<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>

#define pii pair<int,int>

class Solution {
public:
    int dp[9][9][9][9][130];
    bool canMouseWin(vector<string>& grid, int catJump, int mouseJump) {
        int m = grid.size(), n = grid[0].size();
        memset(dp, -1, sizeof(dp));

        pii mouseloc, catloc, food;
        for(int i=0;i<m;i++) {
            for(int j=0;j<n;j++) {
                if(grid[i][j] == 'M') mouseloc = {i, j};
                else if(grid[i][j] == 'C') catloc = {i, j};
                else if(grid[i][j] == 'F') food = {i, j};
            }
        }

        vector<int>dirs = {-1, 0, 1, 0, -1};
        function<int(pii, pii, int)> solve = [&](pii cat, pii mouse, int moves) {
            if(cat == mouse) return 0;
            if(cat == food) return 0;
            if(moves == m*n*2) return 0;
            if(mouse == food) return 1;

            if(dp[cat.first][cat.second][mouse.first][mouse.second][moves] != -1) {
                return dp[cat.first][cat.second][mouse.first][mouse.second][moves];
            }
            if(moves%2 == 0) { //mouse turn
                for(int i=0;i<4;i++) {
                    for(int j=0;j<=mouseJump;j++) {
                        int x = mouse.first + j*dirs[i], y = mouse.second + j*dirs[i+1];
                        if(x >= 0 && x < m && y >= 0 &&  y < n && grid[x][y] != '#') {
                            pii nextPos = {x, y};
                            if(solve(cat, nextPos, moves+1)) {
                                return dp[cat.first][cat.second][mouse.first][mouse.second][moves] = 1;
                            }
                        }
                        else break;
                    }
                }
                return dp[cat.first][cat.second][mouse.first][mouse.second][moves] = 0;
            }
            else { //cat turn
                for(int i=0;i<4;i++) {
                    for(int j=0;j<=catJump;j++) {
                        int x = cat.first + j*dirs[i], y = cat.second + j*dirs[i+1];
                        if(x >= 0 && x < m && y >= 0 && y < n && grid[x][y] != '#') {
                            pii nextPos = {x, y};
                            if(!solve(nextPos, mouse, moves+1)) {
                                return dp[cat.first][cat.second][mouse.first][mouse.second][moves] = 0;
                            }
                        }
                        else break;
                    }
                }
                return dp[cat.first][cat.second][mouse.first][mouse.second][moves] = 1;
            }
        };

        return solve(catloc, mouseloc, 0) == 1;
    }
};
16800