Kth Smallest Element in an Array

My Thought Process (Java DSA)

When I came across this problem, it initially looked slightly complex. Instead of directly writing code, I tried to understand what “kth smallest” actually means.

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Problem Statement

We are given:

• An array of integers arr[]
• An integer k

The task is to find the kth smallest element in the array.

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Initial Thinking

Let’s take an example:

arr = [10, 5, 4, 3, 48, 6, 2, 33, 53, 10]
k = 4

If I arrange the array in sorted order:

[2, 3, 4, 5, 6, 10, 10, 33, 48, 53]

Now the 4th smallest element becomes:

5

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Key Observation

The term “kth smallest” directly relates to sorted order.
So one straightforward approach is:

• Sort the array
• Return the element at index k - 1

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Approach

1. Sort the array
2. Access the element at index k - 1
3. Return the result

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HOW it Runs

arr = [7, 10, 4, 3, 20, 15]
k = 3

Sorted → [3, 4, 7, 10, 15, 20]

Answer → arr[2] = 7

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Code (Java)

import java.util.*;

class Solution {
    public int kthSmallest(int[] arr, int k) {
        Arrays.sort(arr);
        return arr[k - 1];
    }
}

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Why This Works

• Sorting arranges elements in increasing order
• The kth smallest element will always be at position k - 1
• The approach is simple and easy to implement

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Complexity Analysis

• Time Complexity: O(n log n)
• Space Complexity: O(1)

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Final Thought

This problem shows that understanding the requirement clearly can lead to a simple solution.
Instead of overthinking, identifying that “kth smallest” depends on ordering helps in solving it directly.

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