<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 dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};
int dp[9][9][9][9][2][100];
int dfs(int cx,int cy,int mx,int my,vector<string>&a,int c,int ms,bool turn,int n,int m,int mm)
{
    if(mm>70)
    return false;
    if(cx==mx && cy==my)
    return false;
    if(a[cx][cy]=='F')
    return false;
    if(a[mx][my]=='F')
    return true;
    if(dp[cx][cy][mx][my][turn][mm] != -1) return dp[cx][cy][mx][my][turn][mm];
    for(int i=0;i<4;i++)
    {
        if(turn)
        {
            for(int j=0;j<=ms;j++)
            {
                int nx=mx+dx[i]*j;
                int ny=my+dy[i]*j;
                if(nx>=0 && ny>=0 && nx<n && ny<m && a[nx][ny]!='#')
                {
                    if(dfs(cx,cy,nx,ny,a,c,ms,!turn,n,m,mm+1))
                    return dp[cx][cy][mx][my][turn][mm] = true;
                }
                    
                     else {
                        break;
                    }
                
            }

            
    }
            else
            {
                for(int j=0;j<=c;j++)
                {
                    int nx=cx+dx[i]*j;
                    int ny=cy+dy[i]*j;
                    if(nx>=0 && ny>=0 && nx<n && ny<m && a[nx][ny]!='#')
                    {
                        if(!dfs(nx,ny,mx,my,a,c,ms,!turn,n,m,mm))
                        return dp[cx][cy][mx][my][turn][mm] = false;
                     }
                      else
                        break; 
                    
                }
            }
        }
    

 
        if(turn) return dp[cx][cy][mx][my][turn][mm] = false;
        return dp[cx][cy][mx][my][turn][mm] = true;
}
    bool canMouseWin(vector<string>& a, int c, int ms) {
        int n=a.size(),m=a[0].size();
        int ci,cj,mi,mj;
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<m;j++)
            {
                if(a[i][j]=='C')
                {
                    ci=i;
                    cj=j;
                }

                if(a[i][j]=='M')
                {
                    mi=i;
                    mj=j;
                }
            }
        }

        memset(dp,-1,sizeof(dp));
return dfs(ci , cj , mi , mj , a , c , ms , true , n , m , 0);
    }
};
17600