{ "data": { "question": { "questionId": "864", "questionFrontendId": "835", "categoryTitle": "Algorithms", "boundTopicId": 1722, "title": "Image Overlap", "titleSlug": "image-overlap", "content": "

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.

\n\n

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.

\n\n

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.

\n\n

Return the largest possible overlap.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: img1 = [[1,1,0],[0,1,0],[0,1,0]], img2 = [[0,0,0],[0,1,1],[0,0,1]]\nOutput: 3\nExplanation: We translate img1 to right by 1 unit and down by 1 unit.\n\"\"\nThe number of positions that have a 1 in both images is 3 (shown in red).\n\"\"\n
\n\n

Example 2:

\n\n
\nInput: img1 = [[1]], img2 = [[1]]\nOutput: 1\n
\n\n

Example 3:

\n\n
\nInput: img1 = [[0]], img2 = [[0]]\nOutput: 0\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "图像重叠", "translatedContent": "

给你两个图像 img1 和 img2 ，两个图像的大小都是 n x n ，用大小相同的二进制正方形矩阵表示。二进制矩阵仅由若干 0 和若干 1 组成。

\n\n

转换 其中一个图像，将所有的 1 向左，右，上，或下滑动任何数量的单位；然后把它放在另一个图像的上面。该转换的 重叠 是指两个图像 都 具有 1 的位置的数目。

\n\n
\n
\n

请注意，转换 不包括 向任何方向旋转。越过矩阵边界的 1 都将被清除。

\n\n

最大可能的重叠数量是多少？

\n\n

 

\n\n

示例 1：

\n\"\"\n
\n输入：img1 = [[1,1,0],[0,1,0],[0,1,0]], img2 = [[0,0,0],[0,1,1],[0,0,1]]\n输出：3\n解释：将 img1 向右移动 1 个单位，再向下移动 1 个单位。\n\"\"\n两个图像都具有 1 的位置的数目是 3（用红色标识）。\n\"\"\n
\n\n

示例 2：

\n\n
\n输入：img1 = [[1]], img2 = [[1]]\n输出：1\n
\n\n

示例 3：

\n\n
\n输入：img1 = [[0]], img2 = [[0]]\n输出：0\n
\n\n

 

\n\n

提示：

\n\n\n
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