Leetcode #1277: Count Square Submatrices with All Ones
In this guide, we solve Leetcode #1277 Count Square Submatrices with All Ones in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given a m * n matrix of ones and zeros, return how many square submatrices have all ones. Example 1: Input: matrix = [ [0,1,1,1], [1,1,1,1], [0,1,1,1] ] Output: 15 Explanation: There are 10 squares of side 1.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Dynamic Programming, Matrix
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: matrix =
[
[0,1,1,1],
[1,1,1,1],
[0,1,1,1]
]
Output: 15
Explanation:
There are 10 squares of side 1.
There are 4 squares of side 2.
There is 1 square of side 3.
Total number of squares = 10 + 4 + 1 = 15.
Python Solution
class Solution:
def countSquares(self, matrix: List[List[int]]) -> int:
m, n = len(matrix), len(matrix[0])
f = [[0] * n for _ in range(m)]
ans = 0
for i, row in enumerate(matrix):
for j, v in enumerate(row):
if v == 0:
continue
if i == 0 or j == 0:
f[i][j] = 1
else:
f[i][j] = min(f[i - 1][j - 1], f[i - 1][j], f[i][j - 1]) + 1
ans += f[i][j]
return ans
Complexity
The time complexity is O(n·m) (typical). The space complexity is O(n·m) or optimized.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.