<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:
    def longestIncreasingPath(self, matrix: List[List[int]]) -> int:
        """
        
        
        3. return the max travel distance
        """
        m = len(matrix)
        n = len(matrix[0])
        directions = [(-1, 0), (1, 0), (0, -1), (0, 1)] 
        neighbors = {} # key: (i, j); value: list of neighbors

        # 1. compute adjacency dictionary
        for i in range(m):
            for j in range(n):
                for incrementI, incrementJ in directions:
                    if self.isValid(matrix[i][j], i + incrementI, j + incrementJ, matrix):
                        neighbor = (i + incrementI, j + incrementJ)
                        if (i, j) in neighbors:
                            neighbors[(i, j)].append(neighbor)
                        else:
                            neighbors[(i, j)] = [neighbor]
        
        """
        2. do a dfs for each element in the matrix
            each element in the stack = ((i, j), curCount), where curCount is how much we have  traveled so far to get to the point (i, j), which is a neighbor of the current node
        """
        dic = {} # key: (i, j); value: longest distance that we can travel from the node (i, j)
        def dfs(i, j):
            if (i, j) in dic:
                return dic[(i, j)]
            elif (i, j) not in neighbors:
                return 1
            
            counts = []
            for newI, newJ in neighbors[(i, j)]:
                counts.append(dfs(newI, newJ) + 1)
            
            dic[(i, j)] = max(counts)
            return dic[(i, j)]
        
        for i in range(m):
            for j in range(n):
                dfs(i, j)
        
        print(dic)
        print(neighbors)
        ans = 1
        for k in dic:
            ans = max(ans, dic[k])
    
        return ans




                        
                

        

        
    
    def isValid(self, curValue, i, j, matrix):
        """
        Returns True if matrix[i][j] is within matrix boundaries and matrix[i][j] > curValue
        """
        return i >= 0 and j >= 0 and i < len(matrix) and j < len(matrix[0]) and matrix[i][j] > curValue


25225