<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>

map<pair<int,int>, int> mp;
class Solution {
public:
    bool validPoint(pair<int,int> p, int m, int n) {
        if(p.first >=0 && p.first<m && p.second>=0 && p.second<n) {
            return true;
        }
        return false;
    }
    bool validPath(vector<vector<int>>& matrix, pair<int,int> curr, pair<int,int> p) {
        if(matrix[p.first][p.second] > matrix[curr.first][curr.second] && matrix[curr.first][curr.second]>=0) {
            return true;
        }
        return false;
    }
    int longest(vector<vector<int>>& matrix, pair<int,int> curr) {
        if(mp.find(curr) != mp.end()) {
            return mp[curr];
        }
        int m = matrix.size();
        int n = matrix[0].size();

        pair<int,int> p1 = {curr.first-1, curr.second};
        pair<int,int> p2 = {curr.first, curr.second+1};
        pair<int,int> p3 = {curr.first+1, curr.second};
        pair<int,int> p4 = {curr.first, curr.second-1};

        int p1Len=0, p2Len=0, p3Len=0, p4Len = 0;
        if(validPoint(p1, m, n)) {
            if(validPath(matrix, p1, curr)) {
                matrix[curr.first][curr.second] = -1*matrix[curr.first][curr.second];
                p1Len = longest(matrix, p1);
                matrix[curr.first][curr.second] = -1*matrix[curr.first][curr.second];
            }
        }
        if(validPoint(p2, m, n)) {
            if(validPath(matrix, p2, curr)) {
                matrix[curr.first][curr.second] = -1*matrix[curr.first][curr.second];
                p2Len = longest(matrix, p2);
                matrix[curr.first][curr.second] = -1*matrix[curr.first][curr.second];
            }
        }
        if(validPoint(p3, m, n)) {
            if(validPath(matrix, p3, curr)) {
                matrix[curr.first][curr.second] = -1*matrix[curr.first][curr.second];
                p3Len = longest(matrix, p3);
                matrix[curr.first][curr.second] = -1*matrix[curr.first][curr.second];
            }
        }
        if(validPoint(p4, m, n)) {
            if(validPath(matrix, p4, curr)) {
                matrix[curr.first][curr.second] = -1*matrix[curr.first][curr.second];
                p4Len = longest(matrix, p4);
                matrix[curr.first][curr.second] = -1*matrix[curr.first][curr.second];
            }
        }

        mp[curr] = 1+max(p1Len, max(p2Len, max(p3Len, p4Len)));
        return mp[curr];
    }
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        mp.clear();
        int m = matrix.size();
        int n = matrix[0].size();
        int maxLen = 0;
        for(int i=0; i<m; i++) {
            for(int j=0; j<n; j++) {
                int temp = longest(matrix, make_pair(i,j));
                if(temp>maxLen) {
                    maxLen = temp;
                }
            }
        }
        return maxLen;
    }
};
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