The actual code of divide and conquer and merge sort

In computer science, sorting algorithms are a very important class of tools that help us arrange a set of data in a specific order.

Merge Sort is a classic Divide and Conquer application that recursively divides an array into smaller subarrays and then merges these subarrays to achieve the purpose of sorting.

What is Divide and Conquer?.

Divide and conquer is a problem-solving strategy that decomposes a complex problem into two or more identical or similar sub-problems until the last sub-problem can be solved simply and directly. The solution of the original problem is the combination of the solutions of the sub-problems.

Merge sort takes advantage of this strategy by continuously dividing the array in two until each sub-array has only one element, and then merging these sub-arrays in pairs to finally get an ordered array.

Merge sort steps.

1. # Decomposition #: Divide the current sequence from the middle into two parts, the front and the back.

2. # Solve #: recursively merge and sort the two parts before and after.

3. # Merge #: Combine two sorted parts into one ordered sequence.

Code implementation.

The following is the merge sort code implemented in Python:

def merge_sort(arr):
    if len(arr) <= 1:
        return arr
    
    # 分解步骤
    mid = len(arr) // 2
    left_half = merge_sort(arr[:mid])
    right_half = merge_sort(arr[mid:])
    
    # 合并步骤
    return merge(left_half, right_half)

def merge(left, right):
    sorted_array = []
    left_index = right_index = 0
    
    # 比较左右两部分的元素，按顺序添加到结果数组中
    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
    
    # 如果左半部分还有剩余，添加到结果数组中
    sorted_array.extend(left[left_index:])
    # 如果右半部分还有剩余，添加到结果数组中
    sorted_array.extend(right[right_index:])
    
    return sorted_array

Time complexity analysis.

The time complexity of merge sort is O (n log n), where n is the length of the array.

This time complexity comes from two aspects: 1. # Decomposition process #: Divide the array into two halves each time, this process needs to log n times (because the length of each count is halved).

2. # Merge Process #: Each merge operation requires linear time, that is, O (n).

Since the decomposition and merging processes are performed in parallel, the total time complexity is O (n log n).

This time complexity makes merge sorting ideal for handling large datasets.

Practical application.

Merge sort is not only important in theory, but also widely used in practical applications.

For example, in a database management system, merge sort can be used to optimize query operations; in a file system, merge sort can be used to merge multiple sorted file segments.

In addition, merge sort is also the basis of many advanced sorting algorithms, such as Timsort (Python built-in sorting algorithm) and so on.

Summarize.

Merge sort is an efficient and stable sorting algorithm. It uses divide and conquer method to simplify the problem, solve sub-problems recursively, and finally solve the whole problem by merging.

Its average time complexity is O (n log n), which makes it very efficient when dealing with large-scale data.

I hope that through this article, you can have an in-depth understanding of merge sorting and be able to use it flexibly in actual projects.