861590. Minimize the Difference
Minimize the Difference
Slug: minimize-the-difference
Difficulty: Medium
Id: 861590
Topic Tags: Map, Arrays, Data Structures
Company Tags: None
Summary
Given an array arr of integers and a positive integer k, find the minimum difference between any two elements in the array that are at least k apart. In other words, for each element x in the array, we need to find another element y such that |x-y| is minimized and the distance between them (i.e., |x-y|) is at least k. This problem involves manipulating arrays and using data structures like maps to optimize our solution.
Detailed Explanation
To solve this problem, we can iterate through the array and maintain a map of elements with their indices. For each element, we find the minimum difference between it and any other element that is at least k apart from it. We keep track of the minimum difference found so far and return it as our result.
Here's the step-by-step breakdown:
- Initialize an empty map
indexMapto store elements with their indices. - Iterate through the array
arr. - For each element
xin the array, find all elementsysuch that|x-y| >= k. We can use our mapindexMapto efficiently look up these elements. - Calculate the minimum difference between
xand any of these elementsyand update our global minimum difference if necessary. - Return the global minimum difference found.
Time complexity: O(n), where n is the size of the array, since we're iterating through the array once and looking up elements in our map at most twice (once for each element). Space complexity: O(n), as we're storing all elements with their indices in our map.
Optimized Solutions
Java
import java.util.HashMap;
import java.util.Map;
public int minimizeTheDifference(int[] arr, int k) {
Map<Integer, Integer> indexMap = new HashMap<>();
for (int i = 0; i < arr.length; i++) {
indexMap.put(arr[i], i);
}
int minDiff = Integer.MAX_VALUE;
for (int x : arr) {
int lowerBound = Math.max(0, x - k);
int upperBound = x + k;
for (int y = lowerBound; y <= upperBound; y++) {
if (!indexMap.containsKey(y)) continue;
int diff = Math.abs(x - y);
minDiff = Math.min(minDiff, diff);
}
}
return minDiff;
}