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#2817
Medium Algorithms

Minimum absolute difference between elements with constraint

Array Binary Search Ordered Set
37.2% acceptance
Feb 25, 2026
767
78
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. In other words, find two indices i and j such that abs(i - j) >= x and abs(nums[i] - nums[j]) is minimized. Return an integer denoting the minimum absolute difference between two elements that are at least x indices apart.

Solution

Rust
Time O(n log n)
Space O(n)
LeetCode
solution.rs 
impl Solution {
  pub fn min_absolute_difference(nums: Vec<i32>, x: i32) -> i32 {
    use std::collections::BTreeSet;
    let x = x as usize;
    let n = nums.len();
    let mut set: BTreeSet<i32> = BTreeSet::new();
    let mut ans = i32::MAX;
    for j in x..n {
      set.insert(nums[j - x]);
      let v = nums[j];
      if let Some(&a) = set.range(..=v).next_back() { ans = ans.min(v - a); }
      if let Some(&b) = set.range(v..).next() { ans = ans.min(b - v); }
    }
    ans
  }
}