Sum of all possible expressions of a numeric string possible by inserting addition operators

Last Updated : 04 Jan, 2021

Given a numeric string str of length N, the task is to find the sum of all possible expressions by inserting the ‘+’ operator between the characters of the string any number of times.

Examples:

Input: str = “125”
Output: 176
Explanation:
Inserting “+” after 1st index modifies str to “1+25” and value = 26
Inserting “+” after 2nd index modifies str to “12+5” and value = 17
Inserting “+” after both 1st and 2nd index modifies str to “1+2+5” and value = 8
Therefore, the total sum of all possible expression is 125 + 26 + 17 + 8 = 176

Input: str = “9999999999”
Output: 12656242944

Approach: The idea is to insert the ‘+’ operator at all possible index of the string in all possible ways and calculate the sum. Finally, print the total sum obtained. Follow the steps below to solve the problem:

Initialize a variable say, sumOfExp to store the sum of all possible expression by inserting the ‘+’ operator at all possible indices of the string.
Generate all possible subset of indices of the string iteratively. For every subset of indices inserts the ‘+’ operator at elements of the subset and increment sumOfExp by the sum of the current expression.
Finally, print the value of sumOfExp.

Below is the implementation of the above approach:

Python3

# Python program to implement 
# the above approach 
  
# Function to find sum of all expressions by 
# inserting '+' operator at all possible indices 
def findSumOfExpressions(S, N): 
  
    # Stores sum of all expressions by inserting 
    # '+' operator at all possible indices 
    sumOfExp = 0
  
    # Generate all possible subset 
    # of indices iteratively 
    for i in range(2 ** (N - 1)): 
  
        # Stores sum of  
        # current expressions 
        ans_sub = 0
  
        # Stores numbers of 
        # current expressions 
        subst = S[0] 
  
        # Traverse the string at insert + at 
        # current subset of indices 
        for j in range(N - 1): 
  
            # If current index exists 
            # in the current subset 
            if (i >> j) & 1: 
  
                # Update ans_sub 
                ans_sub += int(subst) 
  
                # Update subst 
                subst = S[j + 1] 
            else: 
  
                # Update subst 
                subst += S[j + 1] 
  
            # + can't be inserted after 
            # the last index     
            if j == N - 2: 
                ans_sub += int(subst) 
  
        # Update ans 
        sumOfExp += ans_sub 
  
    # Base case      
    if N == 1: 
        print(int(S)) 
    else: 
  
        # Print answer 
        print(sumOfExp) 
  
# Driver Code 
if __name__ == '__main__': 
      
    # Given string 
    S = "9999999999"
      
    # Length of the string 
    N = len(S) 
  
    # Function call 
    findSumOfExpressions(S, N) 

Output:

12656242944

Time Complexity: O(2^N * N)
Auxiliary Space: O(1)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes

Related Articles

Python3