# Image Overlap Problem

## Description

LeetCode Problem 835.

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:

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Input: img1 = [[1,1,0],[0,1,0],[0,1,0]], img2 = [[0,0,0],[0,1,1],[0,0,1]]
Output: 3

Example 2:

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

Example 3:

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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.

## Sample C++ Code

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class Solution {
public:
int largestOverlap(vector<vector<int>>& img1, vector<vector<int>>& img2) {
int n = img1.size();
vector<pair<int,int>> vec_a;
vector<pair<int,int>> vec_b;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (img1[i][j] == 1) {
vec_a.push_back({i, j});
}
if (img2[i][j] == 1) {
vec_b.push_back({i, j});
}
}
}
int ans = 0;
map<pair<int,int>,int> m;
for (auto [i1, j1] : vec_a) {
for (auto [i2, j2] : vec_b) {
m[{i1-i2, j1-j2}]++;
ans = max(ans, m[{i1-i2, j1-j2}]);
}
}
return ans;
}
};