<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>> moves{{1, 0}, {0, 1}, {-1, 0}, {0, -1}};

    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int rows = matrix.size(), cols = matrix[0].size(), result = 0;
        vector<vector<int>> dp(rows, vector<int>(cols, 0));
        stack<vector<int>> check;
        vector<int> memory, newMove;
        // Find all cells, which only have higher neigbors. From them, fill the matrix, since they have to be the begining of the result.
        for(int row = 0; row < rows; row++){
            for(int col = 0; col < cols; col++){
                if(dp[row][col] == 0 &&
                (!validMove(row+1, col, rows, cols) || matrix[row][col] <= matrix[row+1][col]) && (!validMove(row-1, col, rows, cols) || matrix[row][col] <= matrix[row-1][col]) &&
                (!validMove(row, col+1, rows, cols) || matrix[row][col] <= matrix[row][col+1]) && (!validMove(row, col-1, rows, cols) || matrix[row][col] <= matrix[row][col-1])){
                    dp[row][col] = 1;
                    check.push({row, col});
                    while(!check.empty()){
                        memory = check.top();
                        check.pop();
                        for(vector<int> move : moves){
                            newMove = {memory[0]+move[0], memory[1]+move[1]};
                            if(validMove(newMove[0], newMove[1], rows, cols) && matrix[memory[0]][memory[1]] < matrix[newMove[0]][newMove[1]] && 
                            dp[memory[0]][memory[1]] >= dp[newMove[0]][newMove[1]]){
                                dp[newMove[0]][newMove[1]] = dp[memory[0]][memory[1]]+1;
                                check.push({newMove[0], newMove[1]});
                            }
                        }
                    }
                }
            }   
        }
        for(vector<int> row : dp){
            for(int i : row){
                result = max(result, i);
            }
        }
        return result;
    }

    bool validMove(int row, int col, int rows, int cols){
        if(row == -1 || row == rows || col == -1 || col == cols) return false;
        else return true;
    }
};
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