Given a n × m binary matrix, count the number of sets where a set can be formed one or more same values in a row or column.
Input: 1 0 1 0 1 0 Output: 8 Explanation: There are six one-element sets (three 1s and three 0s). There are two two- element sets, the first one consists of the first and the third cells of the first row. The second one consists of the first and the third cells of the second row. Input: 1 0 1 1 Output: 6
The number of non-empty subsets of x elements is 2x – 1. We traverse every row and calculate numbers of 1’s and 0’s cells. For every u zeros and v ones, total sets is 2u – 1 + 2v – 1. We then traverse all columns and compute same values and compute overall sum. We finally subtract m x n from the overall sum as single elements are considered twice.
Time Complexity: O(n * m)
This article is contributed by Raj. 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.
- Program to check if a matrix is Binary matrix or not
- Nearest 1 in a binary matrix
- Count all 0s which are blocked by 1s in binary matrix
- Unique cells in a binary matrix
- Maximize the binary matrix by filpping submatrix once
- Distance of nearest cell having 1 in a binary matrix
- Total coverage of all zeros in a binary matrix
- Find if there is a rectangle in binary matrix with corners as 1
- Construct Ancestor Matrix from a Given Binary Tree
- Find duplicate rows in a binary matrix
- Maximum decimal value path in a binary matrix
- Maximum size rectangle binary sub-matrix with all 1s
- Minimum operations required to set all elements of binary matrix
- Find size of the largest '+' formed by all ones in a binary matrix
- Find if a binary matrix exists with given row and column sums
Improved By : vt_m