added combinational sum

Author: bhagyashree-06

Backtracking/combinational_sum.py

@@ -0,0 +1,80 @@
+"""
+DESCRIPTION :
+Given an array of integers and a sum B, find all unique combinations in the array where the sum is equal to B. 
+The same number may be chosen from the array any number of times to make B.
+NOTE :
+        1. All numbers will be positive integers.
+        2. Elements in a combination (a1, a2, …, ak) must be in non-descending order. (ie, a1 ≤ a2 ≤ … ≤ ak).
+        3. The combinations themselves must be sorted in ascending order.
+        
+EXAMPLE :
+
+Input:
+N = 4
+arr[] = {7,2,6,5}
+B = 16
+Output:
+(2 2 2 2 2 2 2 2)
+(2 2 2 2 2 6)
+(2 2 2 5 5)
+(2 2 5 7)
+(2 2 6 6)
+(2 7 7)
+(5 5 6)
+Constraints:
+1 <= N <= 30
+1 <= A[i] <= 20
+1 <= B <= 100
+"""
+
+# SOLUTION IN PYTHON3
+
+
+import atexit
+import io
+import sys
+
+
+class Solution:
+    
+    
+    def combinationalSum(self,A, B):
+        partialpath=[]
+        allpath=[]
+        A = sorted(list(set(A)))
+        def find(start,target,partialpath,allpath,A):
+            
+            if(sum(partialpath)==target):
+                allpath.append(partialpath[:])
+                return
+            if(sum(partialpath)>target):
+                return
+            for i in range(start,len(A)):
+                partialpath.append(A[i])
+                find(i,target,partialpath,allpath,A)
+                partialpath.pop()
+        find(0,B,partialpath,allpath,A)
+        return allpath
+     
+
+if __name__ == '__main__':
+    test_cases = int(input())
+    for cases in range(test_cases):
+        n = int(input())
+        a = list(map(int,input().strip().split()))
+        s = int(input())
+        ob = Solution()
+        result = ob.combinationalSum(a,s)
+        if(not len(result)):
+            print("Empty")
+            continue
+        for i in range(len(result)):
+            print("(", end="")
+            size = len(result[i])
+            for j in range(size - 1):
+                print(result[i][j], end=" ")
+            if (size):
+                print(result[i][size - 1], end=")")
+            else:
+                print(")", end="")
+        print()