Find K Closest Elements
You are given a sorted integer array arr
, and two integers k
and x
. You have to find the k
closest integers to x
in the array.
Here’s a simple stepbystep approach to finding the k closest elements:
Algorithm
Binary Search: Since the array is sorted, we can use a binary search to find the index where
x
would fit in the array.Initialize Pointers: Initialize two pointers,
left
andright
, whereleft
points to the index found in step 1 andright
points to the next index.Find Closest Elements: Compare the elements pointed by
left
andright
to decide which one is closer tox
, and move the pointers accordingly. Repeat this step until you have foundk
closest elements.Gather Result: Return the
k
elements pointed byleft
andright
.
Code


Explanation
 The code first finds the index where
x
would fit in the array.  It then initializes two pointers to find the closest elements on both sides of
x
.  The loop continues until
k
closest elements are found, moving the pointers based on which element is closer tox
.  Finally, it returns the result as the portion of the array between the two pointers.
Insights
 Time Complexity: The binary search takes (O(\log n)), and finding the closest elements takes (O(k)), resulting in a total time complexity of (O(\log n + k)).
 Space Complexity: (O(1)) as we are only using constant extra space.
This solution efficiently finds the k closest elements in a sorted array using binary search and a twopointer technique, fulfilling the given constraints.
Define the Terms
Define the Interface Input: array (integers) already sorted, k (size of the output), x (integer) Output: array (integers)  must be sorted
Analyze the Input and Output
[1,2,3,4,5]
a  x < b  x (whichever has the smallest diff wins) a  x == b  x and a < b (Tie breaking condition)
The output must contain the numbers with the closest to x, in sorted order
Find the diff (numbers are sorted by diff in ascending diff value) diff = [3,2,4,1,5] Grab the first k elements from the diff array output = [3,2,4,1] sort this output [1,2,3,4]
Keep a hash with with key as the element and the diff as the value. It may not be possible if duplicates are allowed in the input.
1  3 = 2 (a = 1) 2  3 = 1 (b = 2) 3  3 = 0 4  3 = 1 5  3 = 2
1 and 5 have the same difference, since a < b, we pick 1.
What are the four numbers that is closest to 3. x = 3
output: [2,3,4,1] because k = 4
Identify the Invariants
Identify the constraints
Search the Problem Space
Classify the Problem
Analyze the Examples
Solve the Problem by Hand
Describe the Pattern
Distill the Observations to Create Insights
Brute Force Approach
Analyze Time and Space Complexity

