Added BacktrackingAlgorithmForSubsetSum.c

Algorithm/BacktrackingAlgorithmforSubsetSum.c

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+// Rajshree Mondal github: rajshree2000
+/* Subset sum problem is to find subset of elements that are selected from a given set whose sum adds up to a given number K. We are considering the set contains non-negative values. It is assumed that the input set is unique (no duplicates are presented).
+Using exhaustive search we consider all subsets irrespective of whether they satisfy given constraints or not. Backtracking can be used to make a systematic consideration of the elements to be selected.
+*/
+
+#include <stdio.h> 
+#include <stdlib.h> 
+
+#define ARRAYSIZE(a) (sizeof(a))/(sizeof(a[0])) 
+
+static int total_nodes; 
+// prints subset found 
+void printSubset(int A[], int size) 
+{ 
+	for(int i = 0; i < size; i++) 
+	{ 
+		printf("%*d", 5, A[i]); 
+	} 
+
+	printf("n"); 
+} 
+
+// inputs 
+// s		 - set vector 
+// t		 - tuplet vector 
+// s_size	 - set size 
+// t_size	 - tuplet size so far 
+// sum		 - sum so far 
+// ite		 - nodes count 
+// target_sum - sum to be found 
+void subset_sum(int s[], int t[], 
+				int s_size, int t_size, 
+				int sum, int ite, 
+				int const target_sum) 
+{ 
+	total_nodes++; 
+	if( target_sum == sum ) 
+	{ 
+		// We found subset 
+		printSubset(t, t_size); 
+		// Exclude previously added item and consider next candidate 
+		subset_sum(s, t, s_size, t_size-1, sum - s[ite], ite + 1, target_sum); 
+		return; 
+	} 
+	else
+	{ 
+		// generate nodes along the breadth 
+		for( int i = ite; i < s_size; i++ ) 
+		{ 
+			t[t_size] = s[i]; 
+			// consider next level node (along depth) 
+			subset_sum(s, t, s_size, t_size + 1, sum + s[i], i + 1, target_sum); 
+		} 
+	} 
+} 
+
+// Wrapper to print subsets that sum to target_sum 
+// input is weights vector and target_sum 
+void generateSubsets(int s[], int size, int target_sum) 
+{ 
+	int *tuplet_vector = (int *)malloc(size * sizeof(int)); 
+
+	subset_sum(s, tuplet_vector, size, 0, 0, 0, target_sum); 
+
+	free(tuplet_vector); 
+} 
+
+int main() 
+{ 
+	int weights[] = {10, 7, 5, 18, 12, 20, 15}; 
+	int size = ARRAYSIZE(weights); 
+
+	generateSubsets(weights, size, 35); 
+	printf("Nodes generated %dn", total_nodes); 
+	return 0; 
+}