<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:
    vector<vector<int>>validNeigh(vector<vector<int>>&matrix, int i, int j, int m,int n){
         vector<vector<int>> res;
         int curr = matrix[i][j];
         if(i>0 && matrix[i-1][j] > curr){
            res.push_back({i-1,j});
         }
         if(j>0 && matrix[i][j-1] > curr){
            res.push_back({i,j-1});
         }
         if(i<m-1 && matrix[i+1][j] > curr){
            res.push_back({i+1,j});
         }
         if(j<n-1 && matrix[i][j+1] > curr){
            res.push_back({i,j+1});
         }

         return res;
    }

    int longestIncreasingPathUtil(vector<vector<int>>& matrix, vector<vector<int>>& visited, int i, int j, int m, int n){
        vector<vector<int>> neigh = validNeigh(matrix, i, j, m,n);

        //base case
        if(neigh.size() == 0){ 
            return 1;
            }

        int maxLen =1;
        // neighbours
        for(auto item : neigh){
             cout<<"item "<<item[0]<<" "<<item[1]<<" "<<matrix[item[0]][item[1]]<< " "<<matrix[i][j]<<"\n";
            if(visited[item[0]][item[1]] != 0) {
               maxLen = max( maxLen, visited[item[0]][item[1]]);
               continue;}
              
               visited[item[0]][item[1]] = longestIncreasingPathUtil(matrix, visited, item[0], item[1], m, n);
             maxLen = max( maxLen, visited[item[0]][item[1]]);
        }

        visited[i][j]= 1+maxLen;

        return 1 + maxLen;
    }


    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        if(m==0) return 0;
        if(m==1 && n ==1) return 1;

        vector<vector<int>> visited(m, vector<int>(n,0));

        int maxLen = 1;

        for(int i =0; i<m; i++){
            for(int j =0; j<n;j++){
                if(visited[i][j] == 0)
              { maxLen = max(maxLen,longestIncreasingPathUtil(matrix, visited, i, j, m, n));}
              else{
                maxLen = max(maxLen, visited[i][j]);
              }
            }
        }

        for(int i =0;i<m;i++){
            for(int j =0; j<n;j++){
                cout<<visited[i][j]<<" ";
            }
            cout<<"\n";
        }
      
        return maxLen;

    }
};
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