Quick sort algorithm in detail

Quick sort algorithm in detail.

In computer science, sorting algorithms are one of the cornerstones of data processing.

Whether it is retrieving, analyzing or displaying data, sorting is an indispensable step.

Today, we will delve into a classic and efficient sorting algorithm-QuickSort (QuickSort).

Quicksort not only has excellent performance in theory, but is also widely used in practical programming due to its simplicity and efficiency.

\n#

The basic idea of quick sort.

The core idea of quicksort is "Divide and Conquer" (Divide and Conquer).

The basic steps are as follows: 1. # Select base value #: Select an element from the array as a base value (pivot).

2. # Partition operation #: Divide the array into two parts, one part contains all elements less than the reference value, and the other part contains all elements greater than or equal to the reference value.

3. # Recursive Sort #: Quicksort the above two parts respectively until the entire array is ordered.

\n#

Detailed explanation of the partitioning process.

Partition operation is the most core step in quicksort, which determines the efficiency and correctness of the algorithm.

We take ascending sorting as an example to explain the process of partitioning in detail: 1. # Select base value #: Usually select the first or last element of the array as the base value.

Here we select the last element as the reference value.

2. # Initialization pointer #: Set two pointers, leftPoints to the first element of the array, rightPoints to the penultimate element of the array.

3. # move pointer #: traverse the array from left to right, find the first element greater than or equal to the reference value, and combine it with leftThe element pointed to by the pointer is swapped, then leftThe pointer moves one bit to the right.

4. # Repeat step 3 #: Continue to traverse from left to right until leftPointer over rightPointer.

5. # final exchange #: combine the reference value with leftThe element pointed by the pointer is exchanged to complete the partitioning operation.

At this point, all elements on the left side of the reference value are less than the reference value, and all elements on the right side are greater than or equal to the reference value.

\n#

Recursively implement quick sort.

Next, we implement quicksort through Python code and annotate each step in detail:

def quicksort(arr):
    """
    快速排序函数
    :param arr: 待排序的数组
    :return: 已排序的数组
    """
    if len(arr) <= 1:
        return arr
    else:
        # 选择基准值，这里选择最后一个元素
        pivot = arr[-1]
        # 分区操作，返回基准值的正确位置
        left = [x for x in arr[:-1] if x <= pivot]
        right = [x for x in arr[:-1] if x > pivot]
        # 递归排序左右两部分，并将基准值插入中间
        return quicksort(left) + [pivot] + quicksort(right)

# 示例使用
array = [3, 6, 8, 10, 1, 2, 1]
print("原数组:", array)
sorted_array = quicksort(array)
print("排序后:", sorted_array)

\n#

Code parsing.

1. # Base case #: If the length of the array is less than or equal to 1, return the array directly, because a single element or an empty array is itself ordered.

2. # Select reference value #: Here we simply select the last element of the array as the reference value.

3. # Partition Operation #: - Use list inference to put elements less than or equal to the reference value into leftList.

- Use another list inference to put elements greater than the reference value into rightList.

4. # recursive call #: right leftSumrightThe lists are quicksorted separately, and the reference values are inserted between the two to form a final ordered array.

\n#

Precautions in practical applications.

Although quick sort has a time complexity of O (n log n) on average, its worst-case time complexity is O (n ^ 2).

Therefore, in practical applications, there are several points to note: 1. # Randomized benchmark value #: In order to avoid the worst-case scenario of choosing the same benchmark value each time, an element can be randomly selected as the benchmark value.

2. # Three numbers take the middle method #: Select the median of the first, last and middle elements as the base value, which can reduce the probability of the worst case.

3. # Small array switch sort method #: For smaller arrays, simpler sort algorithms such as insertion sort can be used to improve overall efficiency.

\n#

Summarize.

Quick sort is an efficient and widely used sorting algorithm, the core of which lies in clever partition operation and recursive thinking.

By reasonably selecting the benchmark value and optimizing the partitioning process, the performance of quick sort can be further improved.

I hope this article can help you better understand and apply quicksort algorithms and solve more sorting problems in actual programming.