<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>

/*
 * @lc app=leetcode id=329 lang=cpp
 *
 * [329] Longest Increasing Path in a Matrix
 */

// @lc code=start
class Solution {
public:
    int dfs(vector<vector<int>>& matrix, int i, int j, int rows, int columns, vector<vector<int>>&memo){
        if(memo[i][j] != -1){
            return memo[i][j];
        }
        int len = 1;
        vector<int> dx = {0, 0, 1, -1};
        vector<int> dy = {1, -1, 0, 0};
        for(int k = 0; k < 4; k++){
            int newX = i + dx[k];
            int newY = j + dy[k];
            if(newX >= 0 && newX < rows && newY >= 0 && newY < columns && matrix[newX][newY] > matrix[i][j]){
                len = max(len, 1 + dfs(matrix, newX, newY, rows, columns, memo));                
            }
        }
        return memo[i][j] = len;
    }
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        ios_base::sync_with_stdio(false);
        cin.tie(nullptr);
        cout.tie(nullptr);

        int rows = matrix.size();
        int columns = matrix[0].size();
        int length = INT_MIN;
        vector<vector<int>>memo(rows, vector<int>(columns, -1));
        for(int i = 0; i < rows; i++){
            for(int j = 0; j < columns; j++){
                int temp = dfs(matrix, i, j, rows, columns, memo);
                length = max(temp, length);
            }
        }
        return length;
    }
};
// @lc code=end


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