<p>A game on an <strong>undirected</strong> graph is played by two players, Mouse and Cat, who alternate turns.</p>

<p>The graph is given as follows: <code>graph[a]</code> is a list of all nodes <code>b</code> such that <code>ab</code> is an edge of the graph.</p>

<p>The mouse starts at node <code>1</code> and goes first, the cat starts at node <code>2</code> and goes second, and there is a hole at node <code>0</code>.</p>

<p>During each player&#39;s turn, they <strong>must</strong> travel along one&nbsp;edge of the graph that meets where they are.&nbsp; For example, if the Mouse is at node 1, it <strong>must</strong> travel to any node in <code>graph[1]</code>.</p>

<p>Additionally, it is not allowed for the Cat to travel to the Hole (node <code>0</code>).</p>

<p>Then, the game can end in three&nbsp;ways:</p>

<ul>
	<li>If ever the Cat occupies the same node as the Mouse, the Cat wins.</li>
	<li>If ever the Mouse reaches the Hole, the Mouse wins.</li>
	<li>If ever a position is repeated (i.e., the players are in the same position as a previous turn, and&nbsp;it is the same player&#39;s turn to move), the game is a draw.</li>
</ul>

<p>Given a <code>graph</code>, and assuming both players play optimally, return</p>

<ul>
	<li><code>1</code>&nbsp;if the mouse wins the game,</li>
	<li><code>2</code>&nbsp;if the cat wins the game, or</li>
	<li><code>0</code>&nbsp;if the game is a draw.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/17/cat1.jpg" style="width: 300px; height: 300px;" />
<pre>
<strong>Input:</strong> graph = [[2,5],[3],[0,4,5],[1,4,5],[2,3],[0,2,3]]
<strong>Output:</strong> 0
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/17/cat2.jpg" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> graph = [[1,3],[0],[3],[0,2]]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>3 &lt;= graph.length &lt;= 50</code></li>
	<li><code>1&nbsp;&lt;= graph[i].length &lt; graph.length</code></li>
	<li><code>0 &lt;= graph[i][j] &lt; graph.length</code></li>
	<li><code>graph[i][j] != i</code></li>
	<li><code>graph[i]</code> is unique.</li>
	<li>The mouse and the cat can always move.&nbsp;</li>
</ul>

class Solution {
public:
    enum {D, M, C}; 
    using T = tuple<int,int,int>;

    vector<T> parents(int i, int j, int t, vector<vector<int>>& g) {
        vector<T> v;
        if (t == C) {
            for (auto x : g[i])
                v.push_back({x, j, M});
        } else {
            for (auto x : g[j]) if (x != 0)
                v.push_back({i, x, C});
        }
        return v;
    }

    int catMouseGame(vector<vector<int>>& g) {
        int n = g.size();
        int degree[50][50][3], color[50][50][3];
        memset(degree, 0, sizeof(degree));
        memset(color, 0, sizeof(color));

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                degree[i][j][M] = g[i].size();
                degree[i][j][C] = g[j].size();
                for (auto x : g[j]) if (x == 0) { 
                    degree[i][j][C]--;
                    break;
                }
            }
        }
        queue<T> q;
        for (int i = 0; i < n; i++) {
            for (int t = 1; t <= 2; t++) {
                color[0][i][t] = M;
                q.push({0, i, t});
                if (i != 0) {
                    color[i][i][t] = C;
                    q.push({i,i,t});
                }
            }
        }

        while (!q.empty()) {
            auto [i, j, t] = q.front();
            int c = color[i][j][t];
            q.pop();

            // for all the nodes that can reach this node:
            for (auto [i2,j2,t2] : parents(i,j,t,g)) {
                if (color[i2][j2][t2] != D) continue;
                if (t2 == c) {
                    color[i2][j2][t2] = c;
                    q.push({i2,j2,t2});
                } else {
                    degree[i2][j2][t2]--;
                    if (degree[i2][j2][t2] == 0) {
                        color[i2][j2][t2] = 3-t2;
                        q.push({i2,j2,t2});
                    }
                }
            }
        }

        return color[1][2][1];
    }
};
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