Algorithme de tri : Tri par sélection - Selection Sort

Introduction

This tutorial provides a comprehensive guide to the selection sort algorithm, including visual representations and implementations in Python. Selection sort is a straightforward sorting algorithm that works by repeatedly selecting the smallest (or largest) element from the unsorted portion of the list and moving it to the beginning. Understanding this algorithm is crucial for grasping more complex sorting techniques.

Step 1: Understand the Concept of Selection Sort

• Selection sort works by dividing the list into two parts: the sorted part and the unsorted part.
• Initially, the sorted part is empty, and the unsorted part contains all elements.
• The algorithm proceeds by finding the minimum element from the unsorted part and swapping it with the leftmost unsorted element, effectively growing the sorted part.

Practical Tip

• Visualize the sorting process with a simple array to better understand how elements are moved.

Step 2: Visual Representation of Selection Sort

• Use animations or diagrams to illustrate how selection sort works:
  • Highlight the current minimum element.
  • Show swaps between the minimum element and the first unsorted element.
• This visualization helps solidify your understanding of the algorithm's mechanics.

Step 3: Implement Iterative Selection Sort in Python

To implement selection sort iteratively, follow these steps:

1. Create a function named selection_sort that takes a list as an argument.
2. Iterate through each element in the list.
3. For each position, find the index of the minimum element in the unsorted portion.
4. Swap the found minimum element with the current position.

Sample Code

def selection_sort(arr):
    n = len(arr)
    for i in range(n):
        min_index = i
        for j in range(i + 1, n):
            if arr[j] < arr[min_index]:
                min_index = j
        arr[i], arr[min_index] = arr[min_index], arr[i]  # Swap
    return arr

Common Pitfalls

• Forgetting to initialize min_index at the start of the outer loop can lead to incorrect results.
• Ensure the inner loop only considers unsorted elements.

Step 4: Explore Recursive Selection Sort

Selection sort can also be implemented recursively. Here's how:

1. Create a recursive function that accepts the list and the current index.
2. If the current index is equal to the length of the list, return the list as it is already sorted.
3. Find the minimum element in the unsorted portion.
4. Swap it with the current index.
5. Call the function recursively for the next index.

Sample Code

def recursive_selection_sort(arr, index=0):
    if index == len(arr):
        return arr
    
    min_index = index
    for j in range(index + 1, len(arr)):
        if arr[j] < arr[min_index]:
            min_index = j
            
    arr[index], arr[min_index] = arr[min_index], arr[index]  # Swap
    return recursive_selection_sort(arr, index + 1)

Practical Tip

• Debug by printing the array at each recursive call to trace the sorting process.

Conclusion

In this tutorial, you learned about the selection sort algorithm, both iteratively and recursively. By understanding its mechanics and implementing it in Python, you can better appreciate sorting algorithms' foundational concepts. Next, consider experimenting with more complex algorithms, such as quicksort or mergesort, to further enhance your programming skills.