minimum-number-of-vertices-to-reach-all-nodes

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Algorithms

Given a&nbsp;directed acyclic graph,&nbsp;with&nbsp;<code>n</code>&nbsp;vertices numbered from&nbsp;<code>0</code>&nbsp;to&nbsp;<code>n-1</code>,&nbsp;and an array&nbsp;<code>edges</code>&nbsp;where&nbsp;<code>edges[i] = [fromi, toi]</code>&nbsp;represents a directed edge from node&nbsp;<code>fromi</code>&nbsp;to node&nbsp;<code>toi</code>.

Find the smallest set of vertices from which all nodes in the graph are reachable. It&#39;s guaranteed that a unique solution exists.

Notice that you can return the vertices in any order.

&nbsp;
Example 1:

<img alt="" src="https://assets.leetcode.com/uploads/2020/07/07/untitled22.png" style="width: 231px; height: 181px;" />

<pre>
Input: n = 6, edges = [[0,1],[0,2],[2,5],[3,4],[4,2]]
Output: [0,3]
Explanation: It&#39;s not possible to reach all the nodes from a single vertex. From 0 we can reach [0,1,2,5]. From 3 we can reach [3,4,2,5]. So we output [0,3].</pre>

Example 2:

<img alt="" src="https://assets.leetcode.com/uploads/2020/07/07/untitled.png" style="width: 201px; height: 201px;" />

<pre>
Input: n = 5, edges = [[0,1],[2,1],[3,1],[1,4],[2,4]]
Output: [0,2,3]
Explanation: Notice that vertices 0, 3 and 2 are not reachable from any other node, so we must include them. Also any of these vertices can reach nodes 1 and 4.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= n &lt;= 10^5</code></li>
	<li><code>1 &lt;= edges.length &lt;= min(10^5, n * (n - 1) / 2)</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= fromi,&nbsp;toi &lt; n</code></li>
	<li>All pairs <code>(fromi, toi)</code> are distinct.</li>
</ul>

findSmallestSetOfVertices

Minimum Number of Vertices to Reach All Nodes

Graph

给你一个 有向无环图&nbsp;， <code>n</code>&nbsp;个节点编号为 <code>0</code>&nbsp;到 <code>n-1</code>&nbsp;，以及一个边数组 <code>edges</code>&nbsp;，其中 <code>edges[i] = [fromi, toi]</code>&nbsp;表示一条从点&nbsp;&nbsp;<code>fromi</code>&nbsp;到点&nbsp;<code>toi</code>&nbsp;的有向边。

找到最小的点集使得从这些点出发能到达图中所有点。题目保证解存在且唯一。

你可以以任意顺序返回这些节点编号。

&nbsp;

示例 1：

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/08/22/5480e1.png" style="height: 181px; width: 231px;">

<pre>输入：n = 6, edges = [[0,1],[0,2],[2,5],[3,4],[4,2]]
输出：[0,3]
解释：从单个节点出发无法到达所有节点。从 0 出发我们可以到达 [0,1,2,5] 。从 3 出发我们可以到达 [3,4,2,5] 。所以我们输出 [0,3] 。</pre>

示例 2：

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/08/22/5480e2.png" style="height: 201px; width: 201px;">

<pre>输入：n = 5, edges = [[0,1],[2,1],[3,1],[1,4],[2,4]]
输出：[0,2,3]
解释：注意到节点 0，3 和 2 无法从其他节点到达，所以我们必须将它们包含在结果点集中，这些点都能到达节点 1 和 4 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>2 &lt;= n &lt;= 10^5</code></li>
	<li><code>1 &lt;= edges.length &lt;= min(10^5, n * (n - 1) / 2)</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>0 &lt;= fromi,&nbsp;toi &lt; n</code></li>
	<li>所有点对&nbsp;<code>(fromi, toi)</code>&nbsp;互不相同。</li>
</ul>