Find the K Closest Pairs in a Sorted Array

Question

The question asks the candidate to find the K closest pairs in a sorted array, which involves identifying pairs of elements that are closest in value.

Codemia · Accepted Answer

To find the K closest pairs in a sorted array, we can utilize the two-pointer technique. Since the array is sorted, we can efficiently find pairs by maintaining two pointers that traverse the array. This allows us to systematically explore potential pairs while minimizing unnecessary comparisons.

1. Initialize two pointers, `i` at the start and `j` at the end of the array.
2. Create a min-heap to store the pairs along with their differences.
3. While `i < j`, calculate the difference between the current pair and push it into the heap.
4. If the heap exceeds size K, remove the largest element.
5. Continue until all pairs are evaluated, then extract the K closest pairs from the heap.

The time complexity of this approach is O(N log K), where N is the number of elements in the array. This is due to the fact that we are iterating through the array once and performing log K operations for each insertion into the heap. The space complexity is O(K) for storing the K closest pairs.

```python
import heapq

def find_k_closest_pairs(arr, K):
    min_heap = []
    n = len(arr)
    for i in range(n):
        for j in range(i + 1, n):
            diff = abs(arr[i] - arr[j])
            heapq.heappush(min_heap, (diff, (arr[i], arr[j])))
            if len(min_heap) > K:
                heapq.heappop(min_heap)
    return [heapq.heappop(min_heap)[1] for _ in range(len(min_heap))]
```
This code snippet implements the outlined algorithm, using a min-heap to efficiently track the K closest pairs.

This approach is efficient for moderate values of K. However, if K is very large or if the array size is significantly large, we might consider alternative methods such as a more advanced data structure or a different algorithm to reduce the number of comparisons. Additionally, if the array is not sorted, we would need to sort it first, which would increase the time complexity.

Find the K Closest Pairs in a Sorted Array

Apple

What the Interviewer Expects

Key Topics to Cover

How to Approach This

Possible Follow-up Questions

Sharpen Your Skills on Codemia

Sample Answer

Approach

Algorithm

Submit Your Answer

Apple Software Engineer Interview Guide

Related Questions

Binary Search on graph

Count kth largest element in array

Find connected components in string

Merge Three Sorted strings

Binary Search on string