Image Overlap

arraymatrix

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 0 s and 1 s 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 .

Examples

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
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 .

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicMatrix