<p>Given an <code>m x n</code> integers <code>matrix</code>, return <em>the length of the longest increasing path in </em><code>matrix</code>.</p>

<p>From each cell, you can either move in four directions: left, right, up, or down. You <strong>may not</strong> move <strong>diagonally</strong> or move <strong>outside the boundary</strong> (i.e., wrap-around is not allowed).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/05/grid1.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> matrix = [[9,9,4],[6,6,8],[2,1,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The longest increasing path is <code>[1, 2, 6, 9]</code>.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/27/tmp-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> matrix = [[3,4,5],[3,2,6],[2,2,1]]
<strong>Output:</strong> 4
<strong>Explanation: </strong>The longest increasing path is <code>[3, 4, 5, 6]</code>. Moving diagonally is not allowed.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> matrix = [[1]]
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= matrix[i][j] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>


int MAX(vector<int> V) {
    int res = INT_MIN;
    for (int i = 0; i < V.size(); i++) {
        res = max(V[i], res);
    }
    return res;
}



class Solution {
public:
    int solve(vector<vector<int>>& matrix,vector<vector<int>>&dp,int i,int j){
        if(dp[i][j]>= 0){
            return dp[i][j];
        }
        else{
            vector<int>dir;
            int d,u,r,l;
            if(i+1<dp.size() && matrix[i+1][j] >matrix[i][j]){
                d = solve(matrix,dp,i+1,j);
                dir.push_back(d);

            }
            if(i-1>=0 && matrix[i-1][j] >matrix[i][j]){
                u = solve(matrix,dp,i-1,j);
                dir.push_back(u);
            }
            if(j+1<dp[0].size() && matrix[i][j+1] >matrix[i][j]){
                r = solve(matrix,dp,i,j+1);
                dir.push_back(r);
            }
            if(j-1>= 0 && matrix[i][j-1] >matrix[i][j]){
                l = solve(matrix,dp,i,j-1);
                dir.push_back(l);
            }
            if(dir.empty()){
                return dp[i][j] = 1;
            }
            else{
                int M = MAX(dir);
                return dp[i][j] = M+1;
            }
        }
    }
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        vector<vector<int>>dp(m,vector<int>(n,-1));
        solve(matrix,dp,0,0);
        int M = -1;
        for(int i = 0;i<m;i++){
            for(int j = 0;j<n;j++){
                // M = max(M,dp[i][j]);
                if(dp[i][j] == -1){
                    solve(matrix,dp,i,j);
                    M = max(M,dp[i][j]);
                }
                else{
                    M = max(M,dp[i][j]);
                }
                
            }
        }
        return M;
        
        
    }
};
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