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Split With Minimum Sum

Difficulty: Easy

Problem Description

Given a positive integer num, split it into two non-negative integers num1 and num2 such that the concatenation of num1 and num2 is a permutation of num. Return the minimum possible sum of num1 and num2.

Key Insights

  • The digits of the number should be distributed between num1 and num2 to minimize their sum.
  • To achieve the minimal sum, the smaller digits should be placed in the more significant positions of the two numbers.
  • By sorting the digits of the number and then alternately placing them into num1 and num2, we can ensure that the resulting numbers are as small as possible.

Space and Time Complexity

Time Complexity: O(d log d), where d is the number of digits in num (for sorting). Space Complexity: O(d), for storing the digits.

Solution

The solution involves the following steps:

  1. Convert the number into its constituent digits and sort them.
  2. Alternate placing the digits into two numbers (num1 and num2) to ensure that the smaller digits are in the more significant places.
  3. Convert num1 and num2 back to integers and return their sum.

The algorithm uses sorting to arrange the digits and basic arithmetic operations to compute the final result.

Code Solutions

def split_with_minimum_sum(num):
    # Convert the number to a list of its digits
    digits = sorted(str(num))
    
    num1, num2 = "", ""
    
    # Distribute the digits into num1 and num2
    for i in range(len(digits)):
        if i % 2 == 0:
            num1 += digits[i]
        else:
            num2 += digits[i]
    
    # Convert strings to integers and return their sum
    return int(num1) + int(num2)
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