【排序算法】八种排序算法可视化过程_哔哩哔哩_bilibili
1,冒泡排序:
冒泡排序(Bubble Sort):
- 冒泡排序是一种简单的排序算法,它通过重复地交换相邻的元素,直到整个序列有序。
- 算法思路是:从第一个元素开始,依次比较相邻的两个元素,如果前者大于后者,就交换它们的位置。这样一轮下来,最大的元素就会"冒泡"到数组的末尾。
- 重复这个过程,直到整个数组有序。
C语言实现:
void bubble_sort(int arr[], int n) {
// 冒泡排序实现
for (int i = 0; i < n - 1; i++) {
for (int j = 0; j < n - i - 1; j++) {
if (arr[j] > arr[j + 1]) {
// 交换 arr[j] 和 arr[j+1]
int temp = arr[j];
arr[j] = arr[j + 1];
arr[j + 1] = temp;
}
}
}
}
python实现:
def bubble_sort(arr):
n = len(arr)
for i in range(n):
for j in range(0, n - i - 1):
if arr[j] > arr[j + 1]:
arr[j], arr[j + 1] = arr[j + 1], arr[j]
return arr
2,选择排序:
选择排序(Selection Sort):
- 选择排序是一种简单直观的排序算法。
- 算法思路是:首先在未排序序列中找到最小(大)元素,存放到排序序列的起始位置,然后,再从剩余未排序元素中继续寻找最小(大)元素,放到已排序序列的末尾。
- 重复这个过程,直到整个数组有序。
C语言实现:
void selection_sort(int arr[], int n) {
// 选择排序实现
for (int i = 0; i < n - 1; i++) {
int min_idx = i;
for (int j = i + 1; j < n; j++) {
if (arr[j] < arr[min_idx]) {
min_idx = j;
}
}
// 交换 arr[i] 和 arr[min_idx]
int temp = arr[i];
arr[i] = arr[min_idx];
arr[min_idx] = temp;
}
}
python实现:
def selection_sort(arr):
n = len(arr)
for i in range(n):
min_idx = i
for j in range(i+1, n):
if arr[j] < arr[min_idx]:
min_idx = j
arr[i], arr[min_idx] = arr[min_idx], arr[i]
return arr
3,插入排序:
插入排序(Insertion Sort):
- 插入排序是一种简单直观的排序算法。
- 算法思路是:将数组中的元素逐个插入到已排序的子数组中,直到整个数组有序。
- 具体过程是:从第二个元素开始,将当前元素与已排序的子数组进行比较和插入。
C语言实现:
void insertion_sort(int arr[], int n) {
// 插入排序实现
for (int i = 1; i < n; i++) {
int key = arr[i];
int j = i - 1;
while (j >= 0 && arr[j] > key) {
arr[j + 1] = arr[j];
j--;
}
arr[j + 1] = key;
}
}
python实现:
def insertion_sort(arr):
n = len(arr)
for i in range(1, n):
key = arr[i]
j = i - 1
while j >= 0 and key < arr[j]:
arr[j + 1] = arr[j]
j -= 1
arr[j + 1] = key
return arr
4, 堆排序:
堆排序(Heap Sort):
- 堆排序利用二叉堆的特性进行排序。
- 算法思路是:首先将待排序数组构建成一个最大堆,然后将堆顶元素(即最大值)与堆末尾元素交换,然后对剩余元素重新调整为最大堆,重复这个过程直到整个数组有序。
C语言实现:
void heapify(int arr[], int n, int i) {
// // 堆排序实现
int largest = i;
int left = 2 * i + 1;
int right = 2 * i + 2;
if (left < n && arr[left] > arr[largest])
largest = left;
if (right < n && arr[right] > arr[largest])
largest = right;
if (largest != i) {
// 交换 arr[i] 和 arr[largest]
int temp = arr[i];
arr[i] = arr[largest];
arr[largest] = temp;
heapify(arr, n, largest);
}
}
void heap_sort(int arr[], int n) {
// 堆排序实现
// 构建最大堆
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
// 从堆中提取元素
for (int i = n - 1; i > 0; i--) {
// 交换 arr[0] 和 arr[i]
int temp = arr[0];
arr[0] = arr[i];
arr[i] = temp;
heapify(arr, i, 0);
}
}
python实现:
def heapify(arr, n, i):
largest = i
left = 2 * i + 1
right = 2 * i + 2
if left < n and arr[largest] < arr[left]:
largest = left
if right < n and arr[largest] < arr[right]:
largest = right
if largest != i:
arr[i], arr[largest] = arr[largest], arr[i]
heapify(arr, n, largest)
def heap_sort(arr):
n = len(arr)
# 构建大顶堆
for i in range(n // 2 - 1, -1, -1):
heapify(arr, n, i)
# 逐步将堆顶元素与末尾元素交换并重新调整堆
for i in range(n - 1, 0, -1):
arr[i], arr[0] = arr[0], arr[i]
heapify(arr, i, 0)
return arr
5,快速排序:
它的基本思想是:
- 从数列中挑出一个元素,称为 "基准"(pivot)。
- 重新排序数列,所有元素比基准值小的摆放在基准前面,所有元素比基准值大的摆在基准的后面。在这个分区结束之后,该基准就处于数列的中间位置。这个称为分区(partition)操作。
- 递归地把小于基准值元素的子数列和大于基准值元素的子数列排序。
C语言实现:
//快速排序
// 交换两个元素
void swap(int *a, int *b) {
int temp = *a;
*a = *b;
*b = temp;
}
// 分区操作
int partition(int arr[], int low, int high) {
int pivot = arr[high]; // 将最后一个元素选为基准
int i = (low - 1); // 较小元素的索引
for (int j = low; j <= high - 1; j++) {
// 如果当前元素小于或等于 pivot
if (arr[j] <= pivot) {
i++; // 将较小元素的索引递增
swap(&arr[i], &arr[j]);
}
}
swap(&arr[i + 1], &arr[high]);
return (i + 1);
}
// 快速排序函数
void quickSort(int arr[], int low, int high) {
if (low < high) {
int pi = partition(arr, low, high);
// 递归地对分区进行排序
quickSort(arr, low, pi - 1);
quickSort(arr, pi + 1, high);
}
}
python实现:
def partition(arr, low, high):
i = (low-1)
pivot = arr[high]
for j in range(low, high):
if arr[j] < pivot:
i = i+1
arr[i], arr[j] = arr[j], arr[i]
arr[i+1], arr[high] = arr[high], arr[i+1]
return (i+1)
6,并归排序:
- 归并排序是一种采用分治策略的高效排序算法。
- 算法思路是:将待排序数组递归地分成两半,直到每个子数组只有一个元素,然后将这些子数组合并,得到最终有序的数组。
- 具体过程是:将数组一分为二,递归地对两个子数组进行排序,然后将两个有序的子数组合并成一个有序数组。
C语言实现:
// 并归排序
void merge(int arr[], int left[], int left_size, int right[], int right_size) {
int i = 0, j = 0, k = 0;
// 合并 left 和 right 数组
while (i < left_size && j < right_size) {
if (left[i] < right[j]) {
arr[k++] = left[i++];
} else {
arr[k++] = right[j++];
}
}
// 将剩余元素添加到 arr 中
while (i < left_size) {
arr[k++] = left[i++];
}
while (j < right_size) {
arr[k++] = right[j++];
}
}
void merge_sort(int arr[], int size) {
if (size <= 1) {
return;
}
int mid = size / 2;
int *left = (int *)malloc(mid * sizeof(int));
int *right = (int *)malloc((size - mid) * sizeof(int));
// 递归地对左右子数组进行排序
for (int i = 0; i < mid; i++) {
left[i] = arr[i];
}
merge_sort(left, mid);
for (int i = mid; i < size; i++) {
right[i - mid] = arr[i];
}
merge_sort(right, size - mid);
// 合并左右子数组
merge(arr, left, mid, right, size - mid);
// 释放动态分配的内存
free(left);
free(right);
}
python实现:
def merge_sort(arr):
if len(arr) > 1:
mid = len(arr) // 2
L = arr[:mid]
R = arr[mid:]
merge_sort(L)
merge_sort(R)
i = j = k = 0
while i < len(L) and j < len(R):
if L[i] < R[j]:
arr[k] = L[i]
i += 1
else:
arr[k] = R[j]
j += 1
k += 1
while i < len(L):
arr[k] = L[i]
i += 1
k += 1
while j < len(R):
arr[k] = R[j]
j += 1
k += 1
return arr
7,举例子
来随机生成一个长度为100,000的一维数组,并使用上述算法进行排序。
(由于数据量太大,电脑可能由于内存问题,一块运行会导致C语言代码崩溃,建议便注释边运行,python不会出现种情况。非计算机专业学生,说法错误欢迎指正)
C语言版代码:
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <string.h>
#define SIZE 100000
void bubble_sort(int arr[], int n) {
// 冒泡排序实现
for (int i = 0; i < n - 1; i++) {
for (int j = 0; j < n - i - 1; j++) {
if (arr[j] > arr[j + 1]) {
// 交换 arr[j] 和 arr[j+1]
int temp = arr[j];
arr[j] = arr[j + 1];
arr[j + 1] = temp;
}
}
}
}
void selection_sort(int arr[], int n) {
// 选择排序实现
for (int i = 0; i < n - 1; i++) {
int min_idx = i;
for (int j = i + 1; j < n; j++) {
if (arr[j] < arr[min_idx]) {
min_idx = j;
}
}
// 交换 arr[i] 和 arr[min_idx]
int temp = arr[i];
arr[i] = arr[min_idx];
arr[min_idx] = temp;
}
}
void insertion_sort(int arr[], int n) {
// 插入排序实现
for (int i = 1; i < n; i++) {
int key = arr[i];
int j = i - 1;
while (j >= 0 && arr[j] > key) {
arr[j + 1] = arr[j];
j--;
}
arr[j + 1] = key;
}
}
void heapify(int arr[], int n, int i) {
// // 堆排序实现
int largest = i;
int left = 2 * i + 1;
int right = 2 * i + 2;
if (left < n && arr[left] > arr[largest])
largest = left;
if (right < n && arr[right] > arr[largest])
largest = right;
if (largest != i) {
// 交换 arr[i] 和 arr[largest]
int temp = arr[i];
arr[i] = arr[largest];
arr[largest] = temp;
heapify(arr, n, largest);
}
}
void heap_sort(int arr[], int n) {
// 堆排序实现
// 构建最大堆
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
// 从堆中提取元素
for (int i = n - 1; i > 0; i--) {
// 交换 arr[0] 和 arr[i]
int temp = arr[0];
arr[0] = arr[i];
arr[i] = temp;
heapify(arr, i, 0);
}
}
// 并归排序
void merge(int arr[], int left[], int left_size, int right[], int right_size) {
int i = 0, j = 0, k = 0;
// 合并 left 和 right 数组
while (i < left_size && j < right_size) {
if (left[i] < right[j]) {
arr[k++] = left[i++];
} else {
arr[k++] = right[j++];
}
}
// 将剩余元素添加到 arr 中
while (i < left_size) {
arr[k++] = left[i++];
}
while (j < right_size) {
arr[k++] = right[j++];
}
}
void merge_sort(int arr[], int size) {
if (size <= 1) {
return;
}
int mid = size / 2;
int *left = (int *)malloc(mid * sizeof(int));
int *right = (int *)malloc((size - mid) * sizeof(int));
// 递归地对左右子数组进行排序
for (int i = 0; i < mid; i++) {
left[i] = arr[i];
}
merge_sort(left, mid);
for (int i = mid; i < size; i++) {
right[i - mid] = arr[i];
}
merge_sort(right, size - mid);
// 合并左右子数组
merge(arr, left, mid, right, size - mid);
// 释放动态分配的内存
free(left);
free(right);
}
//快速排序
// 交换两个元素
void swap(int *a, int *b) {
int temp = *a;
*a = *b;
*b = temp;
}
// 分区操作
int partition(int arr[], int low, int high) {
int pivot = arr[high]; // 将最后一个元素选为基准
int i = (low - 1); // 较小元素的索引
for (int j = low; j <= high - 1; j++) {
// 如果当前元素小于或等于 pivot
if (arr[j] <= pivot) {
i++; // 将较小元素的索引递增
swap(&arr[i], &arr[j]);
}
}
swap(&arr[i + 1], &arr[high]);
return (i + 1);
}
// 快速排序函数
void quickSort(int arr[], int low, int high) {
if (low < high) {
int pi = partition(arr, low, high);
// 递归地对分区进行排序
quickSort(arr, low, pi - 1);
quickSort(arr, pi + 1, high);
}
}
int main() {
int arr[SIZE];
// 生成随机数组
srand(time(NULL));
for (int i = 0; i < SIZE; i++) {
arr[i] = rand() % 1000000;
}
// 冒泡排序 // Bubble sort time: 21.614000 seconds
int bubble_arr[SIZE];
memcpy(bubble_arr, arr, sizeof(arr));
clock_t bubble_start = clock();
bubble_sort(bubble_arr, SIZE);
clock_t bubble_end = clock();
printf("Bubble sort time: %f seconds\n", (double)(bubble_end - bubble_start) / CLOCKS_PER_SEC);
//
// // 选择排序 //Selection sort time: 4.120000 seconds
// int select_arr[SIZE];
// memcpy(select_arr, arr, sizeof(arr));
// clock_t select_start = clock();
// selection_sort(select_arr, SIZE);
// clock_t select_end = clock();
// printf("Selection sort time: %f seconds\n", (double)(select_end - select_start) / CLOCKS_PER_SEC);
//
// // 插入排序 //Insertion sort time: 2.663000 seconds
// int insert_arr[SIZE];
// memcpy(insert_arr, arr, sizeof(arr));
// clock_t insert_start = clock();
// insertion_sort(insert_arr, SIZE);
// clock_t insert_end = clock();
// printf("Insertion sort time: %f seconds\n", (double)(insert_end - insert_start) / CLOCKS_PER_SEC);
//
// // 堆排序 //Heap sort time: 0.015000 seconds
// int heap_arr[SIZE];
// memcpy(heap_arr, arr, sizeof(arr));
// clock_t heap_start = clock();
// heap_sort(heap_arr, SIZE);
// clock_t heap_end = clock();
// printf("Heap sort time: %f seconds\n", (double)(heap_end - heap_start) / CLOCKS_PER_SEC);
//
// // 归并排序 //Merge sort time: 0.035000 seconds
// int merge_arr[SIZE];
// memcpy(merge_arr, arr, sizeof(arr));
// clock_t merge_start = clock();
// merge_sort(merge_arr, SIZE);
// clock_t merge_end = clock();
// printf("Merge sort time: %f seconds\n", (double)(merge_end - merge_start) / CLOCKS_PER_SEC);
// //快速排序 //Quick sort time: 0.010000 seconds
// int quickSort_arr[SIZE];
// memcpy(quickSort_arr, arr, sizeof(arr));
// clock_t quick_start = clock();
// int n = sizeof(quickSort_arr) / sizeof(quickSort_arr[0]);
// quickSort(quickSort_arr, 0, n-1);
// clock_t quick_end = clock();
// printf("Quick sort time: %f seconds\n", (double)(quick_end - quick_start) / CLOCKS_PER_SEC);
return 0;
}
python版代码:
import random
import time
# 冒泡排序: Bubble sort time: 663.5839667320251 seconds
def bubble_sort(arr):
n = len(arr)
for i in range(n):
for j in range(0, n - i - 1):
if arr[j] > arr[j + 1]:
arr[j], arr[j + 1] = arr[j + 1], arr[j]
return arr
# 选择排序: Selection sort time: 285.8419885635376 seconds
def selection_sort(arr):
n = len(arr)
for i in range(n):
min_idx = i
for j in range(i+1, n):
if arr[j] < arr[min_idx]:
min_idx = j
arr[i], arr[min_idx] = arr[min_idx], arr[i]
return arr
# 插入排序:
def insertion_sort(arr):
n = len(arr)
for i in range(1, n):
key = arr[i]
j = i - 1
while j >= 0 and key < arr[j]:
arr[j + 1] = arr[j]
j -= 1
arr[j + 1] = key
return arr
# 归并排序: Merge sort time: 0.539679765701294 seconds
def merge_sort(arr):
if len(arr) > 1:
mid = len(arr) // 2
L = arr[:mid]
R = arr[mid:]
merge_sort(L)
merge_sort(R)
i = j = k = 0
while i < len(L) and j < len(R):
if L[i] < R[j]:
arr[k] = L[i]
i += 1
else:
arr[k] = R[j]
j += 1
k += 1
while i < len(L):
arr[k] = L[i]
i += 1
k += 1
while j < len(R):
arr[k] = R[j]
j += 1
k += 1
return arr
# 快速排序: Quick sort time: 0.31060314178466797 seconds
def partition(arr, low, high):
i = (low-1)
pivot = arr[high]
for j in range(low, high):
if arr[j] < pivot:
i = i+1
arr[i], arr[j] = arr[j], arr[i]
arr[i+1], arr[high] = arr[high], arr[i+1]
return (i+1)
def quick_sort(arr, low, high):
if low < high:
pi = partition(arr, low, high)
quick_sort(arr, low, pi-1)
quick_sort(arr, pi+1, high)
return arr
# 堆排序
def heapify(arr, n, i):
largest = i
left = 2 * i + 1
right = 2 * i + 2
if left < n and arr[largest] < arr[left]:
largest = left
if right < n and arr[largest] < arr[right]:
largest = right
if largest != i:
arr[i], arr[largest] = arr[largest], arr[i]
heapify(arr, n, largest)
def heap_sort(arr):
n = len(arr)
# 构建大顶堆
for i in range(n // 2 - 1, -1, -1):
heapify(arr, n, i)
# 逐步将堆顶元素与末尾元素交换并重新调整堆
for i in range(n - 1, 0, -1):
arr[i], arr[0] = arr[0], arr[i]
heapify(arr, i, 0)
return arr
# 生成随机数组
data = [random.randint(0, 1000000) for _ in range(100000)]
# 冒泡排序 Bubble sort time: 663.5839667320251 seconds
start_time = time.time()
bubble_sorted = bubble_sort(data.copy())
bubble_time = time.time() - start_time
print("Bubble sort time:", bubble_time, "seconds")
#
# 选择排序 Selection sort time: 285.8419885635376 seconds
start_time = time.time()
selection_sorted = selection_sort(data.copy())
selection_time = time.time() - start_time
print("Selection sort time:", selection_time, "seconds")
#
# 插入排序 Insertion sort time: 396.2825345993042 seconds
start_time = time.time()
insertion_sorted = insertion_sort(data.copy())
insertion_time = time.time() - start_time
print("Insertion sort time:", insertion_time, "seconds")
#
# 归并排序 Merge sort time: 0.539679765701294 seconds
start_time = time.time()
merge_sorted = merge_sort(data.copy())
merge_time = time.time() - start_time
print("Merge sort time:", merge_time, "seconds")
#
# 快速排序 Quick sort time: 0.31060314178466797 seconds
start_time = time.time()
quick_sorted = quick_sort(data.copy(), 0, len(data) - 1)
quick_time = time.time() - start_time
print("Quick sort time:", quick_time, "seconds")
# 堆排序 heap_sorted time: heap_sorted time: 0.8571550846099854 seconds
start_time = time.time()
heap_sorted = heap_sort(data.copy())
heap_sorted_time = time.time() - start_time
print("heap_sorted time:", heap_sorted_time, "seconds")
结果对比:
不仅是算法上,C与python的执行效率上都有区别 (实验存在偶然性,本文提供代码可以自己验证)
绘图代码:
import matplotlib.pyplot as plt
algorithms_c = ['Bubble Sort',
'Selection Sort',
'Insertion Sort',
'Merge Sort',
'Quick Sort',
'Heap Sort']
times_c = ['21.614000',
'4.120000',
'2.663000',
'0.035000',
'0.010000',
'0.015000']
algorithms_python = ['Bubble Sort',
'Selection Sort',
'Insertion Sort',
'Merge Sort',
'Quick Sort',
'Heap Sort']
times_python = ['663.583',
'285.841',
'396.282',
'0.539',
'0.310',
'0.857']
plt.figure(figsize=(25, 12))
plt.subplot(1, 2, 1)
plt.bar(algorithms_c, times_c)
plt.xlabel('Sorting Algorithms')
plt.ylabel('Time (seconds)')
plt.title('Comparison of Sorting Algorithms')
plt.xticks(rotation=45)
plt.title('Inference Time of Sorting Algorithms in C')
plt.subplot(1,2,2)
plt.bar(algorithms_c, times_c,color='red')
plt.xlabel('Sorting Algorithms')
plt.ylabel('Time (seconds)')
plt.title('Comparison of Sorting Algorithms')
plt.xticks(rotation=45)
plt.title('Inference Time of Sorting Algorithms in Python')
plt.show()
【排序算法】八种排序算法可视化过程_哔哩哔哩_bilibili