<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:
int dp[401][51][51];
int search(vector<vector<int>>&graph,int t,int m,int c){
    int n=graph.size();
    if(t==6*n){
        return 0;
    }
    if(m==c)return dp[t][m][c]=2;
    if(m==0)return dp[t][m][c]=1;
    if(dp[t][m][c]!=-1)return dp[t][m][c];
    int turn =t%2;
    bool flag;
    if(turn==0){
        flag=true;
        for(int i=0;i<graph[m].size();i++){
            if(graph[m][i]!=c){
            int nxt=search(graph,t+1,graph[m][i],c);
            if(nxt==1)return dp[t][m][c]=1;
            else if(nxt!=2)flag=false;
        }
        }
        if(flag)return dp[t][m][c]=2;
        else return dp[t][m][c]=0;
    }
        else {
            flag =true;
            for(int i=0;i<graph[c].size();i++){
                if(graph[c][i]!=0){
            int nxt=search(graph,t+1,m,graph[c][i]);
            if(nxt==2)return dp[t][m][c]=2;
            else if(nxt!=1)flag=false;
        }}
        if(flag)return dp[t][m][c]=1;
        else return dp[t][m][c]=0;
        }
    }
    int catMouseGame(vector<vector<int>>& graph) {
       memset(dp,-1,sizeof dp);
       return search(graph,0,1,2);
    }
}; 
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