835. Image Overlap

Medium (Trung bình) Python 🔗 Xem trên LeetCode

📋 Đề Bài

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.

🧠 Thuật Toán & Kỹ Thuật

Hash Table (Bảng băm)Matrix (Ma trận)
⏱️ Thời gian O(n²)
💾 Không gian O(n)

💻 Lời Giải

Python 0835-image-overlap.py 
class Solution:
    def largestOverlap(self, img1: List[List[int]], img2: List[List[int]]) -> int:
        cnt = defaultdict(int)
        maxOverlap = 0
        n = len(img1)
        d1, d2 = [], []
        
        for i in range(n):
            for j in range(n):
                if img1[i][j] == 1:
                    d1.append((i, j))
                if img2[i][j] == 1:
                    d2.append((i, j))
                    
        for x1, y1 in d1:
            for x2, y2 in d2:
                d = ((x2 - x1), (y2 - y1))
                cnt[d] += 1
                maxOverlap = max(maxOverlap, cnt[d])
                
        return maxOverlap