Java Program for Counting sets of 1s and 0s in a binary matrix Last Updated : 20 Apr, 2023 Comments Improve Suggest changes Like Article Like Report 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. Examples: 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. Java // Java program to compute number of sets // in a binary matrix. class GFG { static final int m = 3; // no of columns static final int n = 2; // no of rows // function to calculate the number of // non empty sets of cell static long countSets(int a[][]) { // stores the final answer long res = 0; // traverses row-wise for (int i = 0; i < n; i++) { int u = 0, v = 0; for (int j = 0; j < m; j++) { if (a[i][j] == 1) u++; else v++; } res += Math.pow(2, u) - 1 + Math.pow(2, v) - 1; } // traverses column wise for (int i = 0; i < m; i++) { int u = 0, v = 0; for (int j = 0; j < n; j++) { if (a[j][i] == 1) u++; else v++; } res += Math.pow(2, u) - 1 + Math.pow(2, v) - 1; } // at the end subtract n*m as no of // single sets have been added twice. return res - (n * m); } // Driver code public static void main(String[] args) { int a[][] = {{1, 0, 1}, {0, 1, 0}}; System.out.print(countSets(a)); } } // This code is contributed by Anant Agarwal. Output: 8 Time Complexity: O(n * m) Space Complexity: O(1) as no extra space has been taken. Please refer complete article on Counting sets of 1s and 0s in a binary matrix for more details! Comment More infoAdvertise with us Next Article Java Program for Find the number of islands | Set 1 (Using DFS) K kartik Follow Improve Article Tags : Java Practice Tags : Java Similar Reads Java Program to Count set bits in an integer Write an efficient program to count number of 1s in binary representation of an integer. Examples :Input : n = 6Output : 2Binary representation of 6 is 110 and has 2 set bitsInput : n = 13Output : 3Binary representation of 11 is 1101 and has 3 set bits1. Simple Method Loop through all bits in an int 2 min read Java Program to Count set bits in an integer Write an efficient program to count number of 1s in binary representation of an integer. Examples :Input : n = 6Output : 2Binary representation of 6 is 110 and has 2 set bitsInput : n = 13Output : 3Binary representation of 11 is 1101 and has 3 set bits1. Simple Method Loop through all bits in an int 2 min read Java Program for Find the number of islands | Set 1 (Using DFS) Given a boolean 2D matrix, find the number of islands. A group of connected 1s forms an island. For example, the below matrix contains 5 islandsExample: Input : mat[][] = {{1, 1, 0, 0, 0}, {0, 1, 0, 0, 1}, {1, 0, 0, 1, 1}, {0, 0, 0, 0, 0}, {1, 0, 1, 0, 1} Output : 5 This is a variation of the standa 4 min read Java BitSet | cardinality() BitSet is a class defined in the java.util package. It creates an array of bits represented by 0s and 1s. Syntax public int cardinality() Explanation: The method returns the number of 1s in this BitSet. Examples: Input : set1 : {1, 2, 4} set2 : {} Output : 3 0 Java // Java program illustrating Bitse 1 min read Java BitSet | cardinality() BitSet is a class defined in the java.util package. It creates an array of bits represented by 0s and 1s. Syntax public int cardinality() Explanation: The method returns the number of 1s in this BitSet. Examples: Input : set1 : {1, 2, 4} set2 : {} Output : 3 0 Java // Java program illustrating Bitse 1 min read Java Program to Count 1's in a sorted binary array Given a binary array sorted in non-increasing order, count the number of 1's in it. Examples: Input: arr[] = {1, 1, 0, 0, 0, 0, 0} Output: 2 Input: arr[] = {1, 1, 1, 1, 1, 1, 1} Output: 7 Input: arr[] = {0, 0, 0, 0, 0, 0, 0} Output: 0 A simple solution is to linearly traverse the array. The time c 3 min read Like