Kth Smallest Element - CA07

My Thinking and Approach

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Introduction

In this problem, I was given an array of integers and asked to find the kth smallest element in the array.

The kth smallest element is based on the sorted order of the array.

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Problem Statement

• Given an array of integers arr

• Given an integer k

• Find the kth smallest element

• Note:

  • The kth smallest is based on sorted order

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My Initial Thought

At first, I considered:

• Sorting the array
• Returning the element at index k - 1

This approach is simple and works correctly.

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Key Observation

Sorting gives the correct answer:

• After sorting:

  • 1st smallest → index 0
  • kth smallest → index k - 1

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Optimized Approach

I decided to:

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

Logic:

• Sort the array in ascending order
• Return arr[k - 1]

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My Approach (Step-by-Step)

1. Sort the array
2. Find the element at index k - 1
3. Return that element

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Code (Python)

def kthSmallest(arr, k):
    arr.sort()
    return arr[k - 1]

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Example Walkthrough

Input:

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

Steps:

• Sort → [2, 3, 4, 5, 6, 10, 10, 33, 48, 53]
• 4th smallest → index 3 → value = 5

Output:

5

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Complexity Analysis

Type	Complexity
Time Complexity	O(n log n)
Space Complexity	O(1)

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Key Takeaways

• Sorting helps in finding order-based elements
• Indexing plays an important role
• Simple approach is often sufficient

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Conclusion

This problem helped me understand how sorting can be used to solve order-based problems like finding the kth smallest element.

It is simple and effective for most cases.

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