{ "data": { "question": { "questionId": "1431", "questionFrontendId": "2192", "categoryTitle": "Algorithms", "boundTopicId": 1308876, "title": "All Ancestors of a Node in a Directed Acyclic Graph", "titleSlug": "all-ancestors-of-a-node-in-a-directed-acyclic-graph", "content": "

You are given a positive integer n representing the number of nodes of a Directed Acyclic Graph (DAG). The nodes are numbered from 0 to n - 1 (inclusive).

\n\n

You are also given a 2D integer array edges, where edges[i] = [fromi, toi] denotes that there is a unidirectional edge from fromi to toi in the graph.

\n\n

Return a list answer, where answer[i] is the list of ancestors of the ith node, sorted in ascending order.

\n\n

A node u is an ancestor of another node v if u can reach v via a set of edges.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: n = 8, edgeList = [[0,3],[0,4],[1,3],[2,4],[2,7],[3,5],[3,6],[3,7],[4,6]]\nOutput: [[],[],[],[0,1],[0,2],[0,1,3],[0,1,2,3,4],[0,1,2,3]]\nExplanation:\nThe above diagram represents the input graph.\n- Nodes 0, 1, and 2 do not have any ancestors.\n- Node 3 has two ancestors 0 and 1.\n- Node 4 has two ancestors 0 and 2.\n- Node 5 has three ancestors 0, 1, and 3.\n- Node 6 has five ancestors 0, 1, 2, 3, and 4.\n- Node 7 has four ancestors 0, 1, 2, and 3.\n
\n\n

Example 2:

\n\"\"\n
\nInput: n = 5, edgeList = [[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]\nOutput: [[],[0],[0,1],[0,1,2],[0,1,2,3]]\nExplanation:\nThe above diagram represents the input graph.\n- Node 0 does not have any ancestor.\n- Node 1 has one ancestor 0.\n- Node 2 has two ancestors 0 and 1.\n- Node 3 has three ancestors 0, 1, and 2.\n- Node 4 has four ancestors 0, 1, 2, and 3.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "有向无环图中一个节点的所有祖先", "translatedContent": "

给你一个正整数 n ，它表示一个 有向无环图 中节点的数目，节点编号为 0 到 n - 1 （包括两者）。

\n\n

给你一个二维整数数组 edges ，其中 edges[i] = [fromi, toi] 表示图中一条从 fromi 到 toi 的单向边。

\n\n

请你返回一个数组 answer，其中 answer[i]是第 i 个节点的所有 祖先 ，这些祖先节点 升序 排序。

\n\n

如果 u 通过一系列边，能够到达 v ，那么我们称节点 u 是节点 v 的 祖先 节点。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
输入：n = 8, edgeList = [[0,3],[0,4],[1,3],[2,4],[2,7],[3,5],[3,6],[3,7],[4,6]]\n输出：[[],[],[],[0,1],[0,2],[0,1,3],[0,1,2,3,4],[0,1,2,3]]\n解释：\n上图为输入所对应的图。\n- 节点 0 ，1 和 2 没有任何祖先。\n- 节点 3 有 2 个祖先 0 和 1 。\n- 节点 4 有 2 个祖先 0 和 2 。\n- 节点 5 有 3 个祖先 0 ，1 和 3 。\n- 节点 6 有 5 个祖先 0 ，1 ，2 ，3 和 4 。\n- 节点 7 有 4 个祖先 0 ，1 ，2 和 3 。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
输入：n = 5, edgeList = [[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]\n输出：[[],[0],[0,1],[0,1,2],[0,1,2,3]]\n解释：\n上图为输入所对应的图。\n- 节点 0 没有任何祖先。\n- 节点 1 有 1 个祖先 0 。\n- 节点 2 有 2 个祖先 0 和 1 。\n- 节点 3 有 3 个祖先 0 ，1 和 2 。\n- 节点 4 有 4 个祖先 0 ，1 ，2 和 3 。\n
\n\n

 

\n\n

提示：

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