Leetcode #835: Image Overlap
In this guide, we solve Leetcode #835 Image Overlap 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
You are given two images, img1 and img2, represented as binary, square matrices of size n x n. A binary matrix has only 0s and 1s as values.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Matrix
Intuition
Grid problems are easiest when you define clear row/column boundaries.
A consistent traversal order prevents off-by-one errors.
Approach
Iterate by rows, columns, or layers depending on the requirement.
Keep bounds updated as the traversal progresses.
Steps:
- Define bounds or directions.
- Visit cells in order.
- Update result and move bounds.
Example
Input: img1 = [[1,1,0],[0,1,0],[0,1,0]], img2 = [[0,0,0],[0,1,1],[0,0,1]]
Output: 3
Explanation: We translate img1 to right by 1 unit and down by 1 unit.
The number of positions that have a 1 in both images is 3 (shown in red).
Python Solution
class Solution:
def largestOverlap(self, img1: List[List[int]], img2: List[List[int]]) -> int:
n = len(img1)
cnt = Counter()
for i in range(n):
for j in range(n):
if img1[i][j]:
for h in range(n):
for k in range(n):
if img2[h][k]:
cnt[(i - h, j - k)] += 1
return max(cnt.values()) if cnt else 0
Complexity
The time complexity is , and the space complexity is , where is the side length of . The space complexity is , where is the side length of .
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.