<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 {
private:
    vector<int> dirs_x = {0, -1, 0, 1};
    vector<int> dirs_y = {-1, 0, 1, 0};
    bool isValid(int row, int col, int n, int m) {
        if (row>=0 and row<n and col>=0 and col<m) return true;
        return false;
    }
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        vector<pair<int, pair<int, int>>> numbers;
        int n = matrix.size();
        int m = matrix[0].size();
        int ans=1;
        vector<vector<int>> increasing_path_matrix;
        increasing_path_matrix.resize(n);
        for (int i=0;i<n;i++) {
            for (int j=0;j<m;j++) {
                numbers.push_back(make_pair(matrix[i][j], make_pair(i,j) ));
                increasing_path_matrix[i].push_back(1);
            }
        }
        sort(numbers.begin(), numbers.end());
        for (int i=0;i<numbers.size();i++) {
            int row = numbers[i].second.first;
            int col = numbers[i].second.second;
            for (int j=0;j<4;j++) {
                int new_x = row+dirs_x[j];
                int new_y = col+dirs_y[j];
                if (isValid(new_x, new_y, n, m) and matrix[new_x][new_y] < matrix[row][col]) {
                   increasing_path_matrix[row][col] = max(increasing_path_matrix[row][col], increasing_path_matrix[new_x][new_y] + 1);
                }
            }
            // cout<<row<<" "<<col<<" "<<increasing_path_matrix[row][col]<<endl;
            ans=max(ans, increasing_path_matrix[row][col]);
        }
        return ans;
    }
};
28040