find-closest-node-to-given-two-nodes

Find Closest Node to Given Two Nodes

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You are given a directed graph of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code>, where each node has at most one outgoing edge.

The graph is represented with a given 0-indexed array <code>edges</code> of size <code>n</code>, indicating that there is a directed edge from node <code>i</code> to node <code>edges[i]</code>. If there is no outgoing edge from <code>i</code>, then <code>edges[i] == -1</code>.

You are also given two integers <code>node1</code> and <code>node2</code>.

Return the index of the node that can be reached from both <code>node1</code> and <code>node2</code>, such that the maximum between the distance from <code>node1</code> to that node, and from <code>node2</code> to that node is minimized. If there are multiple answers, return the node with the smallest index, and if no possible answer exists, return <code>-1</code>.

Note that <code>edges</code> may contain cycles.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2022/06/07/graph4drawio-2.png" style="width: 321px; height: 161px;" />
<pre>
Input: edges = [2,2,3,-1], node1 = 0, node2 = 1
Output: 2
Explanation: The distance from node 0 to node 2 is 1, and the distance from node 1 to node 2 is 1.
The maximum of those two distances is 1. It can be proven that we cannot get a node with a smaller maximum distance than 1, so we return node 2.
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2022/06/07/graph4drawio-4.png" style="width: 195px; height: 161px;" />
<pre>
Input: edges = [1,2,-1], node1 = 0, node2 = 2
Output: 2
Explanation: The distance from node 0 to node 2 is 2, and the distance from node 2 to itself is 0.
The maximum of those two distances is 2. It can be proven that we cannot get a node with a smaller maximum distance than 2, so we return node 2.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == edges.length</code></li>
	<li><code>2 &lt;= n &lt;= 105</code></li>
	<li><code>-1 &lt;= edges[i] &lt; n</code></li>
	<li><code>edges[i] != i</code></li>
	<li><code>0 &lt;= node1, node2 &lt; n</code></li>
</ul>

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