Check if There is a Path With Equal Number of 0's And 1's — LeetCode 2510 Python Solution

The problem

You are given a 0-indexed m x n binary matrix grid. You can move from a cell (row, col) to any of the cells (row + 1, col) or (row, col + 1).

Example

Input

grid = [[0,1,0,0],[0,1,0,0],[1,0,1,0]]

Output

true

Explanation

The path colored in blue in the above diagram is a valid path because we have 3 cells with a value of 1 and 3 with a value of 0. Since there is a valid path, we return true.

Python solution

class Solution:
    def isThereAPath(self, grid: List[List[int]]) -> bool:
        @cache
        def dfs(i, j, k):
            if i >= m or j >= n:
                return False
            k += grid[i][j]
            if k > s or i + j + 1 - k > s:
                return False
            if i == m - 1 and j == n - 1:
                return k == s
            return dfs(i + 1, j, k) or dfs(i, j + 1, k)

        m, n = len(grid), len(grid[0])
        s = m + n - 1
        if s & 1:
            return False
        s >>= 1
        return dfs(0, 0, 0)

Complexity

Pattern: Matrix and Grid

Treat a 2-D grid as a graph whose neighbours are the four adjacent cells. LeetCode 2510. Check if There is a Path With Equal Number of 0's And 1's is filed here because LeetCode tags it Matrix, which is the vocabulary this hub collects.

The matrix and grid guide has the Python template for the pattern and the 216 LeetCode problems that use it.

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