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This solution involves shifting one image over another in all possible positions and counting how many ones overlap. By varying the horizontal and vertical shifts, and calculating overlaps with respect to the position of img2, the solution finds the maximum overlap. This approach iterates over all possible translations, moving img1 relative to img2 and keeping track of the maximum overlap seen.
Time Complexity: O(n^4), where n is the size of the matrix, due to the two nested loops and a cross-sectional overlap check for each.
Space Complexity: O(1), since the solution uses constant space apart from input storage.
1function largestOverlap(img1, img2) {
2 function overlapCount(xShift, yShift) {
3 let n = img1.length, count = 0;
4 for (let r = 0; r < n; ++r) {
5 for (let c = 0; c < n; ++c) {
6 if ((r + xShift >= 0 && r + xShift < n) && (c + yShift >= 0 && c + yShift < n)) {
7 count += img1[r][c] & img2[r + xShift][c + yShift];
8 }
9 }
10 }
11 return count;
12 }
13
14 let n = img1.length, maxOverlap = 0;
15 for (let xShift = -n + 1; xShift < n; ++xShift) {
16 for (let yShift = -n + 1; yShift < n; ++yShift) {
17 maxOverlap = Math.max(maxOverlap, overlapCount(xShift, yShift));
18 }
19 }
20 return maxOverlap;
21}
22
23const img1 = [[1,1,0],[0,1,0],[0,1,0]];
24const img2 = [[0,0,0],[0,1,1],[0,0,1]];
25console.log("Max Overlap:", largestOverlap(img1, img2));JavaScript's function implementation of largestOverlap and overlapCount follows a logical structure for determining substantial grid translations. The blend of max within loops ensures apt tracking of maximum overlaps before output.
This solution uses the concept of convolution by considering the images as arrays of points. We tallied the number of overlapping 1s for each relative translation using convolution properties without directly shifting arrays and used efficient matrix operations to compute overlaps.
Time Complexity: O(n^4), as it traverses through each overlap position and checks all cells.
Space Complexity: O(n), due to the allocation of cumulative arrays.
1
The JavaScript implementation converts potential translation tuples into strings, strengthening dictionary-based overlap counting to deliver effective results. Array methods deliver an intuitive fashion for overlap evaluation.