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-20261014-advance-20261104-r06-spanning-tree-foundations · 2026-10-14 · 100 題
欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[1,2],[2,3],[3,4]],"selected":[0,1,2,3]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 1, 2, 3], 是, 是, 是, 是)
Wave5第四層核對=([0, 1, 2, 3], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[3,4]],"selected":[0,2,3,4]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 3, 4], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 3, 4], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[3,4]],"selected":[0,2,3,4]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 3, 4], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 3, 4], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],"selected":[0,3,4,5]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 3, 4, 5], 是, 是, 是, 是)
Wave5第四層核對=([0, 3, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[3,4]],"selected":[0,1,3,4]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 1, 3, 4], 是, 是, 是, 是)
Wave5第四層核對=([0, 1, 3, 4], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 4, 5], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 4, 5], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,3,5,6]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 3, 5, 6], 是, 是, 是, 是)
Wave5第四層核對=([0, 3, 5, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[3,4]],"selected":[0,1,3,4]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 1, 3, 4], 是, 是, 是, 是)
Wave5第四層核對=([0, 1, 3, 4], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 4, 5], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 4, 5], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,3,5,6]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 3, 5, 6], 是, 是, 是, 是)
Wave5第四層核對=([0, 3, 5, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,1,4,5]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 1, 4, 5], 是, 是, 是, 是)
Wave5第四層核對=([0, 1, 4, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 5, 6], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 5, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 5, 6], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 5, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,3,6,7]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 3, 6, 7], 是, 是, 是, 是)
Wave5第四層核對=([0, 3, 6, 7], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[1,2],[2,3],[2,4],[3,4]],"selected":[0,1,2,4]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 1, 2, 4], 是, 是, 是, 是)
Wave5第四層核對=([0, 1, 2, 4], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 3, 5], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 3, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 3, 5], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 3, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,3,4,6]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 3, 4, 6], 是, 是, 是, 是)
Wave5第四層核對=([0, 3, 4, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,1,3,5]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 1, 3, 5], 是, 是, 是, 是)
Wave5第四層核對=([0, 1, 3, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 4, 6], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 4, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 2, 4, 6], 是, 是, 是, 是)
Wave5第四層核對=([0, 2, 4, 6], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,3,5,7]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 3, 5, 7], 是, 是, 是, 是)
Wave5第四層核對=([0, 3, 5, 7], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-audit；資料={"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],"selected":[0,1,3,5]}。請依 [selected_indices, parent_connected, selected_connected, selected_acyclic, spanning_tree] 欄序回答。
([0, 1, 3, 5], 是, 是, 是, 是)
Wave5第四層核對=([0, 1, 3, 5], 是, 是, 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-audit · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[1,2],[2,3],[3,4]],"selected":[0,1,2,3]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[3,4]],"selected":[0,2,3,4]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[3,4]],"selected":[0,2,3,4]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],"selected":[0,3,4,5]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[3,4]],"selected":[0,1,3,4]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,3,5,6]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[3,4]],"selected":[0,1,3,4]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,3,5,6]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,1,4,5]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,3,6,7]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[1,2],[2,3],[2,4],[3,4]],"selected":[0,1,2,4]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,3,4,6]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,1,3,5]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,3,5,7]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-n-minus-one-certificate；資料={"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],"selected":[0,1,3,5]}。請依 [vertex_count, selected_edge_count, connected, acyclic, edge_count_is_n_minus_one, spanning_tree, boundary] 欄序回答。
(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)
Wave5第四層核對=(5, 4, 是, 是, 是, 是, n_minus_one_alone_insufficient)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-n-minus-one-certificate · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":1,"edges":[],"selected":[]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(1, [], 是, 是)
Wave5第四層核對=(1, [], 是, 是)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[1,2],[2,3],[3,4]],"selected":[0,1,2,3]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 1, 2, 3], 是, 否)
Wave5第四層核對=(5, [0, 1, 2, 3], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[3,4]],"selected":[0,2,3,4]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 3, 4], 是, 否)
Wave5第四層核對=(5, [0, 2, 3, 4], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[3,4]],"selected":[0,2,3,4]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 3, 4], 是, 否)
Wave5第四層核對=(5, [0, 2, 3, 4], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],"selected":[0,3,4,5]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 3, 4, 5], 是, 否)
Wave5第四層核對=(5, [0, 3, 4, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[3,4]],"selected":[0,1,3,4]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 1, 3, 4], 是, 否)
Wave5第四層核對=(5, [0, 1, 3, 4], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 4, 5], 是, 否)
Wave5第四層核對=(5, [0, 2, 4, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 4, 5], 是, 否)
Wave5第四層核對=(5, [0, 2, 4, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,3,5,6]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 3, 5, 6], 是, 否)
Wave5第四層核對=(5, [0, 3, 5, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[3,4]],"selected":[0,1,3,4]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 1, 3, 4], 是, 否)
Wave5第四層核對=(5, [0, 1, 3, 4], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 4, 5], 是, 否)
Wave5第四層核對=(5, [0, 2, 4, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 4, 5], 是, 否)
Wave5第四層核對=(5, [0, 2, 4, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,3,5,6]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 3, 5, 6], 是, 否)
Wave5第四層核對=(5, [0, 3, 5, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,1,4,5]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 1, 4, 5], 是, 否)
Wave5第四層核對=(5, [0, 1, 4, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 5, 6], 是, 否)
Wave5第四層核對=(5, [0, 2, 5, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 5, 6], 是, 否)
Wave5第四層核對=(5, [0, 2, 5, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,3,6,7]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 3, 6, 7], 是, 否)
Wave5第四層核對=(5, [0, 3, 6, 7], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[1,2],[2,3],[2,4],[3,4]],"selected":[0,1,2,4]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 1, 2, 4], 是, 否)
Wave5第四層核對=(5, [0, 1, 2, 4], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 3, 5], 是, 否)
Wave5第四層核對=(5, [0, 2, 3, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 3, 5], 是, 否)
Wave5第四層核對=(5, [0, 2, 3, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,3,4,6]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 3, 4, 6], 是, 否)
Wave5第四層核對=(5, [0, 3, 4, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,1,3,5]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 1, 3, 5], 是, 否)
Wave5第四層核對=(5, [0, 1, 3, 5], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 4, 6], 是, 否)
Wave5第四層核對=(5, [0, 2, 4, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 2, 4, 6], 是, 否)
Wave5第四層核對=(5, [0, 2, 4, 6], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-one-vertex；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,3,5,7]}。請依 [vertex_count, selected_indices, spanning_tree, one_vertex_empty_selection] 欄序回答。
(5, [0, 3, 5, 7], 是, 否)
Wave5第四層核對=(5, [0, 3, 5, 7], 是, 否)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-one-vertex · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[1,2],[2,3],[3,4]],"selected":[0,1,2,3]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[3,4]],"selected":[0,2,3,4]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[3,4]],"selected":[0,2,3,4]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],"selected":[0,3,4,5]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[3,4]],"selected":[0,1,3,4]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],"selected":[0,3,5,6]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[3,4]],"selected":[0,1,3,4]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,2,4,5]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,4],[2,3],[3,4]],"selected":[0,3,5,6]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,1,4,5]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,2,5,6]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[1,4],[2,3],[3,4]],"selected":[0,3,6,7]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[1,2],[2,3],[2,4],[3,4]],"selected":[0,1,2,4]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,2,3,5]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],"selected":[0,3,4,6]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,1,3,5]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,2,4,6]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"selected":[0,3,5,7]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate
完整finite connected simple parent graph與parent edge subset。操作=spantree-non-mst-boundary；資料={"n":5,"edges":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],"selected":[0,1,3,5]}。請依 [spanning_tree, weighted_minimum_claim, boundary] 欄序回答。
第二個否是不作加權最小生成樹聲稱，不是否證目前樹在某個另加權重模型中的最優性。
(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)
Wave5第四層核對=(是, 否, unweighted_spanning_tree_not_minimum_spanning_tree_claim)；依完整明示資料重算；spanning tree含全部vertices且connected acyclic，n-1 alone不足；single vertex合法且不作weighted或minimum claim。
生成樹 · qf-mod35-spantree-non-mst-boundary · candidate