Maximal Square
Given an m x n binary matrix containing only '0' and '1', find the largest square containing only 1s.
Return the area of the largest such square.
Example 1
Input
m = 4
n = 5
matrix =
[
[1, 0, 1, 0, 0],
[1, 0, 1, 1, 1],
[1, 1, 1, 1, 1],
[1, 0, 0, 1, 0]
]Output
4
Explanation
The largest square containing only 1s has side length 2.
For example:
1 1
1 1
Its area is:
2 × 2 = 4
Therefore, the answer is 4.
Example 2
Input
m = 2
n = 2
matrix =
[
[0, 1],
[1, 0]
]Output
1
Explanation
There is no 2 × 2 square containing only 1s.
Each individual 1 forms a square of side length 1.
Therefore, the maximum area is:
1 × 1 = 1
Constraints
Hints:
Hint 1
Let dp[i][j] represent the side length of the largest square of 1s whose bottom-right corner is at (i, j).
Hint 2
If the current cell is 1, look at three neighboring cells:
top
left
top-left
The recurrence is:
dp[i][j] = 1 + min(
dp[i-1][j],
dp[i][j-1],
dp[i-1][j-1]
)
Author & Technical Reviewer
Technically reviewed by: ExamAdda Technical Review Team
Technical Reviewers, ExamAdda
Software engineers at ExamAdda who check every article's definitions, complexity claims and code examples before and after publishing.
Published
Aug 24, 2026
Last updated
Aug 24, 2026
Content Verification Methodology
Definitions and complexity claims were checked against authoritative computer-science references. Code examples were compiled and tested with standard, boundary and edge-case inputs.
Expected Output