注意理解`纯函数` `函数组合` `point-free风格`是如何实现的
时间: 2023-10-23 18:14:55 浏览: 31
纯函数是指在相同的输入条件下,总是返回相同的输出结果,且不会对外部环境产生副作用的函数。这种函数的实现方式是避免在函数中使用全局变量、修改参数等,保证函数内部的计算只依赖于其输入参数。
函数组合是指将多个函数按照一定的顺序组合起来,使得它们的输出结果可以作为下一个函数的输入参数。这种方式可以将多个功能单一的函数组合成一个复杂的函数,提高代码的可读性和可维护性。
Point-free风格是指在编写函数时,不显式地指定函数的参数,而是通过函数的组合来实现参数的传递。这种方式可以使得函数更加易于组合,减少不必要的参数传递,提高代码的简洁性和可读性。
这些概念的实现方式主要是通过函数式编程语言提供的语法特性和函数库来实现的,比如JavaScript中的箭头函数、高阶函数、柯里化等。在实际编程中,可以通过使用这些语法特性和函数库来编写符合纯函数、函数组合和point-free风格的代码。
相关问题
遗传算法求函数最值(C语言实现)
好的,以下是一个遗传算法求函数最值的 C 语言实现代码示例:
```c
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <math.h>
// 遗传算法相关参数
#define POP_SIZE 100 // 种群大小
#define GEN_NUM 100 // 迭代次数
#define CROSSOVER_RATE 0.8 // 交叉概率
#define MUTATION_RATE 0.01 // 变异概率
#define ELITISM 1 // 精英选择
// 函数相关参数
#define X_LOWER_BOUND -10 // 自变量下界
#define X_UPPER_BOUND 10 // 自变量上界
// 目标函数
double target_func(double x) {
return sin(x) * x;
}
// 随机生成一个染色体
double* generate_chromosome() {
double* chromosome = (double*)malloc(sizeof(double));
chromosome[0] = X_LOWER_BOUND + (double)rand() / RAND_MAX * (X_UPPER_BOUND - X_LOWER_BOUND);
return chromosome;
}
// 计算染色体的适应度
double calculate_fitness(double* chromosome) {
double x = chromosome[0];
return target_func(x);
}
// 选择操作
void selection(double** population, double** new_population) {
int i, j;
double fitness_sum = 0.0;
double* fitness = (double*)malloc(sizeof(double) * POP_SIZE);
// 计算所有染色体的适应度总和
for (i = 0; i < POP_SIZE; ++i) {
fitness[i] = calculate_fitness(population[i]);
fitness_sum += fitness[i];
}
// 轮盘赌选择
for (i = 0; i < POP_SIZE; ++i) {
double rand_num = (double)rand() / RAND_MAX * fitness_sum;
double cumulative_fitness = 0.0;
for (j = 0; j < POP_SIZE; ++j) {
cumulative_fitness += fitness[j];
if (rand_num <= cumulative_fitness) {
new_population[i][0] = population[j][0];
break;
}
}
}
free(fitness);
}
// 交叉操作
void crossover(double** population, double** new_population) {
int i, j;
for (i = 0; i < POP_SIZE; i += 2) {
double rand_num = (double)rand() / RAND_MAX;
if (rand_num < CROSSOVER_RATE) {
int crossover_point = rand() % (sizeof(double) * 8);
double temp = population[i][0];
population[i][0] = (population[i][0] & ((-1 << crossover_point))) | (population[i + 1][0] & ((1 << crossover_point) - 1));
population[i + 1][0] = (population[i + 1][0] & ((1 << crossover_point) - 1)) | (temp & ((-1 << crossover_point)));
}
new_population[i][0] = population[i][0];
new_population[i + 1][0] = population[i + 1][0];
}
}
// 变异操作
void mutation(double** population, double** new_population) {
int i, j;
for (i = 0; i < POP_SIZE; ++i) {
double rand_num = (double)rand() / RAND_MAX;
if (rand_num < MUTATION_RATE) {
int mutation_point = rand() % (sizeof(double) * 8);
population[i][0] = population[i][0] ^ (1 << mutation_point);
}
new_population[i][0] = population[i][0];
}
}
// 精英选择
void elitism(double** population, double** new_population) {
int i, j;
int best_chromosome_index = 0;
double best_fitness = calculate_fitness(population[0]);
// 找到当前种群中适应度最好的染色体
for (i = 1; i < POP_SIZE; ++i) {
double fitness = calculate_fitness(population[i]);
if (fitness > best_fitness) {
best_chromosome_index = i;
best_fitness = fitness;
}
}
// 将最好的染色体复制到下一代种群中
for (i = 0; i < ELITISM; ++i) {
new_population[i][0] = population[best_chromosome_index][0];
}
}
int main() {
int i, j;
double** population = (double**)malloc(sizeof(double*) * POP_SIZE);
double** new_population = (double**)malloc(sizeof(double*) * POP_SIZE);
// 随机初始化种群
for (i = 0; i < POP_SIZE; ++i) {
population[i] = generate_chromosome();
new_population[i] = (double*)malloc(sizeof(double));
}
// 迭代
for (i = 0; i < GEN_NUM; ++i) {
selection(population, new_population);
crossover(population, new_population);
mutation(population, new_population);
elitism(population, new_population);
// 将下一代种群复制回当前种群
for (j = 0; j < POP_SIZE; ++j) {
population[j][0] = new_population[j][0];
}
}
// 找到适应度最好的染色体
int best_chromosome_index = 0;
double best_fitness = calculate_fitness(population[0]);
for (i = 1; i < POP_SIZE; ++i) {
double fitness = calculate_fitness(population[i]);
if (fitness > best_fitness) {
best_chromosome_index = i;
best_fitness = fitness;
}
}
// 输出结果
printf("x = %lf, f(x) = %lf\n", population[best_chromosome_index][0], best_fitness);
// 释放内存
for (i = 0; i < POP_SIZE; ++i) {
free(population[i]);
free(new_population[i]);
}
free(population);
free(new_population);
return 0;
}
```
该示例代码实现了一个简单的遗传算法,用于求解一个函数的最大值。通过多次迭代,遗传算法能够不断优化种群,逐渐接近函数的最大值。在本例中,我们以 $y = \sin(x) \times x$ 为目标函数,对 $x$ 进行优化,其中 $x$ 的范围为 $[-10, 10]$。在初始化种群后,算法进行一系列选择、交叉和变异操作,最终得到适应度最好的染色体,即对应的 $x$ 值,即为函数的最大值点。
遗传算法求函数最值(c语言实现
好的,我可以为您提供一个遗传算法求函数最值的C语言实现。下面是代码:
```c
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <math.h>
#define POP_SIZE 100 // 种群数量
#define GENES_LEN 6 // 基因长度
#define CROSSOVER_RATE 0.7 // 交叉概率
#define MUTATION_RATE 0.001 // 变异概率
#define MAX_GENERATION 1000 // 最大迭代次数
// 随机生成一个二进制基因
int *generate_genes() {
int *genes = (int *)malloc(GENES_LEN * sizeof(int));
for (int i = 0; i < GENES_LEN; i++) {
genes[i] = rand() % 2;
}
return genes;
}
// 计算二进制基因所代表的十进制数值
double decode(int *genes) {
double value = 0.0;
for (int i = 0; i < GENES_LEN; i++) {
value += genes[i] * pow(2, GENES_LEN - 1 - i);
}
return value;
}
// 计算目标函数的值
double fitness(double x) {
return sin(10 * M_PI * x) / (2 * x) + pow(x - 1, 4);
}
// 计算种群中每个个体的适应度
double *calculate_fitness(int **pop) {
double *fitness_values = (double *)malloc(POP_SIZE * sizeof(double));
for (int i = 0; i < POP_SIZE; i++) {
double x = decode(pop[i]);
fitness_values[i] = fitness(x);
}
return fitness_values;
}
// 从种群中选择两个个体进行交叉
void crossover(int *parent1, int *parent2, int *child1, int *child2) {
if ((double)rand() / RAND_MAX < CROSSOVER_RATE) {
int crossover_point = rand() % GENES_LEN;
for (int i = 0; i < crossover_point; i++) {
child1[i] = parent1[i];
child2[i] = parent2[i];
}
for (int i = crossover_point; i < GENES_LEN; i++) {
child1[i] = parent2[i];
child2[i] = parent1[i];
}
} else {
for (int i = 0; i < GENES_LEN; i++) {
child1[i] = parent1[i];
child2[i] = parent2[i];
}
}
}
// 对个体进行变异
void mutate(int *genes) {
for (int i = 0; i < GENES_LEN; i++) {
if ((double)rand() / RAND_MAX < MUTATION_RATE) {
genes[i] = !genes[i];
}
}
}
// 选择一个个体
int *select(double *fitness_values, int **pop) {
double sum = 0.0;
for (int i = 0; i < POP_SIZE; i++) {
sum += fitness_values[i];
}
double r = (double)rand() / RAND_MAX * sum;
double s = 0.0;
for (int i = 0; i < POP_SIZE; i++) {
s += fitness_values[i];
if (s >= r) {
return pop[i];
}
}
return pop[POP_SIZE - 1];
}
// 打印最优解
void print_best(double best_x, double best_fitness, int generation) {
printf("Generation %d: x = %lf, f(x) = %lf\n", generation, best_x, best_fitness);
}
int main() {
srand(time(NULL));
// 初始化种群
int **pop = (int **)malloc(POP_SIZE * sizeof(int *));
for (int i = 0; i < POP_SIZE; i++) {
pop[i] = generate_genes();
}
// 开始迭代
double best_fitness = -1e100;
double best_x = 0.0;
for (int generation = 1; generation <= MAX_GENERATION; generation++) {
double *fitness_values = calculate_fitness(pop);
// 计算种群中最优解
for (int i = 0; i < POP_SIZE; i++) {
double x = decode(pop[i]);
double f = fitness(x);
if (f > best_fitness) {
best_fitness = f;
best_x = x;
}
}
print_best(best_x, best_fitness, generation);
// 新种群
int **new_pop = (int **)malloc(POP_SIZE * sizeof(int *));
for (int i = 0; i < POP_SIZE; i++) {
// 选择两个个体进行交叉
int *parent1 = select(fitness_values, pop);
int *parent2 = select(fitness_values, pop);
int *child1 = (int *)malloc(GENES_LEN * sizeof(int));
int *child2 = (int *)malloc(GENES_LEN * sizeof(int));
crossover(parent1, parent2, child1, child2);
// 对交叉后的两个个体进行变异
mutate(child1);
mutate(child2);
new_pop[i] = child1;
new_pop[i + 1] = child2;
}
// 释放旧种群
for (int i = 0; i < POP_SIZE; i++) {
free(pop[i]);
}
free(pop);
// 更新种群
pop = new_pop;
free(fitness_values);
}
return 0;
}
```
这个程序使用遗传算法来求解一个函数的最值。其中,种群数量为100,每个个体的基因长度为6位,交叉概率为0.7,变异概率为0.001,最大迭代次数为1000次。您可以根据需要进行修改。