算法导论代码　第5章　概率分析和随机算法

第5章 概率分析和随机算法

5.1 雇用问题

#include <stdlib.h>
#include <stdio.h>
#include <time.h>
void hire_assistant(int A[], int n)
{
int best = 0;
printf("hire:");
for (int i = 0; i < n; i++) {
if (A[i] > best) {
best = A[i];
printf("%d ", i);
}
}
printf("\n");
}

int main()
{
srand((unsigned)time(NULL));
int a[10];
for (int i = 0; i < 10; i++) {
a[i] = rand() % 100;
printf("%d ", a[i]);
}
printf("\n");
hire_assistant(a, 10);
return 0;
}

5.3 随机算法

5.3.1 通过排序产生随机排列数组

#include <stdio.h>
#include <limits.h>
#include <string.h>
#include <stdlib.h>
#include <time.h>
void merge(void *base, size_t elem_size, size_t left, size_t middle,
size_t right, void *max, int (*comp) (const void *, const void *),
void *buff)
{
char *cbase = base;
char *cbuff = buff;
size_t left_length = middle - left + 1;
size_t right_length = right - middle;
char *left_buff = cbuff;
char *right_buff = &cbuff[(left_length + 1) * elem_size];
for (size_t i = 0; i < left_length; i++) {
memcpy(&left_buff[i * elem_size],
&cbase[(left + i) * elem_size], elem_size);
}
memcpy(&left_buff[left_length * elem_size], max, elem_size);
for (size_t i = 0; i < right_length; i++) {
memcpy(&right_buff[i * elem_size],
&cbase[(middle + 1 + i) * elem_size], elem_size);
}
memcpy(&right_buff[right_length * elem_size], max, elem_size);
for (size_t k = left, i = 0, j = 0; k <= right; k++) {
if (comp(&left_buff[i * elem_size], &right_buff[j * elem_size])
<= 0) {
memcpy(&cbase[k * elem_size], &left_buff[i * elem_size],
elem_size);
i++;
} else {
memcpy(&cbase[k * elem_size],
&right_buff[j * elem_size], elem_size);
j++;
}
}
}

void merge_sort_buff(void *base, size_t elem_size, size_t left, size_t right,
void *max, int (*comp) (const void *, const void *),
void *buff)
{
if (left < right) {
size_t middle = (left + right) / 2;
merge_sort_buff(base, elem_size, left, middle, max, comp, buff);
merge_sort_buff(base, elem_size, middle + 1, right, max, comp,
buff);
merge(base, elem_size, left, middle, right, max, comp, buff);
}
}

void merge_sort(void *base, size_t elem_size, size_t left, size_t right,
void *max, int (*comp) (const void *, const void *))
{
if (left >= right)
return;
size_t length = right - left + 1;	/*数组的长度 */
char buff[(length + 2) * elem_size];	/*+2是因为要在缓存保存两个最大值 */
merge_sort_buff(base, elem_size, left, right, max, comp, buff);
}

struct rand_data {
int rand_num;
void *data;		/*挷定了一个数据的指针 */
};
int cmp_data(const void *p1, const void *p2)
{
const struct rand_data *pa = p1;
const struct rand_data *pb = p2;
return pa->rand_num - pb->rand_num;
}

void permute_by_sorting(void *base, size_t elem_size, int length)
{
char *cbase = base;
/*把原来的数组复制一份 */
char data_copy[elem_size * length];
memcpy(data_copy, base, elem_size * length);
struct rand_data rand_data_array[length];
for (int i = 0; i < length; i++) {
rand_data_array[i].rand_num =
rand() % (length * length * length);
rand_data_array[i].data = &data_copy[i * elem_size];
}
struct rand_data data_max = { INT_MAX, NULL };
merge_sort(rand_data_array, sizeof(struct rand_data), 0, length - 1,
&data_max, cmp_data);
/*根据按随机数排序的结果把数据复制回原来的数组 */
for (int i = 0; i < length; i++) {
memcpy(&cbase[i * elem_size], rand_data_array[i].data,
elem_size);
}
}

void randomized_hire_assistant(int A[], int length)
{
permute_by_sorting(A, sizeof(int), length);
printf("hire:");
int best = 0;
for (int i = 0; i < length; i++) {
if (A[i] > best) {
best = A[i];
printf("%d ", i);
}
}
printf("\n");
}

int main()
{
srand((unsigned)time(NULL));
int a[10];
for (int i = 0; i < 10; i++) {
a[i] = i;
}
randomized_hire_assistant(a, 10);
return 0;
}

5.3.2 通过原地排列产生随机排列数组

#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <string.h>
void swap(void *a, void *b, size_t elem_size)
{
if(a==NULL||b==NULL||a==b)
return;
char temp[elem_size];	/*变长数组 */
memcpy(temp, a, elem_size);
memcpy(a, b, elem_size);
memcpy(b, temp, elem_size);
}
void randomized_in_place(void *array, size_t elem_size, int length)
{
char *carray = array;
for (int i = 0; i < length; i++) {
int rand_index = rand() % (length - i) + i;
swap(&carray[i * elem_size], &carray[rand_index * elem_size],
elem_size);
}
}

void randomized_hire_assistant(int A[], int n)
{
randomized_in_place(A, sizeof(int), n);
int best = 0;
printf("hire:");
for (int i = 0; i < n; i++) {
if (A[i] > best) {
best = A[i];
printf("%d ", i);
}
}
printf("\n");
}

int main()
{
srand((unsigned)time(NULL));
int a[10];
for (int i = 0; i < 10; i++) {
a[i] = i;
}
randomized_hire_assistant(a, 10);
return 0;
}

5.4.4 在线雇用问题

#include <stdio.h>
#include <stdbool.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include <string.h>
#include <limits.h>
int on_line_maximum(int A[], int n, int k)
{
int best_score = -INT_MAX;
for (int i = 0; i < k; i++) {
if (A[i] > best_score) {
best_score = A[i];
}
}
for (int i = k; i < n; i++) {
if (A[i] > best_score) {
return i;
}
}
return n - 1;
}

int main()
{
srand((unsigned)time(NULL));
int a[10];
for (int i = 0; i < 10; i++) {
a[i] = rand() % 100;
}
int n = on_line_maximum(a, 10, 10 / exp(1.0));
/*测试n是不是最好的*/
bool flag = true;
for (int i = 0; i < 10; i++) {
if (a[i] > a
) {
flag = false;
}
}
printf("%s\n",flag?"true":"false");
return 0;
}