<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:

    int dfs(int r_idx, int c_idx, vector<vector<int>>& matrix, vector<vector<bool>>& visited, vector<vector<int> > &m_height) {
        visited[r_idx][c_idx] = true;
        int curr_height = 0;
        for(pair<int, int> neighbour: getNeighbours(r_idx, c_idx, matrix)) {
            if(!visited[neighbour.first][neighbour.second]) {
                curr_height = max(curr_height, dfs(neighbour.first, neighbour.second, matrix, visited, m_height));
            }
            else {
                curr_height = max(curr_height, m_height[neighbour.first][neighbour.second]);
            }
        }
        m_height[r_idx][c_idx] = curr_height + 1;
        return m_height[r_idx][c_idx];
    }

    vector<pair<int, int> > getNeighbours(int r_idx, int c_idx, vector<vector<int>>& matrix) {
        int rows = matrix.size();
        int cols = matrix[0].size();
        vector<int> dx = {0, 0, -1, 1};
        vector<int> dy = {-1, 1, 0, 0};
        vector<pair<int, int> > neighbours;
        for(int idx = 0; idx < 4; idx++) {
            int nr_idx = r_idx + dx[idx];
            int nc_idx = c_idx + dy[idx];
            if(nr_idx < 0 || nr_idx >= rows || nc_idx < 0 || nc_idx >= cols || matrix[nr_idx][nc_idx] <= matrix[r_idx][c_idx]) {
                continue;
            }
            neighbours.push_back({nr_idx, nc_idx});
        }
        return neighbours;
    }


    int longestIncreasingPath(vector<vector<int>>& matrix) {

        int rows = matrix.size();
        int cols = matrix[0].size();
        int max_height = 0;
        vector<vector<bool> > visited(rows, vector<bool>(cols, false));
        vector<vector<int> > m_height(rows, vector<int>(cols, 0));
        for(int r_idx = 0; r_idx < rows; r_idx++) {
            for(int c_idx = 0; c_idx < cols; c_idx++) {
                if(!visited[r_idx][c_idx]) {
                    max_height = max(max_height, dfs(r_idx, c_idx, matrix, visited, m_height));
                }
                else {
                    max_height = max(max_height, m_height[r_idx][c_idx]);
                }
            }
        }
        return max_height;
    }
};
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