2858 - Minimum Edge Reversals So Every Node Is Reachable\.

Hard

There is a simple directed graph with n nodes labeled from 0 to n - 1. The graph would form a tree if its edges were bi-directional.

You are given an integer n and a 2D integer array edges, where <code>edgesi = u_i, v_i</code> represents a directed edge going from node <code>u_i</code> to node <code>v_i</code>.

An edge reversal changes the direction of an edge, i.e., a directed edge going from node <code>u_i</code> to node <code>v_i</code> becomes a directed edge going from node <code>v_i</code> to node <code>u_i</code>.

For every node i in the range [0, n - 1], your task is to independently calculate the minimum number of edge reversals required so it is possible to reach any other node starting from node i through a sequence of directed edges.

Return an integer array answer, where answer[i] is the minimum number of edge reversals required so it is possible to reach any other node starting from node i through a sequence of directed edges.

Example 1:

Input: n = 4, edges = \[\[2,0],2,1,1,3]

Output: 1,1,0,2

Explanation: The image above shows the graph formed by the edges.

For node 0: after reversing the edge 2,0, it is possible to reach any other node starting from node 0.

So, answer0 = 1.

For node 1: after reversing the edge 2,1, it is possible to reach any other node starting from node 1.

So, answer1 = 1.

For node 2: it is already possible to reach any other node starting from node 2.

So, answer2 = 0.

For node 3: after reversing the edges 1,3 and 2,1, it is possible to reach any other node starting from node 3.

So, answer3 = 2.

Example 2:

Input: n = 3, edges = \[\[1,2],2,0]

Output: 2,0,1

Explanation: The image above shows the graph formed by the edges.

For node 0: after reversing the edges 2,0 and 1,2, it is possible to reach any other node starting from node 0.

So, answer0 = 2.

For node 1: it is already possible to reach any other node starting from node 1.

So, answer1 = 0.

For node 2: after reversing the edge 1, 2, it is possible to reach any other node starting from node 2.

So, answer2 = 1.

Constraints:

• <code>2 <= n <= 10⁵</code>

• edges.length == n - 1

• edges[i].length == 2

• <code>0 <= u_i == edges0< n</code>

• <code>0 <= v_i == edges1< n</code>

• <code>u_i != v_i</code>

• The input is generated such that if the edges were bi-directional, the graph would be a tree.