<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 longestIncreasingPath(vector<vector<int>>& matrix) {
        int maxPath = 1;
        vector<vector<int>> visitedAmount(matrix.size(), vector<int>(matrix[0].size(), 0));
        priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, less<tuple<int, int, int>>> pq;

        for(int r = 0; r<matrix.size(); r++){
            for(int c = 0; c<matrix[0].size(); c++){
                pq.push({matrix[r][c], r, c});
            }
        } 

         while(!pq.empty()){
            const auto[num, row, col] = pq.top();
            pq.pop();
            maxPath = max(longestIncreasingPathHelper(matrix, visitedAmount, maxPath, 1, pq, row, col), maxPath);
            // cout << "num:" << num << " row:" << row << " col:" << col << " maxPath:" << maxPath << endl;
        }
        return maxPath;
    }
private:
    int longestIncreasingPathHelper(vector<vector<int>>& matrix, vector<vector<int>>& visitedAmount, int maxPath, int currPath, priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, less<tuple<int, int, int>>>& pq, int row, int col){
        
        if(visitedAmount[row][col] != 0) return currPath + visitedAmount[row][col];

        int currMaxPath = 1;
        vector<pair<int, int>> directions = {{1,0}, {-1, 0}, {0, 1}, {0, -1}};
        for(auto&[dirRow, dirCol]:directions){
            int nextRow = row + dirRow;
            int nextCol = col + dirCol;
            if(nextRow < 0 || nextRow >= matrix.size() || nextCol < 0 || nextCol >= matrix[0].size()) continue;
            if(matrix[nextRow][nextCol] > matrix[row][col]){
                
                currMaxPath = max(longestIncreasingPathHelper(matrix, visitedAmount, maxPath, currPath, pq, nextRow, nextCol), currMaxPath);
                // cout << "\t num:" << matrix[row][col] << " row:" << row << " col:" << col << " next:"<< matrix[nextRow][nextCol] << " nextRow:" << nextRow << " nextCol:" << nextCol << " maxPath:" << maxPath << " currPath:" << currPath << " currMaxPath:" << currMaxPath << endl;
            }
        }
        visitedAmount[row][col] = currMaxPath;

        return max(maxPath, max(currMaxPath, currPath));
    }
};
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