Leetcode #2948: Make Lexicographically Smallest Array by Swapping Elements
In this guide, we solve Leetcode #2948 Make Lexicographically Smallest Array by Swapping Elements in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Union Find, Array, Sorting
Intuition
We need to merge components and check connectivity efficiently.
Union-Find supports near-constant-time merges and finds.
Approach
Initialize each node as its own parent and union pairs as you scan.
Use path compression to keep operations fast.
Steps:
- Initialize parent arrays.
- Union related nodes.
- Use find to check connectivity.
Example
Input: nums = [1,5,3,9,8], limit = 2
Output: [1,3,5,8,9]
Explanation: 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.
Python Solution
class Solution:
def lexicographicallySmallestArray(self, nums: List[int], limit: int) -> List[int]:
n = len(nums)
arr = sorted(zip(nums, range(n)))
ans = [0] * n
i = 0
while i < n:
j = i + 1
while j < n and arr[j][0] - arr[j - 1][0] <= limit:
j += 1
idx = sorted(k for _, k in arr[i:j])
for k, (x, _) in zip(idx, arr[i:j]):
ans[k] = x
i = j
return ans
Complexity
The time complexity is Near O(n) (amortized). The space complexity is O(n).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.