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Split With Minimum Sum

Easy

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Greedy AlgorithmsStringsArrays

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.
- In other words, the sum of the number of occurrences of each digit in num1 and num2 is equal to the number of occurrences of that digit in num.
num1 and num2 can contain leading zeros.

Return the minimum possible sum of num1 and num2.

Notes:

It is guaranteed that num does not contain any leading zeros.
The order of occurrence of the digits in num1 and num2 may differ from the order of occurrence of num.

Example 1:

Input: num = 4325
Output: 59
Explanation: We can split 4325 so that num1 is 24 and num2 is 35, giving a sum of 59. We can prove that 59 is indeed the minimal possible sum.

Example 2:

Input: num = 687
Output: 75
Explanation: We can split 687 so that num1 is 68 and num2 is 7, which would give an optimal sum of 75.

Constraints:

10 <= num <= 10⁹

Try coding it in LeetCode

Split With Minimum Sum

Easy

Asked by:

43 views

Topics:

Greedy AlgorithmsStringsArrays

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.
- In other words, the sum of the number of occurrences of each digit in num1 and num2 is equal to the number of occurrences of that digit in num.
num1 and num2 can contain leading zeros.

Return the minimum possible sum of num1 and num2.

Notes:

It is guaranteed that num does not contain any leading zeros.
The order of occurrence of the digits in num1 and num2 may differ from the order of occurrence of num.

Example 1:

Input: num = 4325
Output: 59
Explanation: We can split 4325 so that num1 is 24 and num2 is 35, giving a sum of 59. We can prove that 59 is indeed the minimal possible sum.

Example 2:

Input: num = 687
Output: 75
Explanation: We can split 687 so that num1 is 68 and num2 is 7, which would give an optimal sum of 75.

Constraints:

10 <= num <= 10⁹

Try coding it in LeetCode

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

Can the input number be negative, zero, or a positive integer?
What is the maximum possible value of the input number?
If there are multiple possible splits that result in the same minimum sum of the two parts, is any valid split acceptable?
Should the output be returned as a string or an integer?
Is the input guaranteed to be a positive number, or should I handle invalid inputs (like non-numeric input)?

Brute Force Solution

Approach

The goal is to divide a number into two parts to minimize the sum of the two parts. A brute force approach explores every possible way to make this split. We evaluate each split and keep track of the smallest sum we have encountered.

Here's how the algorithm would work step-by-step:

Consider every possible place to split the digits of the number into two separate numbers.
For each split, calculate the two resulting numbers.
Add the two numbers together to get their sum.
Compare the sum with the smallest sum found so far.
If the new sum is smaller than the smallest sum so far, remember the new sum as the smallest.
Continue this process until all possible splits have been tried.
The smallest sum remembered at the end is the answer.

Code Implementation

def split_with_minimum_sum_brute_force(number):
    number_string = str(number)
    number_length = len(number_string)
    minimum_sum = float('inf')

    # Iterate through all possible split positions
    for split_position in range(1, number_length):

        # Split the number string into two parts
        first_number_string = number_string[:split_position]
        second_number_string = number_string[split_position:]

        # Convert the two parts into integers
        first_number = int(first_number_string)
        second_number = int(second_number_string)

        current_sum = first_number + second_number

        # Update the minimum_sum if necessary
        if current_sum < minimum_sum:
            minimum_sum = current_sum

    return minimum_sum

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the digits of the number represented as a string, considering each possible split point. For a number with n digits, there are n-1 possible split positions. For each split position, we perform a constant number of operations to create the two numbers and calculate their sum. Therefore, the time complexity is proportional to the number of possible splits, which is n-1. This simplifies to O(n).

Space Complexity

O(1) – The provided brute force algorithm considers different splits of a number's digits. It calculates two numbers for each split and their sum, updating a variable to store the minimum sum found so far. The algorithm uses only a few variables to store intermediate sums and the minimum sum, which takes up constant space regardless of the size of the input number (N). Therefore, the auxiliary space complexity is O(1).

Optimal Solution

Approach

To minimize the sum of two numbers formed by splitting a number's digits, we need to distribute the larger digits as evenly as possible between the two numbers. This is achieved by sorting the digits and assigning them alternately to the two numbers.

Here's how the algorithm would work step-by-step:

First, take the number and break it down into its individual digits.
Then, arrange these digits from smallest to largest.
Next, build two new numbers. Starting with the smallest digit, add the first digit to the first new number, the second digit to the second new number, the third digit to the first new number, and so on, alternating between the two.
Finally, add the two new numbers together. This sum will be the smallest possible sum you can get by splitting the digits.

Code Implementation

def split_with_minimum_sum(number):
    number_string = str(number)
    digits = sorted([int(digit) for digit in number_string])

    first_new_number = ""
    second_new_number = ""

    # Assign digits to the two numbers alternately to minimize the sum.
    for index, digit in enumerate(digits):
        if index % 2 == 0:
            first_new_number += str(digit)
        else:
            second_new_number += str(digit)

    # Handle empty strings by assigning 0; conversion to int needed for addition.
    if not first_new_number:
        first_number_int = 0
    else:
        first_number_int = int(first_new_number)

    if not second_new_number:
        second_number_int = 0
    else:
        second_number_int = int(second_new_number)

    # Summing integers to produce the minimal possible result
    minimum_sum = first_number_int + second_number_int

    return minimum_sum

Big(O) Analysis

Time Complexity

O(n log n) – The algorithm's time complexity is primarily driven by sorting the digits of the input number. We assume the number has 'n' digits. Converting the number to a list of digits takes O(n) time. Sorting these 'n' digits using an efficient sorting algorithm such as merge sort or quicksort takes O(n log n) time. Building the two new numbers and adding them together involves iterating through the sorted digits, which takes O(n) time. Therefore, the dominant operation is sorting, resulting in a time complexity of O(n log n).

Space Complexity

O(N) – The algorithm's space complexity is primarily determined by the sorted list of digits. If the input number has N digits, then storing these digits in a sorted list requires O(N) auxiliary space. The two new numbers themselves only require constant space. Therefore, the dominant factor is the space needed for sorting the digits, resulting in O(N) space complexity.

Edge Cases

Case	How to Handle
Null or empty input string	Return 0 or throw an IllegalArgumentException, depending on requirements, since no split is possible.
Input string contains non-numeric characters	Throw an IllegalArgumentException, since the problem specifies numeric digits.
Input string consists of only '0's	Handle leading zeros properly during conversion and subsequent addition to avoid incorrect sum calculation or overflow.
Input string is a single digit	Treat the input string as two numbers, the first being 0 and the second the single digit, returning the digit itself.
Input string representing a very large number that could lead to integer overflow after splitting and converting	Use long data type to handle large numbers and check for potential overflow before the addition.
The input string is a palindrome	The algorithm should still correctly find the optimal split and minimum sum regardless of the string being a palindrome.
Input string has leading zeros	Handle leading zeros during the conversion of substrings to integers to avoid misinterpretation of the numerical value.
Multiple possible splits result in the same minimum sum	The algorithm should return any one of those splits, as the problem doesn't ask for all splits or a specific one.

Null or empty input string

How to Handle:

Return 0 or throw an IllegalArgumentException, depending on requirements, since no split is possible.

Input string contains non-numeric characters

How to Handle:

Throw an IllegalArgumentException, since the problem specifies numeric digits.

Input string consists of only '0's

How to Handle:

Handle leading zeros properly during conversion and subsequent addition to avoid incorrect sum calculation or overflow.

Input string is a single digit

How to Handle:

Treat the input string as two numbers, the first being 0 and the second the single digit, returning the digit itself.

Input string representing a very large number that could lead to integer overflow after splitting and converting

How to Handle:

Use long data type to handle large numbers and check for potential overflow before the addition.

The input string is a palindrome

How to Handle:

The algorithm should still correctly find the optimal split and minimum sum regardless of the string being a palindrome.

Input string has leading zeros

How to Handle:

Handle leading zeros during the conversion of substrings to integers to avoid misinterpretation of the numerical value.

Multiple possible splits result in the same minimum sum

How to Handle:

The algorithm should return any one of those splits, as the problem doesn't ask for all splits or a specific one.

Solution

Clarifying Questions

When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:

Can the input number be negative, zero, or a positive integer?
What is the maximum possible value of the input number?
If there are multiple possible splits that result in the same minimum sum of the two parts, is any valid split acceptable?
Should the output be returned as a string or an integer?
Is the input guaranteed to be a positive number, or should I handle invalid inputs (like non-numeric input)?

Brute Force Solution

Approach

Here's how the algorithm would work step-by-step:

Consider every possible place to split the digits of the number into two separate numbers.
For each split, calculate the two resulting numbers.
Add the two numbers together to get their sum.
Compare the sum with the smallest sum found so far.
If the new sum is smaller than the smallest sum so far, remember the new sum as the smallest.
Continue this process until all possible splits have been tried.
The smallest sum remembered at the end is the answer.

Code Implementation

def split_with_minimum_sum_brute_force(number):
    number_string = str(number)
    number_length = len(number_string)
    minimum_sum = float('inf')

    # Iterate through all possible split positions
    for split_position in range(1, number_length):

        # Split the number string into two parts
        first_number_string = number_string[:split_position]
        second_number_string = number_string[split_position:]

        # Convert the two parts into integers
        first_number = int(first_number_string)
        second_number = int(second_number_string)

        current_sum = first_number + second_number

        # Update the minimum_sum if necessary
        if current_sum < minimum_sum:
            minimum_sum = current_sum

    return minimum_sum

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

Here's how the algorithm would work step-by-step:

First, take the number and break it down into its individual digits.
Then, arrange these digits from smallest to largest.
Next, build two new numbers. Starting with the smallest digit, add the first digit to the first new number, the second digit to the second new number, the third digit to the first new number, and so on, alternating between the two.
Finally, add the two new numbers together. This sum will be the smallest possible sum you can get by splitting the digits.

Code Implementation

def split_with_minimum_sum(number):
    number_string = str(number)
    digits = sorted([int(digit) for digit in number_string])

    first_new_number = ""
    second_new_number = ""

    # Assign digits to the two numbers alternately to minimize the sum.
    for index, digit in enumerate(digits):
        if index % 2 == 0:
            first_new_number += str(digit)
        else:
            second_new_number += str(digit)

    # Handle empty strings by assigning 0; conversion to int needed for addition.
    if not first_new_number:
        first_number_int = 0
    else:
        first_number_int = int(first_new_number)

    if not second_new_number:
        second_number_int = 0
    else:
        second_number_int = int(second_new_number)

    # Summing integers to produce the minimal possible result
    minimum_sum = first_number_int + second_number_int

    return minimum_sum

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Null or empty input string	Return 0 or throw an IllegalArgumentException, depending on requirements, since no split is possible.
Input string contains non-numeric characters	Throw an IllegalArgumentException, since the problem specifies numeric digits.
Input string consists of only '0's	Handle leading zeros properly during conversion and subsequent addition to avoid incorrect sum calculation or overflow.
Input string is a single digit	Treat the input string as two numbers, the first being 0 and the second the single digit, returning the digit itself.
Input string representing a very large number that could lead to integer overflow after splitting and converting	Use long data type to handle large numbers and check for potential overflow before the addition.
The input string is a palindrome	The algorithm should still correctly find the optimal split and minimum sum regardless of the string being a palindrome.
Input string has leading zeros	Handle leading zeros during the conversion of substrings to integers to avoid misinterpretation of the numerical value.
Multiple possible splits result in the same minimum sum	The algorithm should return any one of those splits, as the problem doesn't ask for all splits or a specific one.

Null or empty input string

How to Handle:

Return 0 or throw an IllegalArgumentException, depending on requirements, since no split is possible.

Input string contains non-numeric characters

How to Handle:

Throw an IllegalArgumentException, since the problem specifies numeric digits.

Input string consists of only '0's

How to Handle:

Handle leading zeros properly during conversion and subsequent addition to avoid incorrect sum calculation or overflow.

Input string is a single digit

How to Handle:

Treat the input string as two numbers, the first being 0 and the second the single digit, returning the digit itself.

Input string representing a very large number that could lead to integer overflow after splitting and converting

How to Handle:

Use long data type to handle large numbers and check for potential overflow before the addition.

The input string is a palindrome

How to Handle:

The algorithm should still correctly find the optimal split and minimum sum regardless of the string being a palindrome.

Input string has leading zeros

How to Handle:

Handle leading zeros during the conversion of substrings to integers to avoid misinterpretation of the numerical value.

Multiple possible splits result in the same minimum sum

How to Handle:

The algorithm should return any one of those splits, as the problem doesn't ask for all splits or a specific one.