MediumNo. 1139
Largest 1-Bordered Square — LeetCode 1139 Python Solution
- Pattern
- Matrix and Grid
- Topics
- Array, Dynamic Programming, Matrix
- Reading time
- 4 min
- Source
- leetcode.com
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
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 0Complexity
- Time
- O(m × n × min(m, n))
- Space · auxiliary
- O(m × n)
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
| No. | Problem | Difficulty |
|---|---|---|
| 0063 | Unique Paths II | Medium |
| 0064 | Minimum Path Sum | Medium |
| 0085 | Maximal Rectangle | Hard |
| 0174 | Dungeon Game | Hard |
| 0221 | Maximal Square | Medium |
| 0329 | Longest Increasing Path in a Matrix | Hard |
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 × n × min(m, n)).
- What is the space complexity of LeetCode 1139. Largest 1-Bordered Square?
The Python solution on this page uses O(m × 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.