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leetcode-problemset/leetcode/originData/all-ancestors-of-a-node-in-a-directed-acyclic-graph.json
2022-05-02 23:44:12 +08:00

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{
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"title": "All Ancestors of a Node in a Directed Acyclic Graph",
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"content": "<p>You are given a positive integer <code>n</code> representing the number of nodes of a <strong>Directed Acyclic Graph</strong> (DAG). The nodes are numbered from <code>0</code> to <code>n - 1</code> (<strong>inclusive</strong>).</p>\n\n<p>You are also given a 2D integer array <code>edges</code>, where <code>edges[i] = [from<sub>i</sub>, to<sub>i</sub>]</code> denotes that there is a <strong>unidirectional</strong> edge from <code>from<sub>i</sub></code> to <code>to<sub>i</sub></code> in the graph.</p>\n\n<p>Return <em>a list</em> <code>answer</code><em>, where </em><code>answer[i]</code><em> is the <strong>list of ancestors</strong> of the</em> <code>i<sup>th</sup></code> <em>node, sorted in <strong>ascending order</strong></em>.</p>\n\n<p>A node <code>u</code> is an <strong>ancestor</strong> of another node <code>v</code> if <code>u</code> can reach <code>v</code> via a set of edges.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2019/12/12/e1.png\" style=\"width: 322px; height: 265px;\" />\n<pre>\n<strong>Input:</strong> n = 8, edgeList = [[0,3],[0,4],[1,3],[2,4],[2,7],[3,5],[3,6],[3,7],[4,6]]\n<strong>Output:</strong> [[],[],[],[0,1],[0,2],[0,1,3],[0,1,2,3,4],[0,1,2,3]]\n<strong>Explanation:</strong>\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</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2019/12/12/e2.png\" style=\"width: 343px; height: 299px;\" />\n<pre>\n<strong>Input:</strong> n = 5, edgeList = [[0,1],[0,2],[0,3],[0,4],[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]\n<strong>Output:</strong> [[],[0],[0,1],[0,1,2],[0,1,2,3]]\n<strong>Explanation:</strong>\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</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 1000</code></li>\n\t<li><code>0 &lt;= edges.length &lt;= min(2000, n * (n - 1) / 2)</code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>0 &lt;= from<sub>i</sub>, to<sub>i</sub> &lt;= n - 1</code></li>\n\t<li><code>from<sub>i</sub> != to<sub>i</sub></code></li>\n\t<li>There are no duplicate edges.</li>\n\t<li>The graph is <strong>directed</strong> and <strong>acyclic</strong>.</li>\n</ul>\n",
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"code": "(define/contract (get-ancestors n edges)\n (-> exact-integer? (listof (listof exact-integer?)) (listof (listof exact-integer?)))\n\n )",
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"code": "defmodule Solution do\n @spec get_ancestors(n :: integer, edges :: [[integer]]) :: [[integer]]\n def get_ancestors(n, edges) do\n\n end\nend",
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"hints": [
"Consider how reversing each edge of the graph can help us.",
"How can performing BFS/DFS on the reversed graph help us find the ancestors of every node?"
],
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