How hard is LeetCode 1091. Shortest Path in Binary Matrix?

LeetCode 1091. Shortest Path in Binary Matrix is rated Medium on LeetCode.

What is the time complexity of LeetCode 1091. Shortest Path in Binary Matrix?

The Python solution on this page runs in O(V+E).

What is the space complexity of LeetCode 1091. Shortest Path in Binary Matrix?

The Python solution on this page uses O(V) auxiliary space.

What topics does LeetCode 1091. Shortest Path in Binary Matrix cover?

LeetCode 1091. Shortest Path in Binary Matrix is tagged Breadth-First Search, Array and Matrix on LeetCode.

Shortest Path in Binary Matrix — LeetCode 1091 Python Solution

MediumBreadth-First SearchArrayMatrix

Problem: #1091
Pattern: Matrix and Grid
Reading time: 3 min
Source: leetcode.com

The problem

Given an n x n binary matrix grid, return the length of the shortest clear path in the matrix. If there is no clear path, return -1.

Example

Input: grid = [[0,1],[1,0]]
Output: 2

Python solution

Python

class Solution:
    def shortestPathBinaryMatrix(self, grid: List[List[int]]) -> int:
        if grid[0][0]:
            return -1
        n = len(grid)
        grid[0][0] = 1
        q = deque([(0, 0)])
        ans = 1
        while q:
            for _ in range(len(q)):
                i, j = q.popleft()
                if i == j == n - 1:
                    return ans
                for x in range(i - 1, i + 2):
                    for y in range(j - 1, j + 2):
                        if 0 <= x < n and 0 <= y < n and grid[x][y] == 0:
                            grid[x][y] = 1
                            q.append((x, y))
            ans += 1
        return -1

Complexity

Measure	Complexity
Time	O(V+E)
Space	O(V) auxiliary

Pattern: Matrix and Grid

Treat a 2-D grid as a graph whose neighbours are the four adjacent cells. LeetCode 1091. Shortest Path in Binary Matrix 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.

Frequently asked questions

How hard is LeetCode 1091. Shortest Path in Binary Matrix?: LeetCode 1091. Shortest Path in Binary Matrix is rated Medium on LeetCode.
What is the time complexity of LeetCode 1091. Shortest Path in Binary Matrix?: The Python solution on this page runs in O(V+E).
What is the space complexity of LeetCode 1091. Shortest Path in Binary Matrix?: The Python solution on this page uses O(V) auxiliary space.
What topics does LeetCode 1091. Shortest Path in Binary Matrix cover?: LeetCode 1091. Shortest Path in Binary Matrix is tagged Breadth-First Search, Array and Matrix on LeetCode.