插入排序

概述

对于少量元素的排序,插入排序是一个有效的算法.对于元素的排序,使用插入排序就像排序手中的扑克牌一样.

伪代码

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INSERTION-SORT(A)
for j = 2 to A.length
    key = A[j]
    // Insert A[j] into the sorted sequence A[1..j-1].
    i = j - 1
    while i > 0 and A[i] > key
        A[i+1] = A[i]
        i = i - 1
    A[i + 1] = key

循环不变式

初始化: 循环的第一次迭代之前,它为真.
保持: 如果循环的某次迭代之前它为真,那么下次迭代之前它仍为真.
终止: 在循环终止时,不变式为我们提供了一个有用的性质,该性质有助于证明算法是正确的.

代码实现

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/* a file named insertion-sort.c  */

#include <stdio.h>

void insertionSort(int *a,int num);
void printNum(int *a,int num);

void printNum(int *a,int num)
{
    int i;
    for(i = 0; i < num; i++){
        printf("%d ",a[i]);
    }
    printf("\n");
}

void insertionSort(int *a,int num)
{
    int i, j, key;
    for(j = 1; j < num; j++){
        key = a[j];
        i = j - 1;
        while(i >= 0 && a[i] > key){
            a[i + 1] = a[i];
            i = i - 1;
        }
        a[i+1]=key;
    }
}

int main()
{
    int n;
    int a[]={5,2,4,6,1,3};
    n = sizeof(a) / sizeof(a[0]);

    printf("insertion sort before: ");
    printNum(a,n);

    insertionSort(a,n);

    printf("insertion sort after: ");
    printNum(a,n);

    return 0;
}

编译并运行:

haha@hello:~/.../test-code$ gcc -g -o insertion-sort insertion-sort.c
haha@hello:~/.../test-code$ ./insertion-sort
insertion sort before: 5 2 4 6 1 3
insertion sort after: 1 2 3 4 5 6
haha@hello:~/.../test-code$