Make Lexicographically Smallest Array by Swapping Elements

arrayunion-findsorting

Problem Statement

You are given a 0-indexed array of positive integers nums and a positive integer limit .

In one operation, you can choose any two indices i and j and swap nums[i] and nums[j] if |nums[i] - nums[j]| <= limit .

Return the lexicographically smallest array that can be obtained by performing the operation any number of times .

An array a is lexicographically smaller than an array b if in the first position where a and b differ, array a has an element that is less than the corresponding element in b . For example, the array [2,10,3] is lexicographically smaller than the array [10,2,3] because they differ at index 0 and 2 < 10 .

Examples

Example 1

Input: nums = [1,5,3,9,8], limit = 2
Output: [1,3,5,8,9]
Apply the operation 2 times:
- Swap nums[1] with nums[2]. The array becomes [1,3,5,9,8]
- Swap nums[3] with nums[4]. The array becomes [1,3,5,8,9]
We cannot obtain a lexicographically smaller array by applying any more operations.
Note that it may be possible to get the same result by doing different operations.

Example 2

Input: nums = [1,7,6,18,2,1], limit = 3
Output: [1,6,7,18,1,2]
Apply the operation 3 times:
- Swap nums[1] with nums[2]. The array becomes [1,6,7,18,2,1]
- Swap nums[0] with nums[4]. The array becomes [2,6,7,18,1,1]
- Swap nums[0] with nums[5]. The array becomes [1,6,7,18,1,2]
We cannot obtain a lexicographically smaller array by applying any more operations.

Example 3

Input: nums = [1,7,28,19,10], limit = 3
Output: [1,7,28,19,10]
[1,7,28,19,10] is the lexicographically smallest array we can obtain because we cannot apply the operation on any two indices.

Constraints

1 <= nums.length <= 10 ^5

1 <= nums[i] <= 10 ^9

1 <= limit <= 10 ^9

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicUnion-Find