<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[130][9][9][9][9];
    int solve(int move, int cx, int cy, int mx, int my, int fx, int fy, int cj, int mj, vector<string>& g){
        int n = g.size(), m = g[0].size();

        if(cx == mx && cy == my)return 0;
        if(cx == fx && cy == fy)return 0;
        if(move == m * n * 2)return 0;
        if(mx == fx && my == fy)return 1;

        if(dp[move][cx][cy][mx][my] != -1)return dp[move][cx][cy][mx][my];

        if(move % 2 == 0){
            int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, -1, 0, 1};

            for(int i = 0; i < 4; i++){
                for(int j = 0; j <= mj; j++){
                    int nx = mx + (dx[i] * j);
                    int ny = my + (dy[i] * j);

                    if(nx >= 0 && ny >= 0 && nx < n && ny < m && g[nx][ny] != '#'){
                        if(solve(move + 1, cx, cy, nx, ny, fx, fy, cj, mj, g))return dp[move][cx][cy][mx][my] = 1;
                    }
                    else break;
                }
            }
            return dp[move][cx][cy][mx][my] = 0;
        }
        else{
            int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, -1, 0, 1};

            for(int i = 0; i < 4; i++){
                for(int j = 0; j <= cj; j++){
                    int nx = cx + (dx[i] * j);
                    int ny = cy + (dy[i] * j);

                    if(nx >= 0 && ny >= 0 && nx < n && ny < m && g[nx][ny] != '#'){
                        if(!solve(move + 1, nx, ny, mx, my, fx, fy, cj, mj, g))return dp[move][cx][cy][mx][my] = 0;
                    }
                    else break;

                }
            }
            return dp[move][cx][cy][mx][my] = 1;
        }

    }
    bool canMouseWin(vector<string>& g, int cj, int mj) {
        int cx, cy, mx, my, fx, fy, n = g.size(), m = g[0].size();

        for(int i = 0; i < n; i++){
            for(int j = 0; j < m; j++){
                if(g[i][j] == 'C')cx = i, cy = j;
                if(g[i][j] == 'M')mx = i, my = j;
                if(g[i][j] == 'F')fx = i, fy = j;
            }
        }
        memset(dp, -1, sizeof(dp));

        return solve(0, cx, cy, mx, my, fx, fy, cj, mj, g);
    }
};
15600