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Given an integer n (in decimal base) and an integer k (the base to convert n to), return the sum of the digits of n after converting n from decimal to base k.

Example:

  1. Input: n = 34, k = 6 Output: 9

    Explanation: 34 in base 6 is 54, which sums to 5 + 4 = 9.

  2. Input: n = 10, k = 10 Output: 1

    Explanation: 10 in base 10 is 10, which sums to 1 + 0 = 1.

Constraints:

Clarifying Questions

  1. Should the output be a single integer representing the sum of the digits?
  2. Are there any special cases we should account for, such as n being a power of k?

Strategy

To solve the problem, we need to perform the following steps:

  1. Convert n from decimal to the given base k.
  2. Extract each digit of the converted number.
  3. Sum the extracted digits.
  4. Return the sum.

Steps to Convert from Decimal to Base k:

  1. Continuously divide the number n by k and record the remainders.
  2. The remainders will represent the digits of the number in base k from least significant to most significant.
  3. Finally, sum these remainders (digits) to get the required result.

Time Complexity:

The time complexity for converting a number to a different base is O(log_k n) due to repeated division. Summing the digits will also take O(log_k n). Therefore, the overall time complexity is O(log_k n).

Code

def sum_base_k(n, k):
    # Initialize sum of digits to 0
    sum_digits = 0
    
    # Convert to base k and sum the digits
    while n > 0:
        remainder = n % k
        sum_digits += remainder
        n //= k
    
    return sum_digits

# Test the function with the given examples
print(sum_base_k(34, 6))  # Should print 9
print(sum_base_k(10, 10)) # Should print 1

This code defines a function sum_base_k that converts n from decimal to base k and then sums its digits. It uses a loop to repeatedly divide the number by k, collecting remainders, summing them, and then reducing the number until it is zero.

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