<p>A game is played by a cat and a mouse named Cat and Mouse.</p>

<p>The environment is represented by a <code>grid</code> of size <code>rows x cols</code>, where each element is a wall, floor, player (Cat, Mouse), or food.</p>

<ul>
	<li>Players are represented by the characters <code>&#39;C&#39;</code>(Cat)<code>,&#39;M&#39;</code>(Mouse).</li>
	<li>Floors are represented by the character <code>&#39;.&#39;</code> and can be walked on.</li>
	<li>Walls are represented by the character <code>&#39;#&#39;</code> and cannot be walked on.</li>
	<li>Food is represented by the character <code>&#39;F&#39;</code> and can be walked on.</li>
	<li>There is only one of each character <code>&#39;C&#39;</code>, <code>&#39;M&#39;</code>, and <code>&#39;F&#39;</code> in <code>grid</code>.</li>
</ul>

<p>Mouse and Cat play according to the following rules:</p>

<ul>
	<li>Mouse <strong>moves first</strong>, then they take turns to move.</li>
	<li>During each turn, Cat and Mouse can jump in one of the four directions (left, right, up, down). They cannot jump over the wall nor outside of the <code>grid</code>.</li>
	<li><code>catJump, mouseJump</code> are the maximum lengths Cat and Mouse can jump at a time, respectively. Cat and Mouse can jump less than the maximum length.</li>
	<li>Staying in the same position is allowed.</li>
	<li>Mouse can jump over Cat.</li>
</ul>

<p>The game can end in 4 ways:</p>

<ul>
	<li>If Cat occupies the same position as Mouse, Cat wins.</li>
	<li>If Cat reaches the food first, Cat wins.</li>
	<li>If Mouse reaches the food first, Mouse wins.</li>
	<li>If Mouse cannot get to the food within 1000 turns, Cat wins.</li>
</ul>

<p>Given a <code>rows x cols</code> matrix <code>grid</code> and two integers <code>catJump</code> and <code>mouseJump</code>, return <code>true</code><em> if Mouse can win the game if both Cat and Mouse play optimally, otherwise return </em><code>false</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/12/sample_111_1955.png" style="width: 580px; height: 239px;" />
<pre>
<strong>Input:</strong> grid = [&quot;####F&quot;,&quot;#C...&quot;,&quot;M....&quot;], catJump = 1, mouseJump = 2
<strong>Output:</strong> true
<strong>Explanation:</strong> Cat cannot catch Mouse on its turn nor can it get the food before Mouse.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/12/sample_2_1955.png" style="width: 580px; height: 175px;" />
<pre>
<strong>Input:</strong> grid = [&quot;M.C...F&quot;], catJump = 1, mouseJump = 4
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [&quot;M.C...F&quot;], catJump = 1, mouseJump = 3
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>rows == grid.length</code></li>
	<li><code>cols = grid[i].length</code></li>
	<li><code>1 &lt;= rows, cols &lt;= 8</code></li>
	<li><code>grid[i][j]</code> consist only of characters <code>&#39;C&#39;</code>, <code>&#39;M&#39;</code>, <code>&#39;F&#39;</code>, <code>&#39;.&#39;</code>, and <code>&#39;#&#39;</code>.</li>
	<li>There is only one of each character <code>&#39;C&#39;</code>, <code>&#39;M&#39;</code>, and <code>&#39;F&#39;</code> in <code>grid</code>.</li>
	<li><code>1 &lt;= catJump, mouseJump &lt;= 8</code></li>
</ul>

class Solution {
public:
    int dp[1001][8][8][8][8];
    vector<string> v;
    int dx[4]={-1,0,1,0};
    int dy[4]={0,-1,0,1};
    bool solve(int moves,int cx,int cy,int mx,int my,int cj,int mj){
        if(moves%2==1){
            if(cx==mx && cy==my) return false;
            if(moves>=128) return false;
            if(v[mx][my]=='F') return true;
            if(v[cx][cy]=='F') return false;
        }
        else{
            if(cx==mx && cy==my) return true;
            if(moves>=1000) return true;
            if(v[mx][my]=='F') return false;
            if(v[cx][cy]=='F') return true;
        }
        if(dp[moves][cx][cy][mx][my]!=-1) return dp[moves][cx][cy][mx][my];
        bool flag=false;
        if(moves%2==1){
            for(int i=0;i<4;i++){
                for(int j=0;j<=mj;j++){
                    int nx=mx+j*dx[i];
                    int ny=my+j*dy[i];
                    if(nx>=0 && nx<v.size() && ny>=0 && ny<v[0].size() && v[nx][ny]!='#'){
                        if(solve(moves+1,cx,cy,nx,ny,cj,mj)==0){
                            flag=true;
                            break;
                        }
                    }
                    else break;
                }
                if(flag) break;
            }
        }
        else{
            for(int i=0;i<4;i++){
                for(int j=0;j<=cj;j++){
                    int nx=cx+j*dx[i];
                    int ny=cy+j*dy[i];
                    if(nx>=0 && nx<v.size() && ny>=0 && ny<v[0].size() && v[nx][ny]!='#'){
                        if(solve(moves+1,nx,ny,mx,my,cj,mj)==0){
                            flag=true;
                            break;
                        }
                    }
                    else break;
                }
                if(flag) break;
            }
        }
        return dp[moves][cx][cy][mx][my]=flag;
    }
    bool canMouseWin(vector<string>& grid, int catJump, int mouseJump) {
        v=grid;
        memset(dp,-1,sizeof(dp));
        int cx,cy,mx,my;
        for(int i=0;i<grid.size();i++){
            for(int j=0;j<grid[0].size();j++){
                if(grid[i][j]=='C'){
                    cx=i;
                    cy=j;
                }
                if(grid[i][j]=='M'){
                    mx=i;
                    my=j;
                }
            }
        }
        return solve(1,cx,cy,mx,my,catJump,mouseJump);
    }
};
30000