First, select the sorting Introduction
Selection Sort (Selection sort) is a straightforward sorting algorithm. First, find the smallest sequence of unsorted (large) element, the starting position is stored in the sorted sequence, and then continue to find the minimum (large) element from the remaining elements of unsorted and sorted into the end of the sequence. And so on, until all the elements are sorted.
The main advantage of the selection sort data related to the movement. If an element is in the correct final position, it will not be moved. Exchange of each selection sort the elements, at least one of them will be moved to its final position, therefore the table to sort n elements for a total of at most n-1 secondary exchange. In all entirely dependent on the switching elements to move in the sorting method, selection sort belonging to one kind of very good.
Second, the choice of ordering principle
- In unsorted sequence finding the minimum (large) element, the starting position is stored in the sorted sequence
- And then from the remaining unsorted continue to search for the minimum (large) element element
- Then put the sorted sequence at the end. And so on, until all the elements are sorted.
Third, the select sort illustrated
Fourth, select the sort summary
- There are N data, the need has never been the sort area selected N-1 times the data has been sorted on the tail area
- Every region has never been the sort selected data to be sorted in the tail
Fifth, the selection sort of python code implementation
# 定义选择排序函数 def selection_sort(list): # 计算需要排序的列表元素个数 N = len(list) # 需要N-1次选择操作 for i in range(N-1): # 记录最小值的小标 minNum_index = i # 未排序区域从i+1到末尾N处，属于未排序区，在未排序区在选出最小值处 for j in range(i+1,N): # 比较大小 if list[minNum_index]>list[j]: #交换 temp = list[minNum_index] list[minNum_index] = list[j] list[j] = temp # 创建一个列表 numList = [19,2,13,8,34,25,7] print("排序前：%s"%numList) # 调用选择排序 selection_sort(numList) print("排序后：%s"%numList)
运行结果为：
排序前：[19, 2, 13, 8, 34, 25, 7]
排序后：[2, 7, 8, 13, 19, 25, 34]
六、选择排序的C语言代码实现
版本一
#include <stdio.h> //定义选择排序函数 void selection_sort(int array[],int arrayLenght) { // 需要N-1次选择操作 for (int i=0; i<arrayLenght-1; i++) { // 记录最小值的下标 int minNum_index = i; // 未排序区域从i+1到末尾N处，属于未排序区，在未排序区再选出最小值处 for (int j = i+1; j<arrayLenght; j++) { // 比较大小 if (array[minNum_index]>array[j]) { // 交换 int temp = array[minNum_index]; array[minNum_index] = array[j]; array[j] = temp; } } } } int main(int argc, const char * argv[]) { // 选择排序函数声明 void selection_sort(int array[],int arrayLenght); // 创建数组 int numArray[] = {19,2,13,8,34,25,7}; // 调用排序 selection_sort(numArray, 7); // 验证 for (int i =0; i<7; i++) { printf("%d ",numArray[i]); } return 0; }
运行结果为：
2 7 8 13 19 25 34
版本二
#include <stdio.h> //定义选择排序函数 void selection_sort1(int array[],int arrayLenght) { // 需要N-1次选择操作 for (int i=0; i<arrayLenght-1; i++) { // 记录最小值的下标 int minNum_index = i; // 未排序区域从i+1到末尾N处，属于未排序区，在未排序区再选出最小值处 for (int j = i+1; j<arrayLenght; j++) { // 比较大小 if (array[minNum_index]>array[j]) { minNum_index = j; } } if (minNum_index != i) { int temp = array[i]; array[i] = array[minNum_index]; array[minNum_index] = temp; } } } int main(int argc, const char * argv[]) { // 选择排序函数声明 void selection_sort1(int array[],int arrayLenght); // 创建数组 int numArray[] = {19,2,13,8,34,25,7}; // 调用排序 selection_sort1(numArray, 7); // 验证 for (int i =0; i<7; i++) { printf("%d ",numArray[i]); } return 0; }
运行结果为：
2 7 8 13 19 25 34
七、选择排序的时间复杂度
- 最优时间复杂度：O(n2)
- 最坏时间复杂度：O(n2)
八、选择排序的稳定性
选择排序是给每个位置选择当前元素最小的，比如给第一个位置选择最小的，在剩余元素里面给第二个元素选择第二小的，依次类推，直到第n-1个元素，第n个元素不用选择了，因为只剩下它一个最大的元素了。那么，在一趟选择，如果一个元素比当前元素小，而该小的元素又出现在一个和当前元素相等的元素后面，那么交换后稳定性就被破坏了。比较拗口，举个例子，序列5 8 5 2 9，我们知道第一遍选择第1个元素5会和2交换，那么原序列中两个5的相对前后顺序就被破坏了，所以选择排序是一个不稳定的排序算法。