【题目10】基本的排序算法

解题思路：排序算法有很多种，插入排序，冒泡排序，希尔排序（ShellSort)，快速

排序，堆排序，归并排序，基排序等。作为一名软件开发人员，需要能够自己动手实

现这些算法，掌握这些算法的思想，以及这些算法的时间复杂度，空间复杂度。虽然

很时候，在实际的工作中，有库函数可以提供给我们使用，但是我们不仅要知其然更

要知其所以然，掌握了它了，或许以后你的程序需要优化的时候会派的上用场呢。

 

说明： 这里的大部分代码都摘自《数据结构与算法分析---C语言描述》。对于大牛写

的代码，不得不膜拜啊。。。

 

1. 插入排序，时间复杂度0（n^2)

#include <stdio.h>void InsertionSort(int *a, int len){int i,j;int tmp;for( i = 1; i < len; i++){tmp = a[i];for(j = i; j > 0 && a[j-1] > tmp; --j)a[j] = a[j-1];a[j] = tmp;}}void Print(int* a, int len){for(int i = 0; i < len; i++)printf("%d ", a[i]);printf("/n");}int main(){int a[5] = {3, 1, 7, 2, 4};int len = sizeof(a)/sizeof(int);Print(a,len);InsertionSort(a, len); Print(a,len);return 0;}

2. 冒泡排序，时间复杂度O（n^2),没有优化

void BubbleSort(int *a, int len){for(int i = 0; i < len; i++){int tmp = a[i];for(int j = i+1; j < len; j++){if(a[j] < a[i]){a[i] = a[j];a[j] = tmp;}}}}

3. 希尔排序

void ShellSort(int *a,int len){int tmp;for(int inc = len/2; inc > 0; inc /= 2)for(int i = inc; i < len; i++){tmp = a[i];for(int j = i; j >= inc; j -= inc)if(tmp < a[j - inc])a[j] = a[j - inc];else break;a[j] = tmp;}}

4. 堆排序

#define LeftChild(i) (2*i + 1) //因为它是从位置0开始的void Swap(int* a, int *b){int tmp = *a;*a = *b;*b = tmp;}void PercDown(int *a, int i, int len){int child;int tmp;for(tmp = a[i]; LeftChild(i) < len; i = child){child = LeftChild(i);if(child != len -1 && a[child + 1] > a[child])child++;if(tmp < a[child])a[i] = a[child]; else break;}a[i] = tmp;}void HeapSort(int* a, int len){int i;for( i = len/2; i >= 0; i--)PercDown(a,i,len); //建堆for( i = len -1; i > 0; i--){Swap(&a[0],&a[i]);PercDown(a,0,i); //调堆}}

5. 归并排序

void Merge(int *a, int *tmpArr, int lPos, int rPos, int rightEnd){int i, leftEnd, numElements, tmpPos;leftEnd = rPos - 1;tmpPos = lPos;numElements = rightEnd - lPos + 1;while(lPos <= leftEnd && rPos <= rightEnd)if(a[lPos] <= a[rPos])tmpArr[tmpPos++] = a[lPos++];elsetmpArr[tmpPos++] = a[rPos++];while(lPos <= leftEnd)tmpArr[tmpPos++] = a[lPos++];while(rPos <= rightEnd)tmpArr[tmpPos++] = a[rPos++];for(i = 0; i < numElements; i++, rightEnd--)a[rightEnd] = tmpArr[rightEnd];}void MSort(int*a, int *tmpArr,int left, int right){int mid;if(left < right){mid = (left + right) /2;MSort(a, tmpArr, left, mid);MSort(a, tmpArr, mid + 1, right);Merge(a, tmpArr, left, mid+1, right);}}void MergeSort(int* a, int len){int *tmpArr;tmpArr = (int*)malloc(len*sizeof(int));if(tmpArr != NULL){MSort(a,tmpArr,0, len-1);free(tmpArr);}elseprintf("Alloc memory failed!");}

6.快速排序

int Median3(int *a, int left, int right){int mid = (left + right)/2;if(a[left] > a[mid])Swap(&a[left],&a[right]);if(a[left] > a[right])Swap(&a[left],&a[right]);if(a[mid] > a[right])Swap(&a[mid],&a[right]);Swap(&a[mid], &a[right -1]);return a[right-1];}#define Cutoff 3void QSort(int *a, int left, int right){int i, j;int pivot;if(left + Cutoff <= right){pivot = Median3(a, left, right);i = left;j = right - 1;for( ; ; ){while(a[++i] < pivot){}while(a[--j] > pivot){}if(i < j)Swap(&a[i],&a[j]);elsebreak;}Swap(&a[i], &a[right-1]);QSort(a,left,i-1);QSort(a,i+1, right);}elseInsertionSort(a+left, right - left +1 );}void QuickSort(int *a, int len){QSort(a, 0, len-1);}