329. Longest Increasing Path in a Matrix

https://leetcode.com/problems/longest-increasing-path-in-a-matrix/description/?envType=company&envId=doordash&favoriteSlug=doordash-thirty-days

Given an m x n integers matrix, return the length of the longest increasing path in matrix.

From each cell, you can either move in four directions: left, right, up, or down. You may not move diagonally or move outside the boundary (i.e., wrap-around is not allowed).

Example 1:

Input: matrix = [[9,9,4],[6,6,8],[2,1,1]]
Output: 4
Explanation: The longest increasing path is [1, 2, 6, 9].

Example 2:

Input: matrix = [[3,4,5],[3,2,6],[2,2,1]]
Output: 4
Explanation: The longest increasing path is [3, 4, 5, 6]. Moving diagonally is not allowed.

Example 3:

Input: matrix = [[1]]
Output: 1

Constraints:

• m == matrix.length

• n == matrix[i].length

• 1 <= m, n <= 200

• 0 <= matrix[i][j] <= 231 - 1

DFS+Memo

大数的值由周围最大的小数的值得来

class Solution:
    def longestIncreasingPath(self, matrix: List[List[int]]) -> int:
        if not matrix or not matrix[0]:
            return 0
        n,m = len(matrix), len(matrix[0])
        cache = [[0]*m for _ in range(n)] 
        dir = [(0,1),(1,0),(0,-1),(-1,0)]
        
        def dfs(x,y):
            if cache[x][y]:
                return cache[x][y]
            for dx,dy in dir:
                    nx, ny = x+dx, y+dy
                    if 0<=nx<n and 0<=ny<m and matrix[nx][ny]<matrix[x][y]:
                        cache[x][y] = max(cache[x][y], dfs(nx,ny))
            cache[x][y] += 1
            return cache[x][y]


        res = 0
        for x in range(n):
            for y in range(m):
                res = max(res, dfs(x,y))
        return res

拓扑排序来做，变形的bfs。 单用bfs不行，因为bfs每个元素仅遍历一次，无法追踪增序数组长度。

Steps:

1. Compute in-degrees (how many smaller neighbors each cell has).

2. Start BFS from nodes with in-degree = 0 (smallest values).

3. Process nodes in layers, updating neighbors and decreasing their in-degrees.

4. Track depth (path length) during BFS.

```python3
class Solution:
    def longestIncreasingPath(self, matrix: List[List[int]]) -> int:
        if not matrix or not matrix[0]:
            return 0
        n,m = len(matrix), len(matrix[0])
        in_degree = [[0]*m for _ in range(n)] 
        dir = [(0,1),(1,0),(0,-1),(-1,0)]
        for x in range(n):
            for y in range(m):
                for dx,dy in dir:
                    nx, ny = x+dx, y+dy
                    if 0<=nx<n and 0<=ny<m and matrix[nx][ny]<matrix[x][y]:
                        in_degree[x][y]+=1
        q = deque([(x,y) for x in range(n) for y in range(m) if in_degree[x][y] == 0])
        res = 0
        while q:
            res +=1
            for _ in range(len(q)):
                x,y = q.popleft()
                for dx,dy in dir:
                    nx, ny = x+dx, y+dy
                    if 0<=nx<n and 0<=ny<m and matrix[nx][ny]>matrix[x][y]:
                        in_degree[nx][ny]-=1
                        if in_degree[nx][ny] == 0:
                            q.append((nx,ny))
        return res
        
```