Largest 1-Bordered Square — LeetCode 1139 Python Solution

MediumArrayDynamic ProgrammingMatrix
Problem
#1139
Reading time
4 min

The problem

Given a 2D grid of 0s and 1s, return the number of elements in the largest square subgrid that has all 1s on its border, or 0 if such a subgrid doesn't exist in the grid.

Example

Input
grid = [[1,1,1],[1,0,1],[1,1,1]]
Output
9

Python solution

Python
class Solution:
    def largest1BorderedSquare(self, grid: List[List[int]]) -> int:
        m, n = len(grid), len(grid[0])
        down = [[0] * n for _ in range(m)]
        right = [[0] * n for _ in range(m)]
        for i in range(m - 1, -1, -1):
            for j in range(n - 1, -1, -1):
                if grid[i][j]:
                    down[i][j] = down[i + 1][j] + 1 if i + 1 < m else 1
                    right[i][j] = right[i][j + 1] + 1 if j + 1 < n else 1
        for k in range(min(m, n), 0, -1):
            for i in range(m - k + 1):
                for j in range(n - k + 1):
                    if (
                        down[i][j] >= k
                        and right[i][j] >= k
                        and right[i + k - 1][j] >= k
                        and down[i][j + k - 1] >= k
                    ):
                        return k * k
        return 0

Complexity

MeasureComplexity
TimeO(m \times n \times \min(m, n))
SpaceO(m \times n) auxiliary

Pattern: Matrix and Grid

Treat a 2-D grid as a graph whose neighbours are the four adjacent cells. LeetCode 1139. Largest 1-Bordered Square 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.

Related problems

Frequently asked questions

How hard is LeetCode 1139. Largest 1-Bordered Square?
LeetCode 1139. Largest 1-Bordered Square is rated Medium on LeetCode.
What is the time complexity of LeetCode 1139. Largest 1-Bordered Square?
The Python solution on this page runs in O(m \times n \times \min(m, n)).
What is the space complexity of LeetCode 1139. Largest 1-Bordered Square?
The Python solution on this page uses O(m \times n) auxiliary space.
What topics does LeetCode 1139. Largest 1-Bordered Square cover?
LeetCode 1139. Largest 1-Bordered Square is tagged Array, Dynamic Programming and Matrix on LeetCode.

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