Check whether row or column swaps produce maximum size binary sub-matrix with all 1s
Given a binary matrix, the task is to find whether row swaps or column swaps give maximum size sub-matrix with all 1’s. In a row swap, we are allowed to swap any two rows. In a column swap we are allowed to swap any two columns. Output “Row Swap” or “Column Swap” and the maximum size.
Input : 1 1 1 1 0 1 Output : Column Swap 4 By swapping column 1 and column 2(0-based indexing), index (0, 0) to (1, 1) makes the largest binary sub-matrix. Input : 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 Output : Row Swap 6 Input : 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 Output : Row Swap 8
The idea is to find both row swap and column swap maximum size binary submatrix and compare.
To find the maximum sized binary sub-matrix with row swaps allowed, make a 2-D array, say dp[i][j]. Each value of dp[i][j] contains the number of consecutive 1s on right side of (i,j) in i-th row. Now, store each column in the 1-D temporary array one by one, say b and sort, and find maximum b[i] * (n – i), since b[i] is indicating the sub-matrix width and (n – i) is sub-matrix height.
Similarly, to find the maximum size binary sub-matrix with column swap allowed, find dp[i][j], where each value contains the number of consecutive 1 below the (i, j) in j-th column. Similarly, store each row in the 1-D temporary array one by one, say b and sort. Find maximum b[i] * (m – i), since b[i] is indicating the submatrix height and (n – i) is submatrix width.
Below is the implementation of this approach:
Row Swap 6
This article is contributed by Anuj Chauhan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.