# 835. Image Overlap

Two images `A` and `B` are given, represented as binary, square matrices of the same size. (A binary matrix has only 0s and 1s as values.)

We translate one image however we choose (sliding it left, right, up, or down any number of units), and place it on top of the other image. After, the overlap of this translation is the number of positions that have a 1 in both images.

(Note also that a translation does not include any kind of rotation.)

What is the largest possible overlap?

Example 1:

Input: A = [[1,1,0], [0,1,0], [0,1,0]] B = [[0,0,0], [0,1,1], [0,0,1]]

Output: 3

Explanation: We slide A to right by 1 unit and down by 1 unit.

Notes:

1. `1 <= A.length = A.length = B.length = B.length <= 30`
2. `0 <= A[i][j], B[i][j] <= 1`

# 思路

A中每个元素的位置都是不同的，当存入LA时也有一个计算方法让LA的每个值都与众不同：i / N * 100 + i % N，我选用100是因为数组的最大长度为30，只要大于2*N - 1都可以

``````class Solution {
public int largestOverlap(int[][] A, int[][] B) {
int N = A.length;
List<Integer> LA = new ArrayList<>(),  LB = new ArrayList<>();
HashMap<Integer, Integer> count = new HashMap<>();
for (int i = 0; i < N * N; ++i)
if (A[i / N][i % N] == 1)
LA.add(i / N * 100 + i % N);
for (int i = 0; i < N * N; ++i)
if (B[i / N][i % N] == 1)
LB.add(i / N * 100 + i % N);
for (int i : LA) for (int j : LB)
count.put(i - j, count.getOrDefault(i - j, 0) + 1);
int res = 0;
for (int i : count.values())
res = Math.max(res, i);
return res;
}
}
``````