<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>> saved_res;

    int longest_path_from_source(vector<vector<int>>& matrix, int row, int col) {
        list<int> paths;
        if (row - 1 >= 0) {
            if (matrix[row][col] < matrix[row-1][col]){
                if (saved_res[row-1][col] != -1){
                    paths.push_back(1 + saved_res[row-1][col]);
                } else {
                    paths.push_back(1 + longest_path_from_source(matrix, row-1, col));
                }
            }
        }
        if (row + 1 < matrix.size()) {
            if (matrix[row][col] < matrix[row+1][col]){
                if (saved_res[row+1][col] != -1){
                    paths.push_back(1 + saved_res[row+1][col]);
                } else {
                    paths.push_back(1 + longest_path_from_source(matrix, row+1, col));    
                }
            }
        }
        if (col - 1 >= 0) {
            if (matrix[row][col] < matrix[row][col-1]){
                if (saved_res[row][col-1] != -1){
                    paths.push_back(1 + saved_res[row][col-1]);
                }
                else {
                    paths.push_back(1 + longest_path_from_source(matrix, row, col-1));
                }
            }
        }
        if (col + 1 < matrix[0].size()) {
            if (matrix[row][col] < matrix[row][col+1]){
                if (saved_res[row][col+1] != -1){
                    paths.push_back(1 + saved_res[row][col+1]);
                } else {
                    paths.push_back(1 + longest_path_from_source(matrix, row, col+1));    
                }
                
            }
        }
        if (paths.size() == 0) {
            return 1;
        }
        int max_in_so_far = paths.front();
        for (auto val: paths) {
            max_in_so_far = max(max_in_so_far, val);
        }
        saved_res[row][col] = max_in_so_far;
        return max_in_so_far;
    }

    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        auto longest_path = INT_MIN;
        
        saved_res.resize(m);
        for (int i=0; i<m; i++) {
            for (int j=0; j < n; j++){
                saved_res[i].push_back(-1);
            }
        }
        
        for (int i=0; i<m; i++) {
            for (int j=0; j < n; j++){
                longest_path = max(longest_path_from_source(matrix, i, j), longest_path);
                
            }
        }
        return longest_path;
    }
};
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