Sum of Digits in Base K

Problem Description

Given an integer n (in base 10) and a base k, return the sum of the digits of n after converting n from base 10 to base k. After converting, each digit should be interpreted as a base 10 number, and the sum should be returned in base 10.

Key Insights

• Convert the integer n from base 10 to base k.
• Extract each digit from the converted number.
• Sum all the digits and return the result.

Space and Time Complexity

Time Complexity: O(log_k(n)), where log_k(n) is the number of digits in the base k representation of n. Space Complexity: O(1), as we only use a fixed amount of space for variables.

Solution

To solve the problem, we need to convert the given integer n from base 10 to base k. This is done by repeatedly dividing n by k and keeping track of the remainders, which represent the digits in the base k system. We then sum these digits together to get the final result.

1. Initialize a variable to store the sum of digits.
2. While n is greater than 0:
   • Find the remainder when n is divided by k (this gives the current digit).
   • Add this digit to the sum.
   • Update n by performing integer division by k.
3. Return the sum.

Code Solutions