Largest 1-Bordered Square - 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.
A square subgrid has all 1s on its border if all the cells on the top, bottom, left, and right edges are 1s. The interior of the square can contain any values.
Input & Output
Example 1 — Perfect Border Square
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Input:
grid = [[1,1,1],[1,0,1],[1,1,1]]
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Output:
9
💡 Note:
The entire 3×3 grid has all 1s on its border (edges), with interior cell [1][1] = 0. This forms a valid 1-bordered square of size 9.
Example 2 — Multiple Small Squares
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Input:
grid = [[1,1,0,0],[1,1,0,0],[0,0,1,1],[0,0,1,1]]
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Output:
4
💡 Note:
We can find 2×2 squares at positions (0,0) and (2,2), each having all border cells as 1s. Maximum area is 2×2 = 4.
Example 3 — No Valid Square
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Input:
grid = [[1,0,1],[0,1,0],[1,0,1]]
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Output:
1
💡 Note:
No square larger than 1×1 has all 1s on its border. The maximum valid square has area 1.
Constraints
- 1 ≤ grid.length, grid[i].length ≤ 15
- grid[i][j] is either 0 or 1
Visualization
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Explanation
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