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Minimum Sum of Four Digit Number After Splitting Digits

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Topics:

ArraysGreedy Algorithms

You are given a positive integer num consisting of exactly four digits. Split num into two new integers new1 and new2 by using the digits found in num. Leading zeros are allowed in new1 and new2, and all the digits found in num must be used.

For example, given num = 2932, you have the following digits: two 2's, one 9 and one 3. Some of the possible pairs [new1, new2] are [22, 93], [23, 92], [223, 9] and [2, 329].

Return the minimum possible sum of new1 and new2.

Example 1:

Input: num = 2932
Output: 52
Explanation: Some possible pairs [new1, new2] are [29, 23], [223, 9], etc.
The minimum sum can be obtained by the pair [29, 23]: 29 + 23 = 52.

Example 2:

Input: num = 4009
Output: 13
Explanation: Some possible pairs [new1, new2] are [0, 49], [490, 0], etc. 
The minimum sum can be obtained by the pair [4, 9]: 4 + 9 = 13.

Constraints:

1000 <= num <= 9999

Try coding it in LeetCode

Minimum Sum of Four Digit Number After Splitting Digits

Easy

Asked by:

19 views

Topics:

ArraysGreedy Algorithms

For example, given num = 2932, you have the following digits: two 2's, one 9 and one 3. Some of the possible pairs [new1, new2] are [22, 93], [23, 92], [223, 9] and [2, 329].

Return the minimum possible sum of new1 and new2.

Example 1:

Input: num = 2932
Output: 52
Explanation: Some possible pairs [new1, new2] are [29, 23], [223, 9], etc.
The minimum sum can be obtained by the pair [29, 23]: 29 + 23 = 52.

Example 2:

Input: num = 4009
Output: 13
Explanation: Some possible pairs [new1, new2] are [0, 49], [490, 0], etc. 
The minimum sum can be obtained by the pair [4, 9]: 4 + 9 = 13.

Constraints:

1000 <= num <= 9999

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:

Is the input `num` always a four-digit positive integer, or can it have leading zeros and/or be zero itself?
Are we guaranteed that `num` will always be a valid number, or do I need to handle cases where it's not?
Is there a specific format or data type expected for the return value beyond just being an integer?
If there are multiple ways to split the digits that result in the same minimum sum, is any one of them acceptable?
Can I assume the digits of the input integer are distinct, or could they be duplicates?

Brute Force Solution

Approach

We need to find the smallest sum we can make by splitting a four-digit number into two two-digit numbers. The brute force method involves trying every possible way to split the digits and then calculating the resulting sum to find the smallest one.

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

Consider all possible ways to separate the four digits into two pairs. This means trying every combination of how the digits can be grouped.
For each combination, form two two-digit numbers from the pairs of digits.
Calculate the sum of the two two-digit numbers you created.
Compare the sum with the smallest sum you've seen so far. Initially, the smallest sum can be a very large number.
If the new sum is smaller than the current smallest sum, replace the smallest sum with the new sum.
After checking all possible combinations, the smallest sum remaining will be the answer.

Code Implementation

def find_minimum_sum_of_split_digits(number):
    number_string = str(number)

    minimum_sum = float('inf')

    # Iterate through all possible combinations of splitting digits
    import itertools
    for permutation in itertools.permutations(number_string):
        first_number = int(permutation[0] + permutation[1])
        second_number = int(permutation[2] + permutation[3])

        current_sum = first_number + second_number
        
        # Update minimum sum if needed
        if current_sum < minimum_sum:
            minimum_sum = current_sum

    return minimum_sum

Big(O) Analysis

Time Complexity

O(1) – The input is a four-digit number, meaning there are a fixed number of digits (n=4). We are considering all possible ways to split the digits into two pairs, effectively generating a fixed number of combinations. Since the number of operations does not scale with an input of arbitrary size, the time complexity is constant, O(1).

Space Complexity

O(1) – The provided algorithm calculates the minimum sum by iterating through different combinations of splitting the four-digit number. It involves forming two two-digit numbers and comparing their sum to the current minimum. Since the algorithm only stores a few variables such as the smallest sum seen so far and temporary variables for calculations, and the number of digits is fixed at four, the space used is constant regardless of the input number. Therefore, the space complexity is O(1).

Optimal Solution

Approach

The key to minimizing the sum is recognizing that the smallest digits should be in the tens place. We want to combine the smallest numbers as tens to reduce their overall impact on the final sum.

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

First, organize the digits from smallest to largest.
Then, create two new numbers. The first number will be made from the two smallest digits.
The second number will be made from the two largest digits.
Finally, add the two new numbers together to get the minimum possible sum.

Code Implementation

def minimum_sum_of_two_numbers(number):
    number_string = str(number)
    digits = sorted(number_string)

    #Combine smallest with the largest digits
    first_new_number = int(digits[0] + digits[2])

    #Combine second smallest with the second largest digits
    second_new_number = int(digits[1] + digits[3])

    return first_new_number + second_new_number

Big(O) Analysis

Time Complexity

O(1) – The input is a four-digit number, meaning we always have exactly four digits to process. Sorting these four digits takes constant time, which can be represented as O(4) but simplifies to O(1). All subsequent operations, such as forming two new numbers and adding them, are also constant time operations. Therefore, the overall time complexity is O(1).

Space Complexity

O(1) – The provided solution sorts the digits, which can be done in-place using an algorithm like insertion sort on the string representation of the number (since there are only four digits). The creation of the two new numbers requires storing only a constant number of integer variables. Therefore, the auxiliary space used does not depend on the input size (N=4 digits) and remains constant. This results in an O(1) space complexity.

Edge Cases

Case	How to Handle
Input is zero (0)	Treat zero as a valid input, splitting into 0 + 0 = 0, and return 0.
All digits are the same (e.g., 1111)	The algorithm should correctly form numbers like 11 and 11, summing to 22.
Input contains leading zeros implicitly (e.g., 0123 is represented as 123)	The solution should still work correctly after considering the implicit leading zeros from the number representation during digit extraction.
Maximum four-digit number (9999)	Handle the edge case of 9999 correctly, which produces 99 + 99 = 198.
Digits are already sorted in ascending order (e.g., 1234)	The sorting step should not be impacted, and the algorithm produces 13 + 24 = 37.
Digits are sorted in descending order (e.g., 4321)	Sorting will reverse the order, after which the algorithm should correctly produce 13 + 24 = 37.
Input is a negative number	The problem statement specifies a four digit integer, so explicitly check if the number is negative, and if so, either return an error, throw an exception, or take the absolute value, depending on the clarified requirements.
Algorithm specific: Integer overflow during addition of new1 and new2	Given constraints, integer overflow is not a concern as the maximum possible sum is 99+99 = 198, which will not cause an integer overflow.

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:

Is the input `num` always a four-digit positive integer, or can it have leading zeros and/or be zero itself?
Are we guaranteed that `num` will always be a valid number, or do I need to handle cases where it's not?
Is there a specific format or data type expected for the return value beyond just being an integer?
If there are multiple ways to split the digits that result in the same minimum sum, is any one of them acceptable?
Can I assume the digits of the input integer are distinct, or could they be duplicates?

Brute Force Solution

Approach

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

Consider all possible ways to separate the four digits into two pairs. This means trying every combination of how the digits can be grouped.
For each combination, form two two-digit numbers from the pairs of digits.
Calculate the sum of the two two-digit numbers you created.
Compare the sum with the smallest sum you've seen so far. Initially, the smallest sum can be a very large number.
If the new sum is smaller than the current smallest sum, replace the smallest sum with the new sum.
After checking all possible combinations, the smallest sum remaining will be the answer.

Code Implementation

def find_minimum_sum_of_split_digits(number):
    number_string = str(number)

    minimum_sum = float('inf')

    # Iterate through all possible combinations of splitting digits
    import itertools
    for permutation in itertools.permutations(number_string):
        first_number = int(permutation[0] + permutation[1])
        second_number = int(permutation[2] + permutation[3])

        current_sum = first_number + second_number
        
        # Update minimum sum if needed
        if current_sum < minimum_sum:
            minimum_sum = current_sum

    return minimum_sum

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

The key to minimizing the sum is recognizing that the smallest digits should be in the tens place. We want to combine the smallest numbers as tens to reduce their overall impact on the final sum.

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

First, organize the digits from smallest to largest.
Then, create two new numbers. The first number will be made from the two smallest digits.
The second number will be made from the two largest digits.
Finally, add the two new numbers together to get the minimum possible sum.

Code Implementation

def minimum_sum_of_two_numbers(number):
    number_string = str(number)
    digits = sorted(number_string)

    #Combine smallest with the largest digits
    first_new_number = int(digits[0] + digits[2])

    #Combine second smallest with the second largest digits
    second_new_number = int(digits[1] + digits[3])

    return first_new_number + second_new_number

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Input is zero (0)	Treat zero as a valid input, splitting into 0 + 0 = 0, and return 0.
All digits are the same (e.g., 1111)	The algorithm should correctly form numbers like 11 and 11, summing to 22.
Input contains leading zeros implicitly (e.g., 0123 is represented as 123)	The solution should still work correctly after considering the implicit leading zeros from the number representation during digit extraction.
Maximum four-digit number (9999)	Handle the edge case of 9999 correctly, which produces 99 + 99 = 198.
Digits are already sorted in ascending order (e.g., 1234)	The sorting step should not be impacted, and the algorithm produces 13 + 24 = 37.
Digits are sorted in descending order (e.g., 4321)	Sorting will reverse the order, after which the algorithm should correctly produce 13 + 24 = 37.
Input is a negative number	The problem statement specifies a four digit integer, so explicitly check if the number is negative, and if so, either return an error, throw an exception, or take the absolute value, depending on the clarified requirements.
Algorithm specific: Integer overflow during addition of new1 and new2	Given constraints, integer overflow is not a concern as the maximum possible sum is 99+99 = 198, which will not cause an integer overflow.