], 55, 44], [[t10, a10], 55, 11]], [[a10, 55, 55, 是], [u10, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0061/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 62. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s11","a11","t11","u11"],"edges":[["s11","a11"],["a11","s11"],["a11","t11"],["t11","a11"]],"source":"s11","sink":"t11","capacities":[60,60,60,60],"flows":[48,24,24,12]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s11, t11, [[[a11, s11], 60, 24], [[a11, t11], 60, 24], [[s11, a11], 60, 48], [[t11, a11], 60, 12]], [[a11, 60, 48, 否], [u11, 0, 0, 是]], 否, [a11, 60, 48, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s11, t11, [[[a11, s11], 60, 24], [[a11, t11], 60, 24], [[s11, a11], 60, 48], [[t11, a11], 60, 12]], [[a11, 60, 48, 否], [u11, 0, 0, 是]], 否, [a11, 60, 48, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0062/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 63. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s12","a12","t12","u12"],"edges":[["s12","a12"],["a12","s12"],["a12","t12"],["t12","a12"]],"source":"s12","sink":"t12","capacities":[65,65,65,65],"flows":[52,26,39,13]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s12, t12, [[[a12, s12], 65, 26], [[a12, t12], 65, 39], [[s12, a12], 65, 52], [[t12, a12], 65, 13]], [[a12, 65, 65, 是], [u12, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s12, t12, [[[a12, s12], 65, 26], [[a12, t12], 65, 39], [[s12, a12], 65, 52], [[t12, a12], 65, 13]], [[a12, 65, 65, 是], [u12, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0063/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 64. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s13","a13","t13","u13"],"edges":[["s13","a13"],["a13","s13"],["a13","t13"],["t13","a13"]],"source":"s13","sink":"t13","capacities":[70,70,70,70],"flows":[56,28,28,14]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s13, t13, [[[a13, s13], 70, 28], [[a13, t13], 70, 28], [[s13, a13], 70, 56], [[t13, a13], 70, 14]], [[a13, 70, 56, 否], [u13, 0, 0, 是]], 否, [a13, 70, 56, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s13, t13, [[[a13, s13], 70, 28], [[a13, t13], 70, 28], [[s13, a13], 70, 56], [[t13, a13], 70, 14]], [[a13, 70, 56, 否], [u13, 0, 0, 是]], 否, [a13, 70, 56, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0064/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 65. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s14","a14","t14","u14"],"edges":[["s14","a14"],["a14","s14"],["a14","t14"],["t14","a14"]],"source":"s14","sink":"t14","capacities":[75,75,75,75],"flows":[60,30,45,15]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s14, t14, [[[a14, s14], 75, 30], [[a14, t14], 75, 45], [[s14, a14], 75, 60], [[t14, a14], 75, 15]], [[a14, 75, 75, 是], [u14, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s14, t14, [[[a14, s14], 75, 30], [[a14, t14], 75, 45], [[s14, a14], 75, 60], [[t14, a14], 75, 15]], [[a14, 75, 75, 是], [u14, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0065/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 66. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s15","a15","t15","u15"],"edges":[["s15","a15"],["a15","s15"],["a15","t15"],["t15","a15"]],"source":"s15","sink":"t15","capacities":[80,80,80,80],"flows":[64,32,32,16]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s15, t15, [[[a15, s15], 80, 32], [[a15, t15], 80, 32], [[s15, a15], 80, 64], [[t15, a15], 80, 16]], [[a15, 80, 64, 否], [u15, 0, 0, 是]], 否, [a15, 80, 64, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s15, t15, [[[a15, s15], 80, 32], [[a15, t15], 80, 32], [[s15, a15], 80, 64], [[t15, a15], 80, 16]], [[a15, 80, 64, 否], [u15, 0, 0, 是]], 否, [a15, 80, 64, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0066/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 67. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s16","a16","t16","u16"],"edges":[["s16","a16"],["a16","s16"],["a16","t16"],["t16","a16"]],"source":"s16","sink":"t16","capacities":[85,85,85,85],"flows":[68,34,51,17]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s16, t16, [[[a16, s16], 85, 34], [[a16, t16], 85, 51], [[s16, a16], 85, 68], [[t16, a16], 85, 17]], [[a16, 85, 85, 是], [u16, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s16, t16, [[[a16, s16], 85, 34], [[a16, t16], 85, 51], [[s16, a16], 85, 68], [[t16, a16], 85, 17]], [[a16, 85, 85, 是], [u16, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0067/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 68. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s17","a17","t17","u17"],"edges":[["s17","a17"],["a17","s17"],["a17","t17"],["t17","a17"]],"source":"s17","sink":"t17","capacities":[90,90,90,90],"flows":[72,36,36,18]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s17, t17, [[[a17, s17], 90, 36], [[a17, t17], 90, 36], [[s17, a17], 90, 72], [[t17, a17], 90, 18]], [[a17, 90, 72, 否], [u17, 0, 0, 是]], 否, [a17, 90, 72, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s17, t17, [[[a17, s17], 90, 36], [[a17, t17], 90, 36], [[s17, a17], 90, 72], [[t17, a17], 90, 18]], [[a17, 90, 72, 否], [u17, 0, 0, 是]], 否, [a17, 90, 72, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0068/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 69. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s18","a18","t18","u18"],"edges":[["s18","a18"],["a18","s18"],["a18","t18"],["t18","a18"]],"source":"s18","sink":"t18","capacities":[95,95,95,95],"flows":[76,38,57,19]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s18, t18, [[[a18, s18], 95, 38], [[a18, t18], 95, 57], [[s18, a18], 95, 76], [[t18, a18], 95, 19]], [[a18, 95, 95, 是], [u18, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s18, t18, [[[a18, s18], 95, 38], [[a18, t18], 95, 57], [[s18, a18], 95, 76], [[t18, a18], 95, 19]], [[a18, 95, 95, 是], [u18, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0069/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 70. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s19","a19","t19","u19"],"edges":[["s19","a19"],["a19","s19"],["a19","t19"],["t19","a19"]],"source":"s19","sink":"t19","capacities":[100,100,100,100],"flows":[80,40,40,20]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s19, t19, [[[a19, s19], 100, 40], [[a19, t19], 100, 40], [[s19, a19], 100, 80], [[t19, a19], 100, 20]], [[a19, 100, 80, 否], [u19, 0, 0, 是]], 否, [a19, 100, 80, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s19, t19, [[[a19, s19], 100, 40], [[a19, t19], 100, 40], [[s19, a19], 100, 80], [[t19, a19], 100, 20]], [[a19, 100, 80, 否], [u19, 0, 0, 是]], 否, [a19, 100, 80, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0070/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 71. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s20","a20","t20","u20"],"edges":[["s20","a20"],["a20","s20"],["a20","t20"],["t20","a20"]],"source":"s20","sink":"t20","capacities":[105,105,105,105],"flows":[84,42,63,21]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s20, t20, [[[a20, s20], 105, 42], [[a20, t20], 105, 63], [[s20, a20], 105, 84], [[t20, a20], 105, 21]], [[a20, 105, 105, 是], [u20, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s20, t20, [[[a20, s20], 105, 42], [[a20, t20], 105, 63], [[s20, a20], 105, 84], [[t20, a20], 105, 21]], [[a20, 105, 105, 是], [u20, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0071/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 72. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s21","a21","t21","u21"],"edges":[["s21","a21"],["a21","s21"],["a21","t21"],["t21","a21"]],"source":"s21","sink":"t21","capacities":[110,110,110,110],"flows":[88,44,44,22]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s21, t21, [[[a21, s21], 110, 44], [[a21, t21], 110, 44], [[s21, a21], 110, 88], [[t21, a21], 110, 22]], [[a21, 110, 88, 否], [u21, 0, 0, 是]], 否, [a21, 110, 88, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s21, t21, [[[a21, s21], 110, 44], [[a21, t21], 110, 44], [[s21, a21], 110, 88], [[t21, a21], 110, 22]], [[a21, 110, 88, 否], [u21, 0, 0, 是]], 否, [a21, 110, 88, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0072/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 73. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s22","a22","t22","u22"],"edges":[["s22","a22"],["a22","s22"],["a22","t22"],["t22","a22"]],"source":"s22","sink":"t22","capacities":[115,115,115,115],"flows":[92,46,69,23]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s22, t22, [[[a22, s22], 115, 46], [[a22, t22], 115, 69], [[s22, a22], 115, 92], [[t22, a22], 115, 23]], [[a22, 115, 115, 是], [u22, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s22, t22, [[[a22, s22], 115, 46], [[a22, t22], 115, 69], [[s22, a22], 115, 92], [[t22, a22], 115, 23]], [[a22, 115, 115, 是], [u22, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0073/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 74. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s23","a23","t23","u23"],"edges":[["s23","a23"],["a23","s23"],["a23","t23"],["t23","a23"]],"source":"s23","sink":"t23","capacities":[120,120,120,120],"flows":[96,48,48,24]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s23, t23, [[[a23, s23], 120, 48], [[a23, t23], 120, 48], [[s23, a23], 120, 96], [[t23, a23], 120, 24]], [[a23, 120, 96, 否], [u23, 0, 0, 是]], 否, [a23, 120, 96, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s23, t23, [[[a23, s23], 120, 48], [[a23, t23], 120, 48], [[s23, a23], 120, 96], [[t23, a23], 120, 24]], [[a23, 120, 96, 否], [u23, 0, 0, 是]], 否, [a23, 120, 96, 否], every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0074/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 75. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-conservation-audit；資料={"vertices":["s24","a24","t24","u24"],"edges":[["s24","a24"],["a24","s24"],["a24","t24"],["t24","a24"]],"source":"s24","sink":"t24","capacities":[125,125,125,125],"flows":[100,50,75,25]}。請依 [source, sink, edge_capacity_flow_rows, internal_balance_rows, conservation_feasible, first_failed_vertex_or_null, certificate] 欄序回答。

查看答案與解釋(s24, t24, [[[a24, s24], 125, 50], [[a24, t24], 125, 75], [[s24, a24], 125, 100], [[t24, a24], 125, 25]], [[a24, 125, 125, 是], [u24, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)

Wave6第七層核對=(s24, t24, [[[a24, s24], 125, 50], [[a24, t24], 125, 75], [[s24, a24], 125, 100], [[t24, a24], 125, 25]], [[a24, 125, 125, 是], [u24, 0, 0, 是]], 是, null, every_internal_vertex_requires_complete_inflow_equals_outflow)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0075/)

有限流網路 · qf-mod44-flow-conservation-audit · candidate





## 76. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s0","a0","t0","u0"],"edges":[["s0","a0"],["a0","s0"],["a0","t0"],["t0","a0"]],"source":"s0","sink":"t0","capacities":[5,5,5,5],"flows":[4,2,3,1]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s0, t0, [[[a0, s0], 5, 2], [[a0, t0], 5, 3], [[s0, a0], 5, 4], [[t0, a0], 5, 1]], 2, 2, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s0, t0, [[[a0, s0], 5, 2], [[a0, t0], 5, 3], [[s0, a0], 5, 4], [[t0, a0], 5, 1]], 2, 2, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0076/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 77. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s1","a1","t1","u1"],"edges":[["s1","a1"],["a1","s1"],["a1","t1"],["t1","a1"]],"source":"s1","sink":"t1","capacities":[10,10,10,10],"flows":[8,4,6,2]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s1, t1, [[[a1, s1], 10, 4], [[a1, t1], 10, 6], [[s1, a1], 10, 8], [[t1, a1], 10, 2]], 4, 4, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s1, t1, [[[a1, s1], 10, 4], [[a1, t1], 10, 6], [[s1, a1], 10, 8], [[t1, a1], 10, 2]], 4, 4, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0077/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 78. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s2","a2","t2","u2"],"edges":[["s2","a2"],["a2","s2"],["a2","t2"],["t2","a2"]],"source":"s2","sink":"t2","capacities":[15,15,15,15],"flows":[12,6,9,3]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s2, t2, [[[a2, s2], 15, 6], [[a2, t2], 15, 9], [[s2, a2], 15, 12], [[t2, a2], 15, 3]], 6, 6, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s2, t2, [[[a2, s2], 15, 6], [[a2, t2], 15, 9], [[s2, a2], 15, 12], [[t2, a2], 15, 3]], 6, 6, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0078/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 79. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s3","a3","t3","u3"],"edges":[["s3","a3"],["a3","s3"],["a3","t3"],["t3","a3"]],"source":"s3","sink":"t3","capacities":[20,20,20,20],"flows":[16,8,12,4]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s3, t3, [[[a3, s3], 20, 8], [[a3, t3], 20, 12], [[s3, a3], 20, 16], [[t3, a3], 20, 4]], 8, 8, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s3, t3, [[[a3, s3], 20, 8], [[a3, t3], 20, 12], [[s3, a3], 20, 16], [[t3, a3], 20, 4]], 8, 8, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0079/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 80. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s4","a4","t4","u4"],"edges":[["s4","a4"],["a4","s4"],["a4","t4"],["t4","a4"]],"source":"s4","sink":"t4","capacities":[25,25,25,25],"flows":[20,10,15,5]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s4, t4, [[[a4, s4], 25, 10], [[a4, t4], 25, 15], [[s4, a4], 25, 20], [[t4, a4], 25, 5]], 10, 10, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s4, t4, [[[a4, s4], 25, 10], [[a4, t4], 25, 15], [[s4, a4], 25, 20], [[t4, a4], 25, 5]], 10, 10, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0080/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 81. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s5","a5","t5","u5"],"edges":[["s5","a5"],["a5","s5"],["a5","t5"],["t5","a5"]],"source":"s5","sink":"t5","capacities":[30,30,30,30],"flows":[24,12,18,6]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s5, t5, [[[a5, s5], 30, 12], [[a5, t5], 30, 18], [[s5, a5], 30, 24], [[t5, a5], 30, 6]], 12, 12, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s5, t5, [[[a5, s5], 30, 12], [[a5, t5], 30, 18], [[s5, a5], 30, 24], [[t5, a5], 30, 6]], 12, 12, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0081/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 82. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s6","a6","t6","u6"],"edges":[["s6","a6"],["a6","s6"],["a6","t6"],["t6","a6"]],"source":"s6","sink":"t6","capacities":[35,35,35,35],"flows":[28,14,21,7]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s6, t6, [[[a6, s6], 35, 14], [[a6, t6], 35, 21], [[s6, a6], 35, 28], [[t6, a6], 35, 7]], 14, 14, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s6, t6, [[[a6, s6], 35, 14], [[a6, t6], 35, 21], [[s6, a6], 35, 28], [[t6, a6], 35, 7]], 14, 14, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0082/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 83. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s7","a7","t7","u7"],"edges":[["s7","a7"],["a7","s7"],["a7","t7"],["t7","a7"]],"source":"s7","sink":"t7","capacities":[40,40,40,40],"flows":[32,16,24,8]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s7, t7, [[[a7, s7], 40, 16], [[a7, t7], 40, 24], [[s7, a7], 40, 32], [[t7, a7], 40, 8]], 16, 16, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s7, t7, [[[a7, s7], 40, 16], [[a7, t7], 40, 24], [[s7, a7], 40, 32], [[t7, a7], 40, 8]], 16, 16, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0083/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 84. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s8","a8","t8","u8"],"edges":[["s8","a8"],["a8","s8"],["a8","t8"],["t8","a8"]],"source":"s8","sink":"t8","capacities":[45,45,45,45],"flows":[36,18,27,9]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s8, t8, [[[a8, s8], 45, 18], [[a8, t8], 45, 27], [[s8, a8], 45, 36], [[t8, a8], 45, 9]], 18, 18, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s8, t8, [[[a8, s8], 45, 18], [[a8, t8], 45, 27], [[s8, a8], 45, 36], [[t8, a8], 45, 9]], 18, 18, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0084/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 85. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s9","a9","t9","u9"],"edges":[["s9","a9"],["a9","s9"],["a9","t9"],["t9","a9"]],"source":"s9","sink":"t9","capacities":[50,50,50,50],"flows":[40,20,30,10]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s9, t9, [[[a9, s9], 50, 20], [[a9, t9], 50, 30], [[s9, a9], 50, 40], [[t9, a9], 50, 10]], 20, 20, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s9, t9, [[[a9, s9], 50, 20], [[a9, t9], 50, 30], [[s9, a9], 50, 40], [[t9, a9], 50, 10]], 20, 20, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0085/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 86. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s10","a10","t10","u10"],"edges":[["s10","a10"],["a10","s10"],["a10","t10"],["t10","a10"]],"source":"s10","sink":"t10","capacities":[55,55,55,55],"flows":[44,22,33,11]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s10, t10, [[[a10, s10], 55, 22], [[a10, t10], 55, 33], [[s10, a10], 55, 44], [[t10, a10], 55, 11]], 22, 22, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s10, t10, [[[a10, s10], 55, 22], [[a10, t10], 55, 33], [[s10, a10], 55, 44], [[t10, a10], 55, 11]], 22, 22, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0086/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 87. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s11","a11","t11","u11"],"edges":[["s11","a11"],["a11","s11"],["a11","t11"],["t11","a11"]],"source":"s11","sink":"t11","capacities":[60,60,60,60],"flows":[48,24,36,12]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s11, t11, [[[a11, s11], 60, 24], [[a11, t11], 60, 36], [[s11, a11], 60, 48], [[t11, a11], 60, 12]], 24, 24, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s11, t11, [[[a11, s11], 60, 24], [[a11, t11], 60, 36], [[s11, a11], 60, 48], [[t11, a11], 60, 12]], 24, 24, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0087/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 88. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s12","a12","t12","u12"],"edges":[["s12","a12"],["a12","s12"],["a12","t12"],["t12","a12"]],"source":"s12","sink":"t12","capacities":[65,65,65,65],"flows":[52,26,39,13]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s12, t12, [[[a12, s12], 65, 26], [[a12, t12], 65, 39], [[s12, a12], 65, 52], [[t12, a12], 65, 13]], 26, 26, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s12, t12, [[[a12, s12], 65, 26], [[a12, t12], 65, 39], [[s12, a12], 65, 52], [[t12, a12], 65, 13]], 26, 26, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0088/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 89. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s13","a13","t13","u13"],"edges":[["s13","a13"],["a13","s13"],["a13","t13"],["t13","a13"]],"source":"s13","sink":"t13","capacities":[70,70,70,70],"flows":[56,28,42,14]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s13, t13, [[[a13, s13], 70, 28], [[a13, t13], 70, 42], [[s13, a13], 70, 56], [[t13, a13], 70, 14]], 28, 28, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s13, t13, [[[a13, s13], 70, 28], [[a13, t13], 70, 42], [[s13, a13], 70, 56], [[t13, a13], 70, 14]], 28, 28, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0089/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 90. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s14","a14","t14","u14"],"edges":[["s14","a14"],["a14","s14"],["a14","t14"],["t14","a14"]],"source":"s14","sink":"t14","capacities":[75,75,75,75],"flows":[60,30,45,15]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s14, t14, [[[a14, s14], 75, 30], [[a14, t14], 75, 45], [[s14, a14], 75, 60], [[t14, a14], 75, 15]], 30, 30, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s14, t14, [[[a14, s14], 75, 30], [[a14, t14], 75, 45], [[s14, a14], 75, 60], [[t14, a14], 75, 15]], 30, 30, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0090/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 91. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s15","a15","t15","u15"],"edges":[["s15","a15"],["a15","s15"],["a15","t15"],["t15","a15"]],"source":"s15","sink":"t15","capacities":[80,80,80,80],"flows":[64,32,48,16]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s15, t15, [[[a15, s15], 80, 32], [[a15, t15], 80, 48], [[s15, a15], 80, 64], [[t15, a15], 80, 16]], 32, 32, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s15, t15, [[[a15, s15], 80, 32], [[a15, t15], 80, 48], [[s15, a15], 80, 64], [[t15, a15], 80, 16]], 32, 32, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0091/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 92. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s16","a16","t16","u16"],"edges":[["s16","a16"],["a16","s16"],["a16","t16"],["t16","a16"]],"source":"s16","sink":"t16","capacities":[85,85,85,85],"flows":[68,34,51,17]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s16, t16, [[[a16, s16], 85, 34], [[a16, t16], 85, 51], [[s16, a16], 85, 68], [[t16, a16], 85, 17]], 34, 34, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s16, t16, [[[a16, s16], 85, 34], [[a16, t16], 85, 51], [[s16, a16], 85, 68], [[t16, a16], 85, 17]], 34, 34, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0092/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 93. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s17","a17","t17","u17"],"edges":[["s17","a17"],["a17","s17"],["a17","t17"],["t17","a17"]],"source":"s17","sink":"t17","capacities":[90,90,90,90],"flows":[72,36,54,18]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s17, t17, [[[a17, s17], 90, 36], [[a17, t17], 90, 54], [[s17, a17], 90, 72], [[t17, a17], 90, 18]], 36, 36, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s17, t17, [[[a17, s17], 90, 36], [[a17, t17], 90, 54], [[s17, a17], 90, 72], [[t17, a17], 90, 18]], 36, 36, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0093/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 94. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s18","a18","t18","u18"],"edges":[["s18","a18"],["a18","s18"],["a18","t18"],["t18","a18"]],"source":"s18","sink":"t18","capacities":[95,95,95,95],"flows":[76,38,57,19]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s18, t18, [[[a18, s18], 95, 38], [[a18, t18], 95, 57], [[s18, a18], 95, 76], [[t18, a18], 95, 19]], 38, 38, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s18, t18, [[[a18, s18], 95, 38], [[a18, t18], 95, 57], [[s18, a18], 95, 76], [[t18, a18], 95, 19]], 38, 38, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0094/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 95. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s19","a19","t19","u19"],"edges":[["s19","a19"],["a19","s19"],["a19","t19"],["t19","a19"]],"source":"s19","sink":"t19","capacities":[100,100,100,100],"flows":[80,40,60,20]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s19, t19, [[[a19, s19], 100, 40], [[a19, t19], 100, 60], [[s19, a19], 100, 80], [[t19, a19], 100, 20]], 40, 40, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s19, t19, [[[a19, s19], 100, 40], [[a19, t19], 100, 60], [[s19, a19], 100, 80], [[t19, a19], 100, 20]], 40, 40, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0095/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 96. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s20","a20","t20","u20"],"edges":[["s20","a20"],["a20","s20"],["a20","t20"],["t20","a20"]],"source":"s20","sink":"t20","capacities":[105,105,105,105],"flows":[84,42,63,21]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s20, t20, [[[a20, s20], 105, 42], [[a20, t20], 105, 63], [[s20, a20], 105, 84], [[t20, a20], 105, 21]], 42, 42, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s20, t20, [[[a20, s20], 105, 42], [[a20, t20], 105, 63], [[s20, a20], 105, 84], [[t20, a20], 105, 21]], 42, 42, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0096/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 97. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s21","a21","t21","u21"],"edges":[["s21","a21"],["a21","s21"],["a21","t21"],["t21","a21"]],"source":"s21","sink":"t21","capacities":[110,110,110,110],"flows":[88,44,66,22]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s21, t21, [[[a21, s21], 110, 44], [[a21, t21], 110, 66], [[s21, a21], 110, 88], [[t21, a21], 110, 22]], 44, 44, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s21, t21, [[[a21, s21], 110, 44], [[a21, t21], 110, 66], [[s21, a21], 110, 88], [[t21, a21], 110, 22]], 44, 44, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0097/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 98. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s22","a22","t22","u22"],"edges":[["s22","a22"],["a22","s22"],["a22","t22"],["t22","a22"]],"source":"s22","sink":"t22","capacities":[115,115,115,115],"flows":[92,46,69,23]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s22, t22, [[[a22, s22], 115, 46], [[a22, t22], 115, 69], [[s22, a22], 115, 92], [[t22, a22], 115, 23]], 46, 46, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s22, t22, [[[a22, s22], 115, 46], [[a22, t22], 115, 69], [[s22, a22], 115, 92], [[t22, a22], 115, 23]], 46, 46, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0098/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 99. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s23","a23","t23","u23"],"edges":[["s23","a23"],["a23","s23"],["a23","t23"],["t23","a23"]],"source":"s23","sink":"t23","capacities":[120,120,120,120],"flows":[96,48,72,24]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s23, t23, [[[a23, s23], 120, 48], [[a23, t23], 120, 72], [[s23, a23], 120, 96], [[t23, a23], 120, 24]], 48, 48, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s23, t23, [[[a23, s23], 120, 48], [[a23, t23], 120, 72], [[s23, a23], 120, 96], [[t23, a23], 120, 24]], 48, 48, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0099/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate





## 100. 有限流網路

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-value-cross-check；資料={"vertices":["s24","a24","t24","u24"],"edges":[["s24","a24"],["a24","s24"],["a24","t24"],["t24","a24"]],"source":"s24","sink":"t24","capacities":[125,125,125,125],"flows":[100,50,75,25]}。請依 [source, sink, edge_capacity_flow_rows, source_net_outflow, sink_net_inflow, net_values_equal, capacity_feasible, conservation_feasible, feasible, maximum_or_min_cut_certificate, boundary] 欄序回答。

源匯net values相等、逐邊capacity、逐內點conservation是不同核對；最後固定的否只不提供maximum/min-cut證書，也不否定特例可能恰為maximum。

查看答案與解釋(s24, t24, [[[a24, s24], 125, 50], [[a24, t24], 125, 75], [[s24, a24], 125, 100], [[t24, a24], 125, 25]], 50, 50, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)

Wave6第七層核對=(s24, t24, [[[a24, s24], 125, 50], [[a24, t24], 125, 75], [[s24, a24], 125, 100], [[t24, a24], 125, 25]], 50, 50, 是, 是, 是, 是, 否, feasible_flow_value_cross_check_does_not_claim_maximality_or_min_cut_equality)；依完整明示資料獨立重算；antiparallel edges明示，zero capacity與disconnected vertices允許；flow value由source與sink交叉計算；feasible不等於maximum，不提前宣稱min-cut equality或augmenting-path optimality。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261113-r07-finite-flow-network-0100/)

有限流網路 · qf-mod44-flow-value-cross-check · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261113-r07-finite-flow-network-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261113-r07-finite-flow-network-foundations/validation-report.json)