Leetcode #2817: Minimum Absolute Difference Between Elements With Constraint
In this guide, we solve Leetcode #2817 Minimum Absolute Difference Between Elements With Constraint 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 integer array nums and an integer x. Find the minimum absolute difference between two elements in the array that are at least x indices apart.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Binary Search, Ordered Set
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: nums = [4,3,2,4], x = 2
Output: 0
Explanation: We can select nums[0] = 4 and nums[3] = 4.
They are at least 2 indices apart, and their absolute difference is the minimum, 0.
It can be shown that 0 is the optimal answer.
Python Solution
class Solution:
def minAbsoluteDifference(self, nums: List[int], x: int) -> int:
sl = SortedList()
ans = inf
for i in range(x, len(nums)):
sl.add(nums[i - x])
j = bisect_left(sl, nums[i])
if j < len(sl):
ans = min(ans, sl[j] - nums[i])
if j:
ans = min(ans, nums[i] - sl[j - 1])
return ans
Complexity
The time complexity is , and the space complexity is . The space complexity is .
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.