What is the difference between a selection sort and an insertion sort in C++?

Table of Contents

• Introduction
• Key Differences Between Selection Sort and Insertion Sort
  • 1. Algorithmic Approach
  • 2. Time Complexity
  • 3. Number of Swaps
• Practical Examples
  • 1. Selection Sort in C++
  • 2. Insertion Sort in C++
• When to Use Selection Sort vs. Insertion Sort
  • Selection Sort:
  • Insertion Sort:
• Conclusion

Introduction

Selection sort and insertion sort are two fundamental sorting algorithms used in C++. Both have the same worst-case time complexity of O(n²), but their approach and performance in different scenarios vary significantly. This article explains the differences between selection sort and insertion sort, their algorithmic approaches, and examples of how to implement them in C++.

Key Differences Between Selection Sort and Insertion Sort

1. Algorithmic Approach

• Selection Sort:
  • Selection sort divides the array into two sections: sorted and unsorted. It repeatedly searches for the smallest element in the unsorted section and swaps it with the first unsorted element. This process continues until the array is fully sorted.
  • Summary: Finds the minimum element from the unsorted portion and swaps it into the correct position.
• Insertion Sort:
  • Insertion sort also divides the array into sorted and unsorted sections. However, instead of finding the minimum element, it picks the first unsorted element and inserts it into its correct position within the sorted section, shifting the other elements as needed.
  • Summary: Takes each unsorted element and inserts it into its correct position in the sorted portion.

2. Time Complexity

• Selection Sort:

  • Best-case time complexity: O(n²)
  • Worst-case time complexity: O(n²)
  • Average time complexity: O(n²)

  Selection sort always makes the same number of comparisons, regardless of whether the array is already sorted.

• Insertion Sort:

  • Best-case time complexity: O(n) (when the array is nearly or fully sorted)
  • Worst-case time complexity: O(n²)
  • Average time complexity: O(n²)

  Insertion sort performs much better than selection sort when the array is already sorted or nearly sorted, as it reduces the number of comparisons and shifts.

3. Number of Swaps

• Selection Sort: Performs O(n) swaps because it only swaps when the minimum element is found.
• Insertion Sort: Swaps or shifts elements based on their relative positions, which can be efficient in the best case but may reach O(n²) in the worst case.

Practical Examples

1. Selection Sort in C++

2. Insertion Sort in C++

When to Use Selection Sort vs. Insertion Sort

Selection Sort:

• Best suited for small datasets where performance is not critical.
• It minimizes the number of swaps, making it useful in scenarios where swaps are expensive.

Insertion Sort:

• More efficient for nearly sorted datasets, as it has a linear time complexity in the best case.
• Ideal when elements need to be dynamically inserted into a sorted array.

Conclusion

The main difference between selection sort and insertion sort in C++ lies in their algorithmic approaches and performance under different conditions. Selection sort consistently takes O(n²) time, regardless of input, while insertion sort can be more efficient when the array is nearly sorted. Knowing these differences will help you choose the most appropriate sorting algorithm depending on the specific needs of your program.