<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 n,m;
int mx,my,cx,cy,fx,fy; // mouse, cat, food initial location
int dxy[4][2]={{0,-1},{-1,0},{0,1},{1,0}};
             // xc,yc- cat  xm,ym=mouse   t-moves   c1-cat jump, m1=mouse jump
int dp[9][9][9][9][130]; 
bool solve(int xc,int yc, int xm, int ym,int t,vector<string> &grid, int c1, int m1){
    if(t>128) return 0;

    if(dp[xc][yc][xm][ym][t]!=-1) return dp[xc][yc][xm][ym][t];

    int res= (t%2==0?0:1);

    if(t%2==0){
        if(xm==xc && ym==yc) {
           res= 0;
        }
        else if(xm==fx && ym==fy) {
            res= 1;
        }
         else if(xc==fx && yc==fy){
            res=0;
        }
        else {
            for(int i=0;i<4;i++){
                for(int j=0;j<=m1;j++){
                    int x= xm + j*dxy[i][0], y= ym + j*dxy[i][1];
                    if(x>=0 && y>=0 && x<n && y<m && grid[x][y]!='#'){
                       if(solve(xc,yc,x,y,t+1,grid,c1,m1)){
                        res= 1;
                        break;
                       }
                    }
                    else{
                        break;
                    }
                }
            }
        }
        
    }

    else {
         if(xm==xc && ym==yc) {
           res= 0;
        }
         else if(xc==fx && yc==fy){
            res= 0;
        }
         else if(xm==fx && ym==fy) {
            res= 1;
        }
        else{
             for(int i=0;i<4;i++){
                for(int j=0;j<=c1;j++){
                    int x= xc + j*dxy[i][0], y= yc+ j*dxy[i][1];
                    if(x>=0 && y>=0 && x<n && y<m && grid[x][y]!='#'){
                       if(solve(x,y,xm,ym,t+1,grid,c1,m1)==0){
                        res= 0;
                        break;
                       }
                    }
                    else{
                        break;
                    }
                }
            }
        }
    }

    return dp[xc][yc][xm][ym][t]=res;
}

    bool canMouseWin(vector<string>& grid, int c1, int m1) {
         n=grid.size(), m= grid[0].size();

         mx=-1,my=-1,cx=-1,cy=-1,fx=-1,fy=-1;

        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                      if(grid[i][j]=='C'){
                        cx=i, cy=j;
                      }
                      else  if(grid[i][j]=='M'){
                        mx=i, my=j;
                      }
                      else  if(grid[i][j]=='F'){
                        fx=i, fy=j;
                      }
            }
        }

        memset(dp,-1,sizeof(dp));

         return solve(cx,cy,mx,my,0,grid,c1,m1);
    }
};
15500