归并排序

归并排序

归并排序是将一个序列逐次对半分组直到数组元素为1，然后逐次两两合并分组直至成一个序列。

在逐次两两合并分组时需要一个临时的buffer。

参考百度百科：http://baike.baidu.com/link?url=OD11jIUEKqkbhY9w0loP9FFlLipaxfq6WkBZo1_O9MMuGMcn3h3rqWoZ0l7hMDKJOQrDlVPf9ELLsLijxSHs6ZapL-BMVl6k9ZEQIIyLOvVXVhm-gQEg9Y_TYwPZGFTZ

递归调用

归并排序的递归调用c代码如下：

void MergePartition_Recursion (int * const piSrc, const int start, const int mid, const int end, int * const piTemp){    int i = start;    int iEnd = mid;    int j = mid + 1;    int jEnd = end;    int k = 0;    while (i<=iEnd && j<=jEnd)    {        if (piSrc[i] > piSrc[j])            piTemp [k++] = piSrc [j++];        else            piTemp [k++] = piSrc [i++];    }    while (i <= iEnd)        piTemp [k++] = piSrc [i++];    while (j <= jEnd)        piTemp [k++] = piSrc [j++];    i = 0;    while (i < k)    {        piSrc [i+start] = piTemp [i];        i ++;    }}void MergeSort_Recursion (int * const pia, const int start, const int end, int * const piTemp){    int mid;    if (start < end)    {        mid = (start + end) >> 1;        MergeSort_Recursion(pia, start, mid, piTemp);        MergeSort_Recursion(pia, mid+1, end, piTemp);        MergePartition_Recursion (pia, start, mid, end, piTemp);    }}

注释：

1. 代码中用到了递归；

2. 在MergePartition_Recursion中将合并数据拷贝到piSrc时，下标是从start开始的；

c完整代码：

#include <stdio.h>#include <stdlib.h>#include<windows.h>void MergePartition_Recursion (int * const piSrc, const int start, const int mid, const int end, int * const piTemp){    int i = start;    int iEnd = mid;    int j = mid + 1;    int jEnd = end;    int k = 0;    while (i<=iEnd && j<=jEnd)    {        if (piSrc[i] > piSrc[j])            piTemp [k++] = piSrc [j++];        else            piTemp [k++] = piSrc [i++];    }    while (i <= iEnd)        piTemp [k++] = piSrc [i++];    while (j <= jEnd)        piTemp [k++] = piSrc [j++];    i = 0;    while (i < k)    {        piSrc [i+start] = piTemp [i];        i ++;    }}void MergeSort_Recursion (int * const pia, const int start, const int end, int * const piTemp){    int mid;    if (start < end)    {        mid = (start + end) >> 1;        MergeSort_Recursion(pia, start, mid, piTemp);        MergeSort_Recursion(pia, mid+1, end, piTemp);        MergePartition_Recursion (pia, start, mid, end, piTemp);    }}int testArray[] = {1,3,5,7,9,2,4,6,8,0, 54, 48, 2 , 5 , 8};//{5,5,5,5,5,5,5,5,5,5,5};//void PrintfIntArray (int * const pia, const int n){    int i;    for (i=0; i<n; i++)        printf("%u ", pia[i]);    printf("\n");}int main(){    DWORD startTime;    DWORD endTime;    int aiTemp[sizeof(testArray)/sizeof(testArray[0])];    printf("Hello world!\n");    startTime = GetTickCount ();    MergeSort_Recursion (testArray, 0, sizeof(testArray)/sizeof(int)-1, aiTemp);    endTime = GetTickCount();    printf ("Sort Time Consumption:%lu ms.\n", endTime-startTime);    PrintfIntArray (testArray, sizeof(testArray)/sizeof(int));    return 0;}

非递归调用

归并排序的递归调用，对栈的消耗还是不小的。根据《大话数据结构》P413页所述，递归深度为log2n，总空间复杂度为O(n+logn)。

参考此书，贴出非递归时的c代码如下：

基本思想是，从底向上两两合并，最开始是一个一个合并，逐次以2的整次幂合并。

 递归中MergePartition_Recursion函数中的k是0开始的，因为piTemp在函数MergePartition_Recursion中仅仅作为临时变量。

非递归中的MergePartition_Iteration函数中的k是从startIndex开始，因为piDest保存的内容没有拷贝到piSrc中。因此，在MergeSort_Iteration函数中piTemp和piSrc交替位置传参。

void MergePartition_Iteration (int * const piDest, const int startIndex, const int midIndex, const int endIndex, int * const piSrc){    int i = startIndex;    int iEnd = midIndex;    int j = iEnd + 1;    int jEnd = endIndex;    int k = startIndex;    while (i<=iEnd && j<=jEnd)    {        if (piSrc[i] > piSrc[j])            piDest[k++] = piSrc[j++];        else            piDest[k++] = piSrc[i++];    }    while (i <= iEnd)        piDest[k++] = piSrc[i++];    while (j <= jEnd)        piDest[k++] = piSrc[j++];}void MergeSort_SplitPartition (int * const piDest, const int splitNum, int * const piSrc, const int len){    int startIndex = 0;    if (NULL!=piDest && NULL!=piSrc)    {        if (splitNum)        {            while (startIndex < len-2*splitNum+1)            {                MergePartition_Iteration (piDest, startIndex, startIndex+splitNum-1, startIndex+2*splitNum-1, piSrc);                startIndex += 2*splitNum;            }            if (startIndex < len-splitNum)                MergePartition_Iteration (piDest, startIndex, startIndex+splitNum-1, len-1, piSrc);            else                while (startIndex < len)                {                    piDest[startIndex] = piSrc[startIndex];                    startIndex ++;                }        }    }}void MergeSort_Iteration (int * const piSrc, const int len, int * const piTemp){    int splitNum = 1;    while (splitNum < len)    {        MergeSort_SplitPartition (piTemp, splitNum, piSrc, len);        splitNum <<= 1;        MergeSort_SplitPartition (piSrc, splitNum, piTemp, len);        splitNum <<= 1;    }}