<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);
    }
};
17500