Algorithme Tri Fusion (Merge Sort) expliqué

Introduction

This tutorial provides a comprehensive guide to the Merge Sort algorithm, a well-known sorting technique that employs the "divide and conquer" approach. With a time complexity of O(n log n), Merge Sort is efficient for sorting large datasets. This guide will explain how the algorithm works and provide a practical implementation in Python.

Step 1: Understanding the Merge Sort Algorithm

Merge Sort operates by dividing the array into smaller subarrays, sorting those subarrays, and then merging them back together. Here’s how it works:

1. Divide: Split the array into two halves.
2. Conquer: Recursively sort both halves.
3. Combine: Merge the sorted halves back together.

Key Concepts

• Recursive Function: A function that calls itself to break down the problem into smaller pieces.
• Base Case: The condition under which the recursion stops, typically when the array size is one or zero.

Step 2: Implementing Merge Sort in Python

Now that you understand the algorithm, let’s implement it in Python.

Step 2.1: Define the Merge Function

The merge function combines two sorted arrays into a single sorted array.

def merge(left, right):
    sorted_array = []
    left_index, right_index = 0, 0

    while left_index < len(left) and right_index < len(right):
        if left[left_index] < right[right_index]:
            sorted_array.append(left[left_index])
            left_index += 1
        else:
            sorted_array.append(right[right_index])
            right_index += 1

    sorted_array.extend(left[left_index:])
    sorted_array.extend(right[right_index:])
    
    return sorted_array

Step 2.2: Define the Merge Sort Function

This function will implement the divide and conquer strategy.

def merge_sort(array):
    if len(array) <= 1:
        return array

    mid = len(array) // 2
    left_half = merge_sort(array[:mid])
    right_half = merge_sort(array[mid:])
    
    return merge(left_half, right_half)

Step 2.3: Testing the Merge Sort Function

You can test the Merge Sort function by using the following code:

unsorted_array = [38, 27, 43, 3, 9, 82, 10]
sorted_array = merge_sort(unsorted_array)
print("Sorted array:", sorted_array)

Conclusion

In this tutorial, we explored the Merge Sort algorithm, its fundamental principles, and how to implement it in Python. You learned about the importance of dividing the array, sorting the halves, and merging them back together.

Key Takeaways

• Merge Sort is efficient with a time complexity of O(n log n).
• The algorithm uses recursion and a merge function to combine sorted arrays.
• Testing the implementation is crucial to ensure correctness.

Next Steps

• Experiment with different datasets to see how Merge Sort performs.
• Explore variations of the Merge Sort algorithm or other sorting algorithms for comparison.