#2160

Easy

auto_awesomeGreedy choice plus invariant validation

LeetCode Problem Workspace

Minimum Sum of Four Digit Number After Splitting Digits

Find the minimum sum of two 2-digit numbers by splitting a four-digit number into two integers.

Problem Statement

You are given a four-digit positive integer, num. Your task is to split the digits of num into two new integers, new1 and new2, using all the digits. Leading zeros are allowed in the integers new1 and new2, and the goal is to minimize the sum of these two integers.

For example, given num = 2932, the digits can be rearranged into several pairs, such as [29, 23], and the minimum sum can be achieved by pairing [29, 23], resulting in 52. The task is to find this minimal sum for any valid four-digit input.

Examples

Example 1

Input: num = 2932

Output: 52

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

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

Solution Approach

Greedy Strategy for Minimum Sum

To achieve the minimum sum, sort the digits of the number in ascending order. Then, pair the digits such that one integer gets the smallest digits while the other gets the larger ones. This guarantees that the two numbers are as balanced and small as possible.

Using Sorting for Pairing Digits

By sorting the digits, we ensure that the smaller digits are grouped together in one number, and the larger digits go into the other. This method minimizes the impact of larger digits on the final sum by distributing them as evenly as possible between the two new integers.

Validating the Approach

After sorting the digits, we will alternately assign them to the two numbers to ensure that the two integers formed are as close as possible. This approach works because any other pairings will result in a higher sum due to the nature of digit values in a four-digit number.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity is dominated by the sorting step, which is O(4 log 4) or simply O(1), since we are always working with exactly four digits. The space complexity is also O(1), as only a constant amount of extra space is needed for the calculations.

What Interviewers Usually Probe

Look for a clear understanding of greedy strategies in number optimization.
Candidates should demonstrate the ability to use sorting effectively in algorithm design.
The approach should validate that splitting digits and minimizing sums is optimal.

Common Pitfalls or Variants

Common pitfalls

Failing to account for leading zeros when forming the two numbers.
Not correctly sorting the digits before pairing them.
Incorrectly assuming that any random splitting of digits will give the smallest sum.

Follow-up variants

Handling different ranges of numbers, such as working with more or fewer digits.
Exploring the same problem with a constraint on no leading zeros.
Adjusting the problem to consider non-greedy approaches or more complex number splits.

FAQ

How do I minimize the sum of two numbers formed from four digits?

Sort the digits of the four-digit number and then alternate the digits between the two numbers to minimize their sum.

What pattern does the problem "Minimum Sum of Four Digit Number After Splitting Digits" follow?

This problem follows a greedy choice plus invariant validation pattern, ensuring the two formed numbers are as small as possible.

What happens if I don't split the digits optimally?

If the digits are not paired optimally, the resulting sum will be higher than the minimum possible sum.

Can I ignore the possibility of leading zeros in this problem?

No, leading zeros are allowed, and you must consider them when forming the two new numbers.

Is this problem related to dynamic programming?

No, this problem can be solved using a greedy algorithm with sorting, not dynamic programming.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def minimumSum(self, num: int) -> int:
        nums = []
        while num:
            nums.append(num % 10)
            num //= 10
        nums.sort()
        return 10 * (nums[0] + nums[1]) + nums[2] + nums[3]

Continue Practicing

#2195 append k integers with minimal sum #2578 split with minimum sum #2607 make k subarray sums equal