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Calculate Digit Sum of a String

Difficulty: Easy

Problem Description

You are given a string s consisting of digits and an integer k. A round can be completed if the length of s is greater than k. In one round, you divide s into consecutive groups of size k, replace each group with the sum of its digits, and merge the results to form a new string. Repeat this until the length of s is less than or equal to k. Return s after all rounds have been completed.

Key Insights

  • The string is processed in rounds, where each round involves grouping and summing the digits.
  • The last group may be smaller than k if the length of s is not a multiple of k.
  • The sum of digits in each group can lead to a significant reduction in string length.
  • The process continues until the resulting string length is less than or equal to k.

Space and Time Complexity

Time Complexity: O(n), where n is the length of the string. Each digit is processed a limited number of times. Space Complexity: O(n), as the output string may require storage proportional to the input size.

Solution

The solution involves using a loop to repeatedly process the string until its length is less than or equal to k. In each iteration, we divide the string into groups of size k, compute the digit sums for each group, and then merge these sums into a new string. This continues until the stopping condition is met.

Code Solutions

def digitSum(s: str, k: int) -> str:
    while len(s) > k:
        # Create a new string to store the results
        new_s = []
        
        # Process the string in chunks of size k
        for i in range(0, len(s), k):
            # Get the current group
            group = s[i:i+k]
            # Calculate the sum of digits in the group
            digit_sum = sum(int(char) for char in group)
            # Append the result to the new string
            new_s.append(str(digit_sum))
        
        # Join the results to form the new string
        s = ''.join(new_s)
    
    return s
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