find_sum_problem_1.py

# Python3 program to find the smallest
# positive value that cannot be
# represented as sum of subsets
# of a given sorted array

# Returns the smallest number
# that cannot be represented as sum
# of subset of elements from set
# represented by sorted array arr[0..n-1]
def findSmallest(arr, n):
    res = 1  # Initialize result

    # Traverse the array and increment
    # 'res' if arr[i] is smaller than
    # or equal to 'res'.
    for i in range(0, n):
        if arr[i] <= res:
            res = res + arr[i]
            # print(res)
        else:
            break
    return res


# Driver program to test above function
arr1 = [1, 3, 4, 5]
n1 = len(arr1)
print(findSmallest(arr1, n1))

arr2 = [1, 2, 6, 10, 11, 15]
n2 = len(arr2)
print(findSmallest(arr2, n2))

arr3 = [1, 1, 1, 1]
n3 = len(arr3)
print(findSmallest(arr3, n3))

arr4 = [1, 1, 3, 4]
n4 = len(arr4)
print(findSmallest(arr4, n4))