835. Image Overlap —— weekly contest 84

Posted 2020-11-05 jinjin-2018

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

 1 class Solution {
 2 public:
 3     int largestOverlap(vector<vector<int>>& A, vector<vector<int>>& B) {
 4         int n = A.size();
 5         int res = 0;
 6         for(int i = -n+1; i < n; i++){
 7             for(int j =-n+1; j < n; j++){
 8                 int count = 0;
 9                 for(int k = max(i,0); k < min(n+i,n); k++){
10                     for(int l = max(j,0); l < min(n+j,n);l++){
11                         if(A[k-i][l-j]==1&&B[k][l]==1){
12                             count++;
13                         }
14                     }
15                 }
16                 res = max(res,count);
17             }
18         }
19         return res;
20     }
21 };

暴力模拟，O(n⁴),模拟过程的边界以及max的使用也没有想象中的那么容易。