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You are given a four-digit number num. You need to split the digits of num into two new numbers and calculate the minimum possible sum of these two new numbers.

For example, if num is 2932, you can split it into 29 and 32 to get the sum 61, or into 23 and 92 to get the sum 115. Your task is to find the combination that results in the minimum possible sum.

Clarifying Questions

  1. Input Constraints:
    • Is num always a four-digit number?
    • Do num’s digits always consist of integers from 0-9?
  2. Output:
    • What should be returned if there are multiple combinations yielding the same minimum sum?

Strategy

  1. Extract Digits:
    • Split the given number num into individual digits.
  2. Sort Digits:
    • Sort these digits to simplify the process of generating the smallest possible numbers.
  3. Form New Numbers:
    • By combining the sorted digits strategically, form the two new numbers such that their sum is minimized.

Code

Here’s the proposed Python implementation:

def minimumSum(num: int) -> int:
    # Step 1: Convert the number into a list of its digits
    digits = list(map(int, str(num)))
    
    # Step 2: Sort the digits
    digits.sort()
    
    # Step 3: Combine the digits to form the minimized sum
    # Smallest number will be one consisting of the smallest and the second smallest digits
    num1 = digits[0] * 10 + digits[2]
    # Second smallest number will be one consisting of the remaining two digits
    num2 = digits[1] * 10 + digits[3]
    
    # Return the sum of these two numbers
    return num1 + num2

# Example usage
print(minimumSum(2932))  # Output: 52

Explanation

  1. Extract Digits:
    • Converting the integer num into a string and mapping each character back to an integer will give us the list of digits.
  2. Sort Digits:
    • Sort the list of digits in ascending order. This helps us to easily form the smallest possible numbers.
  3. Form Two Numbers:
    • The two smallest numbers are formed by combining the smallest digits in such a way that the sum is minimized.
    • After sorting, digits[0] and digits[2] will form one number, and digits[1] and digits[3] will form the other number, ensuring the minimum sum when these numbers are added.

Time Complexity

This algorithm ensures efficient calculation while maintaining simplicity in handling a fixed small number of digits.

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