<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>

class Solution {
public:
    const  vector<vector<int>> dirs = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};

    map<pair<int,int>,int> mp;
    int search(int x, int y){
        if(mp.find({x,y})!=mp.end()) return mp.at({x,y});
        int ans =1;
        for(const vector<int> dir: dirs){
            int newx= dir[0]+x;
            int newy= dir[1]+y;
            if(newx>=0 and newy>=0 and newx<row and newy<col and matrix[x][y]< matrix[newx][newy] )
                ans = max(ans, 1+search(newx,newy) );
        }
        return mp[{x,y}]= ans;
    }
    int row,col;
    vector<vector<int>> matrix;
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int maxDist= 0;
        const int row= matrix.size(), col = matrix[0].size();
        this-> row= row;
        this-> col = col;
        this-> matrix= matrix;
        for(int i=0;i<row;i++){
            for(int j=0;j<col;j++){
                maxDist= max(maxDist, search(i,j));
            }
        }
        return maxDist;
    }
};
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