<p>You are given an integer <code>n</code>, the number of nodes in a directed graph where the nodes are labeled from <code>0</code> to <code>n - 1</code>. Each edge is red or blue in this graph, and there could be self-edges and parallel edges.</p>

<p>You are given two arrays <code>redEdges</code> and <code>blueEdges</code> where:</p>

<ul>
	<li><code>redEdges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is a directed red edge from node <code>a<sub>i</sub></code> to node <code>b<sub>i</sub></code> in the graph, and</li>
	<li><code>blueEdges[j] = [u<sub>j</sub>, v<sub>j</sub>]</code> indicates that there is a directed blue edge from node <code>u<sub>j</sub></code> to node <code>v<sub>j</sub></code> in the graph.</li>
</ul>

<p>Return an array <code>answer</code> of length <code>n</code>, where each <code>answer[x]</code> is the length of the shortest path from node <code>0</code> to node <code>x</code> such that the edge colors alternate along the path, or <code>-1</code> if such a path does not exist.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 3, redEdges = [[0,1],[1,2]], blueEdges = []
<strong>Output:</strong> [0,1,-1]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 3, redEdges = [[0,1]], blueEdges = [[2,1]]
<strong>Output:</strong> [0,1,-1]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 100</code></li>
	<li><code>0 &lt;= redEdges.length,&nbsp;blueEdges.length &lt;= 400</code></li>
	<li><code>redEdges[i].length == blueEdges[j].length == 2</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub>, u<sub>j</sub>, v<sub>j</sub> &lt; n</code></li>
</ul>


class Solution {
public:
    vector<int> shortestAlternatingPaths(int n, vector<vector<int>>& redEdges, vector<vector<int>>& blueEdges) 
    {
        multiset<int> temp;
        vector<multiset<int>> redChilds(n, temp), blueChilds(n, temp);
        for(auto j : redEdges)
        {
            redChilds[j[0]].insert(j[1]);
        }
        for(auto j : blueEdges)
        {
            blueChilds[j[0]].insert(j[1]);
        }
        vector<int> ans(n, -1);
        vector<vector<bool>> visited(n, vector<bool>(2, false)); // 0: red, 1: blue
        queue<pair<int, int>> visit; // node, color (0: red, 1: blue)
        visit.push({0, 0}); // start with red
        visit.push({0, 1}); // start with blue
        int steps = 0;
        while(!visit.empty())
        {
            int size = visit.size();
            for(int j = 0; j < size; j++)
            {
                auto [node, color] = visit.front();
                visit.pop();
                if(ans[node] == -1) ans[node] = steps;
                if(visited[node][color]) continue;
                visited[node][color] = true;
                if(color == 0) // coming from red
                {
                    for(auto next : blueChilds[node])
                    {
                        visit.push({next, 1});
                    }
                }
                else // coming from blue
                {
                    for(auto next : redChilds[node])
                    {
                        visit.push({next, 0});
                    }
                }
            }
            steps++;
        }
        return ans;
    }
};

20498