835. Image Overlap

Problem Link

Description

---

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.

We translate one image however we choose by sliding all the 1 bits left, right, up, and/or down any number of units. We then place it on top of the other image. We can then calculate the overlap by counting the number of positions that have a 1 in both images.

Note also that a translation does not include any kind of rotation. Any 1 bits that are translated outside of the matrix borders are erased.

Return the largest possible overlap.

 

Example 1:

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).

Example 2:

Input: img1 = [[1]], img2 = [[1]]
Output: 1

Example 3:

Input: img1 = [[0]], img2 = [[0]]
Output: 0

 

Constraints:

• n == img1.length == img1[i].length
• n == img2.length == img2[i].length
• 1 <= n <= 30
• img1[i][j] is either 0 or 1.
• img2[i][j] is either 0 or 1.

Solution

---

Python3

class Solution:
    def largestOverlap(self, img1: List[List[int]], img2: List[List[int]]) -> int:
        rows, cols = len(img1), len(img1[0])
        A = [(i, j) for i in range(rows) for j in range(cols) if img1[i][j] == 1]
        B = [(i, j) for i in range(rows) for j in range(cols) if img2[i][j] == 1]
        counter = Counter((a - c, b - d) for a, b in A for c, d in B)
        
        return max(counter.values() or [0])