<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 {
    vector<vector<int>> dp;
    vector<vector<bool>> vis;
public:
    vector<vector<int>> getvert(int i, int j, vector<vector<int>> &matrix){
        vector<vector<int>> ans;
        int m = matrix.size();
        int n = matrix[0].size();
        if(i < m-1 and matrix[i+1][j] > matrix[i][j]){
            ans.push_back({i+1,j});
        }
        if(j < n-1 and matrix[i][j+1] > matrix[i][j]){
            ans.push_back({i,j+1});
        }
        if(i > 0 and matrix[i-1][j] > matrix[i][j]){
            ans.push_back({i-1,j});
        }
        if(j > 0 and matrix[i][j-1] > matrix[i][j]){
            ans.push_back({i, j-1});
        }
        return ans;
    }
    void dfs(int i, int j, vector<vector<int>> &matrix){
        vis[i][j] = true;
        for(auto it:getvert(i, j, matrix)){
            if(!vis[it[0]][it[1]]){
                dfs(it[0], it[1], matrix);
            }
            dp[i][j] = max(dp[i][j], 1 + dp[it[0]][it[1]]);
        }
    }
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        dp = vector<vector<int>> (matrix.size(), vector<int>(matrix[0].size(), 1));
        vis = vector<vector<bool>> (matrix.size(), vector<bool>(matrix[0].size(), false));
        for(int i=0;i<matrix.size();i++){
            for(int j=0;j<matrix[0].size();j++){
                if(!vis[i][j]){
                    dfs(i, j, matrix);
                }
            }
        }
        int ans = 0;
        for(auto it:dp){
            for(auto iter:it){
                ans = max(iter, ans);
            }
        }
        return ans;
    }
};
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