In this problem, there is a given set with some integer elements. And another some value is also provided, we have to find a subset of the given set whose sum is the same as the given sum value.
Here backtracking approach is used for trying to select a valid subset when an item is not valid, we will backtrack to get the previous subset and add another element to get the solution.
Input and Output
Input: This algorithm takes a set of numbers, and a sum value. The Set: {10, 7, 5, 18, 12, 20, 15} The sum Value: 35 Output: All possible subsets of the given set, where sum of each element for every subsets is same as the given sum value. {10, 7, 18} {10, 5, 20} {5, 18, 12} {20, 15}
Algorithm
subsetSum(set, subset, n, subSize, total, node, sum)
Input − The given set and subset, size of set and subset, a total of the subset, number of elements in the subset and the given sum.
Output − All possible subsets whose sum is the same as the given sum.
Begin if total = sum, then display the subset //go for finding next subset subsetSum(set, subset, , subSize-1, total-set[node], node+1, sum) return else for all element i in the set, do subset[subSize] := set[i] subSetSum(set, subset, n, subSize+1, total+set[i], i+1, sum) done End
Example
#include <iostream> using namespace std; void displaySubset(int subSet[], int size) { for(int i = 0; i < size; i++) { cout << subSet[i] << " "; } cout << endl; } void subsetSum(int set[], int subSet[], int n, int subSize, int total, int nodeCount ,int sum) { if( total == sum) { displaySubset(subSet, subSize); //print the subset subsetSum(set,subSet,n,subSize-1,total-set[nodeCount],nodeCount+1,sum); //for other subsets return; }else { for( int i = nodeCount; i < n; i++ ) { //find node along breadth subSet[subSize] = set[i]; subsetSum(set,subSet,n,subSize+1,total+set[i],i+1,sum); //do for next node in depth } } } void findSubset(int set[], int size, int sum) { int *subSet = new int[size]; //create subset array to pass parameter of subsetSum subsetSum(set, subSet, size, 0, 0, 0, sum); delete[] subSet; } int main() { int weights[] = {10, 7, 5, 18, 12, 20, 15}; int size = 7; findSubset(weights, size, 35); }
Output
10 7 18 10 5 20 5 18 12 20 15