折半查找（分治法）

Binary search algorithm

折半查找也称为二分查找，是一个经典的查找算法。

原始数据使用随机函数生成。

采用结构化程序设计，可以很容易改为从标准输入或文件读入数据，只需要修改函数getData即可。

数据个数由宏定义给出，也可以轻松地改为输入。
使用快速排序算法对原始数据进行排序。

这里给出递归和非递归两种过程实现折半查找，非递归的折半查找为正解。

/*
* 折半查找算法程序（测试数据使用快速算法进行排序）
* 这里包括递归算法和非递归算法
*/

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

#include "quicksort.h"

#define N 7

void getData(int [], int);
void outputData(int [], int);
int binsearch1(int a[], int low, int high, int val);
int binsearch2(int a[], int low, int high, int val);

int main(void)
{
int a
, i;

getData(a, N); /* 获得数据放入数组a中 */

printf("Unordered datas: ");
outputData(a, N);

quicksort(a, 0, N - 1);

printf("In sorted order: ");
outputData(a, N);

int index, val;
scanf("%d", &val);
index = binsearch1(a, 0, N-1, val);
if(index == -1)
printf("There is no %d in array A.\n", val);
else
printf("%d is at the %dth unit is array A.\n", val, index);

index = binsearch2(a, 0, N-1, val);
if(index == -1)
printf("There is no %d in array A.\n", val);
else
printf("%d is at the %dth unit is array A.\n", val, index);

return 0;
}

int binsearch1(int a[], int low, int high, int val)
{
int mid;
if(low > high)
return -1;
else
{
mid = (low + high) / 2;
if(a[mid] == val)
return mid;
else if(val > a[mid])
return binsearch1(a, mid+1, high, val);
else /* if(val < a[mid]) */
return binsearch1(a, low, mid-1, val);
}
}

int binsearch2(int a[], int low, int high, int val)
{
int mid;

for(;;)
{
if(low > high)
return -1;
else
{
mid = (low + high) / 2;
if(a[mid] == val)
return mid;
else if(val > a[mid])
low = mid+1;
else /* if(val < a[mid]) */
high = mid-1;
}
}
}

void getData(int d[], int n)
{
time_t t;
srand((unsigned) time(&t));  /* 设置随机数起始值 */

int i;
for(i=0; i < n; i++)
d[i] = rand() % 1000; /* 获得0-999之间的整数值 */
}

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

关键代码：

// 非递归折半查找算法程序
int binsearch2(int a[], int low, int high, int val)
{
int mid;

for(;;)
{
if(low > high)
return -1;
else
{
mid = (low + high) / 2;
if(a[mid] == val)
return mid;
else if(val > a[mid])
low = mid+1;
else /* if(val < a[mid]) */
high = mid-1;
}
}
}

快速排序程序头文件quicksort.h:

void quicksort(int a[], int low, int high);
int split(int a[], int low, int high);

快速排序程序quicksort.c:

#include "quicksort.h"

void quicksort(int a[], int low, int high)
{
int middle;

if (low >= high)
return;
middle = split(a, low, high);
quicksort(a, low, middle - 1);
quicksort(a, middle + 1, high);
}

int split(int a[], int low, int high)
{
int part_element = a[low];

for (;;) {
while (low < high && part_element <= a[high])
high--;
if (low >= high) break;
a[low++] = a[high];

while (low < high && a[low] <= part_element)
low++;
if (low >= high) break;
a[high--] = a[low];
}

a[high] = part_element;

return high;
}