Largest Number After Digit Swaps by Parity

Largest Number After Digit Swaps by Parity

1. What is this problem about?

The Largest Number After Digit Swaps by Parity coding problem gives you a positive integer. You can swap any two digits as long as they have the same parity (both even or both odd). Your goal is to find the largest possible number you can create through any number of these swaps. Essentially, you want to move the largest available even digits and the largest available odd digits to the most significant positions they can occupy.

2. Why is this asked in interviews?

This problem is a great test of a candidate's ability to categorize data and reassemble it under constraints. Companies like Salesforce and Bloomberg use it to evaluate how well you can use data structures like heaps or simple sorting to solve "Easy" difficulty problems efficiently. It’s less about complex algorithms and more about clean, logical implementation of sorting within specific subsets of an input.

3. Algorithmic pattern used

This problem uses the Sorting and Heap (Priority Queue) interview pattern. The most efficient way is to separate the digits into two groups: even and odd. Sort each group in descending order (or use a Max-Heap). Then, iterate through the original number's digit positions. If the original digit was even, replace it with the largest available even digit; if it was odd, replace it with the largest available odd digit.

4. Example explanation

Number: 2471. Parity positions: [Even, Even, Odd, Odd]. Even digits: [2, 4] -> Sorted Desc: [4, 2]. Odd digits: [7, 1] -> Sorted Desc: [7, 1]. Reassembling: 1st pos (Even): use 4. 2nd pos (Even): use 2. 3rd pos (Odd): use 7. 4th pos (Odd): use 1. Result: 4271.

5. Common mistakes candidates make

One common mistake is trying to swap digits arbitrarily without a clear plan, which can be inefficient. Another error is misidentifying the parity of a digit (remember, 0 is even). Some candidates also struggle with converting the number to a string/list and back to an integer, which is usually the easiest way to manipulate individual digits.

6. Interview preparation tip

In "Sorting, Heap interview pattern" problems, always ask yourself if you can break the problem into independent sub-problems. Here, the even digits and odd digits don't interfere with each other's "available slots." Treating them as two separate pools makes the logic much simpler and less prone to errors.