LeetCode #1139 — MEDIUM

Largest 1-Bordered Square

Move from brute-force thinking to an efficient approach using array strategy.

The Problem

Problem Statement

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 1:

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

Example 2:

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

Constraints:

1 <= grid.length <= 100
1 <= grid[0].length <= 100
grid[i][j] is 0 or 1

Step 01

Brute Force Baseline

Problem summary: 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.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Dynamic Programming

Example 1

[[1,1,1],[1,0,1],[1,1,1]]

Example 2

[[1,1,0,0]]

Step 02

Core Insight

What unlocks the optimal approach

For each square, know how many ones are up, left, down, and right of this square. You can find it in O(N^2) using dynamic programming.
Now for each square ( O(N^3) ), we can evaluate whether that square is 1-bordered in O(1).

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1139: Largest 1-Bordered Square
class Solution {
    public int largest1BorderedSquare(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        int[][] down = new int[m][n];
        int[][] right = new int[m][n];
        for (int i = m - 1; i >= 0; --i) {
            for (int j = n - 1; j >= 0; --j) {
                if (grid[i][j] == 1) {
                    down[i][j] = i + 1 < m ? down[i + 1][j] + 1 : 1;
                    right[i][j] = j + 1 < n ? right[i][j + 1] + 1 : 1;
                }
            }
        }
        for (int k = Math.min(m, n); k > 0; --k) {
            for (int i = 0; i <= m - k; ++i) {
                for (int j = 0; j <= n - k; ++j) {
                    if (down[i][j] >= k && right[i][j] >= k && right[i + k - 1][j] >= k
                        && down[i][j + k - 1] >= k) {
                        return k * k;
                    }
                }
            }
        }
        return 0;
    }
}

// Accepted solution for LeetCode #1139: Largest 1-Bordered Square
func largest1BorderedSquare(grid [][]int) int {
	m, n := len(grid), len(grid[0])
	down := make([][]int, m)
	right := make([][]int, m)
	for i := range down {
		down[i] = make([]int, n)
		right[i] = make([]int, n)
	}
	for i := m - 1; i >= 0; i-- {
		for j := n - 1; j >= 0; j-- {
			if grid[i][j] == 1 {
				down[i][j], right[i][j] = 1, 1
				if i+1 < m {
					down[i][j] += down[i+1][j]
				}
				if j+1 < n {
					right[i][j] += right[i][j+1]
				}
			}
		}
	}
	for k := min(m, n); k > 0; k-- {
		for i := 0; i <= m-k; i++ {
			for j := 0; j <= n-k; j++ {
				if down[i][j] >= k && right[i][j] >= k && right[i+k-1][j] >= k && down[i][j+k-1] >= k {
					return k * k
				}
			}
		}
	}
	return 0
}

# Accepted solution for LeetCode #1139: Largest 1-Bordered Square
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

// Accepted solution for LeetCode #1139: Largest 1-Bordered Square
struct Solution;

impl Solution {
    fn largest1_bordered_square(grid: Vec<Vec<i32>>) -> i32 {
        let n = grid.len();
        let m = grid[0].len();
        let mut top = vec![vec![0; m]; n];
        let mut down = vec![vec![0; m]; n];
        let mut left = vec![vec![0; m]; n];
        let mut right = vec![vec![0; m]; n];
        let mut res = 0;

        for i in 0..n {
            for j in 0..m {
                top[i][j] = if grid[i][j] == 1 {
                    1 + if i > 0 { top[i - 1][j] } else { 0 }
                } else {
                    0
                };
                left[i][j] = if grid[i][j] == 1 {
                    1 + if j > 0 { left[i][j - 1] } else { 0 }
                } else {
                    0
                };
            }
        }

        for i in (0..n).rev() {
            for j in (0..m).rev() {
                down[i][j] = if grid[i][j] == 1 {
                    1 + if i + 1 < n { down[i + 1][j] } else { 0 }
                } else {
                    0
                };
                right[i][j] = if grid[i][j] == 1 {
                    1 + if j + 1 < m { right[i][j + 1] } else { 0 }
                } else {
                    0
                };
            }
        }
        for i in 0..n {
            for j in 0..m {
                for k in 1..=(n - i).min(m - j) {
                    if top[i + k - 1][j + k - 1] >= k
                        && down[i][j] >= k
                        && left[i + k - 1][j + k - 1] >= k
                        && right[i][j] >= k
                    {
                        res = res.max(k);
                    }
                }
            }
        }
        (res * res) as i32
    }
}

#[test]
fn test() {
    let grid = vec_vec_i32![[1, 1, 1], [1, 0, 1], [1, 1, 1]];
    let res = 9;
    assert_eq!(Solution::largest1_bordered_square(grid), res);
    let grid = vec_vec_i32![[1, 1, 0, 0]];
    let res = 1;
    assert_eq!(Solution::largest1_bordered_square(grid), res);
}

// Accepted solution for LeetCode #1139: Largest 1-Bordered Square
// Auto-generated TypeScript example from java.
function exampleSolution(): void {
}
// Reference (java):
// // Accepted solution for LeetCode #1139: Largest 1-Bordered Square
// class Solution {
//     public int largest1BorderedSquare(int[][] grid) {
//         int m = grid.length, n = grid[0].length;
//         int[][] down = new int[m][n];
//         int[][] right = new int[m][n];
//         for (int i = m - 1; i >= 0; --i) {
//             for (int j = n - 1; j >= 0; --j) {
//                 if (grid[i][j] == 1) {
//                     down[i][j] = i + 1 < m ? down[i + 1][j] + 1 : 1;
//                     right[i][j] = j + 1 < n ? right[i][j + 1] + 1 : 1;
//                 }
//             }
//         }
//         for (int k = Math.min(m, n); k > 0; --k) {
//             for (int i = 0; i <= m - k; ++i) {
//                 for (int j = 0; j <= n - k; ++j) {
//                     if (down[i][j] >= k && right[i][j] >= k && right[i + k - 1][j] >= k
//                         && down[i][j + k - 1] >= k) {
//                         return k * k;
//                     }
//                 }
//             }
//         }
//         return 0;
//     }
// }

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(m × n × \min(m, n)

Space

O(m × n)

Approach Breakdown

RECURSIVE

O(2ⁿ) time

O(n) space

Pure recursion explores every possible choice at each step. With two choices per state (take or skip), the decision tree has 2ⁿ leaves. The recursion stack uses O(n) space. Many subproblems are recomputed exponentially many times.

DYNAMIC PROGRAMMING

O(n × m) time

O(n × m) space

Each cell in the DP table is computed exactly once from previously solved subproblems. The table dimensions determine both time and space. Look for the state variables — each unique combination of state values is one cell. Often a rolling array can reduce space by one dimension.

Shortcut: Count your DP state dimensions → that’s your time. Can you drop one? That’s your space optimization.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

State misses one required dimension

Wrong move: An incomplete state merges distinct subproblems and caches incorrect answers.

Usually fails on: Correctness breaks on cases that differ only in hidden state.

Fix: Define state so each unique subproblem maps to one DP cell.