<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[101][9][9][9][9];
    int row[4]={-1,0,1,0};
    int col[4]={0,-1,0,1};
    int cj,mj;
    int solve(int ind, int i, int j, int x, int y, vector<string>&a){
        int n=a.size(),m=a[0].size(),flag=ind%2;
        if(ind>=100) return 0;
        if(ind%2==0){
            //if(ind>=70) return 0;
            if(i==x && j==y) return 0;
            if(a[i][j]=='F') return 1;
            if(a[x][y]=='F') return 0;
            if(dp[ind][i][j][x][y]!=-1) return dp[ind][i][j][x][y];

            for(int k=0;k<4;k++){
                for(int z=0;z<=mj;z++){
                    int p=i+z*row[k],q=j+z*col[k];
                    if(p>=0 && p<n && q>=0 && q<m && a[p][q]!='#'){
                        if(solve(ind+1,p,q,x,y,a)){
                            flag=1;
                            break;
                        }
                    }
                    else break;
                }
                if(flag) break;
            }
        }
        else{
            //flag=1;
            //if(ind>=70) return 0;
            if(i==x && j==y) return 0;
            if(a[i][j]=='F') return 1;
            if(a[x][y]=='F') return 0;
            if(dp[ind][i][j][x][y]!=-1) return dp[ind][i][j][x][y];

            for(int k=0;k<4;k++){
                for(int z=0;z<=cj;z++){
                    int p=x+z*row[k],q=y+z*col[k];
                    if(p>=0 && p<n && q>=0 && q<m && a[p][q]!='#'){
                        if(solve(ind+1,i,j,p,q,a)==0){
                            flag=0;
                            break;
                        }
                    }
                    else break;
                }
                //if(flag) break;
            }
        }
        return dp[ind][i][j][x][y]=flag;

    }
    bool canMouseWin(vector<string>& a, int cj, int mj) {
        int n=a.size(),m=a[0].size();
        this->cj=cj;
        this->mj=mj;
        memset(dp,-1,sizeof(dp));
        int p,q,x,y;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(a[i][j]=='M') p=i,q=j;
                if(a[i][j]=='C') x=i,y=j;
            }
        }
        cout<<p<<q<<endl;
        return solve(0,p,q,x,y,a);

    }
};
14600