用c++写一个差分算法
时间: 2024-04-29 07:24:52 浏览: 18
好的,以下是一个基于 C 语言的差分算法的示例代码:
```
#include <stdio.h>
const int MAX_SIZE = 100;
void difference(int arr[], int n) {
int diff[MAX_SIZE];
diff[0] = arr[0];
for (int i = 1; i < n; ++i) {
diff[i] = arr[i] - arr[i - 1];
}
for (int i = 0; i < n; ++i) {
arr[i] = diff[i];
}
}
int main() {
int arr[] = {1, 3, 6, 10, 15};
int n = sizeof(arr) / sizeof(arr[0]);
difference(arr, n);
for (int i = 0; i < n; ++i) {
printf("%d ", arr[i]);
}
printf("\n");
return 0;
}
```
该算法的作用是将一维数组中每个元素与其前一个元素的差值保存到另一个数组中,最后用差分数组替换原数组,可以用于一些数列问题的求解。
相关问题
用C++写一个差分进化算法的实现
差分进化算法是一种全局优化算法,主要用于求解非线性优化问题。以下是用C++实现差分进化算法的示例代码:
```c++
#include <iostream>
#include <cstdlib>
#include <ctime>
#include <cmath>
using namespace std;
const int NP = 50; // 种群大小
const int NGEN = 1000; // 迭代次数
const double CR = 0.5; // 交叉概率
const double F = 0.5; // 缩放因子
double rand01() { return (double)rand() / (double)RAND_MAX; }
// 计算函数值,这里以Rastrigin函数为例
double func(double* x)
{
double sum = 0.0;
for (int i = 0; i < 20; i++) {
sum += x[i] * x[i] - 10.0 * cos(2.0 * M_PI * x[i]);
}
return 10.0 * 20.0 + sum;
}
int main()
{
srand((unsigned int)time(NULL));
// 初始化种群
double pop[NP][20];
for (int i = 0; i < NP; i++) {
for (int j = 0; j < 20; j++) {
pop[i][j] = rand01() * 10.0 - 5.0;
}
}
// 迭代
for (int i = 0; i < NGEN; i++) {
for (int j = 0; j < NP; j++) {
// 随机选择3个不同的个体
int r1, r2, r3;
do { r1 = rand() % NP; } while (r1 == j);
do { r2 = rand() % NP; } while (r2 == j || r2 == r1);
do { r3 = rand() % NP; } while (r3 == j || r3 == r1 || r3 == r2);
// 产生新解
double trial[20];
for (int k = 0; k < 20; k++) {
if (rand01() < CR) {
trial[k] = pop[r1][k] + F * (pop[r2][k] - pop[r3][k]);
}
else {
trial[k] = pop[j][k];
}
}
// 选择
double f = func(trial);
if (f < func(pop[j])) {
for (int k = 0; k < 20; k++) {
pop[j][k] = trial[k];
}
}
}
}
// 输出最优解
double best[20];
double minf = 1e10;
for (int i = 0; i < NP; i++) {
double f = func(pop[i]);
if (f < minf) {
minf = f;
for (int j = 0; j < 20; j++) {
best[j] = pop[i][j];
}
}
}
cout << "最优解:";
for (int i = 0; i < 20; i++) {
cout << best[i] << " ";
}
cout << "函数值:" << minf << endl;
return 0;
}
```
这个实现使用了Rastrigin函数作为优化目标,种群大小为50,迭代次数为1000次。在迭代过程中,对于每个个体,随机选择3个不同的个体产生新解,然后通过比较新解的函数值和原个体的函数值来进行选择。最终输出最优解和函数值。
用c++写一个用差分进化算法拟合分段连续线性数据
差分进化算法(Differential Evolution,DE)是一种基于群体智能的全局优化算法。它可以用于拟合分段连续线性数据。下面是用 C++ 编写的代码:
```
#include <iostream>
#include <vector>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <ctime>
using namespace std;
const double F = 0.8; // 缩放因子
const double CR = 0.6; // 交叉概率
const int NP = 50; // 种群大小
const int MAX_GEN = 100; // 最大迭代次数
const int DIM = 5; // 变量维数
struct Individual
{
vector<double> x; // 个体的参数向量
double fitness; // 适应度值
Individual(int dim)
{
x.resize(dim);
}
};
double func(vector<double> &x)
{
// 计算拟合误差
double error = 0;
double a, b;
for (int i = 0; i < x.size() - 2; i += 2)
{
a = x[i];
b = x[i + 1];
for (int j = (int)x[i]; j <= x[i + 2]; j++)
{
error += pow(j * b + a - x[i + 3], 2);
}
}
return error;
}
void init_population(vector<Individual> &pop, int dim)
{
srand(time(NULL));
for (int i = 0; i < NP; i++)
{
Individual ind(dim);
for (int j = 0; j < dim; j++)
{
ind.x[j] = rand() / double(RAND_MAX);
}
ind.fitness = func(ind.x);
pop.push_back(ind);
}
}
void mutation(vector<Individual> &pop, int dim)
{
for (int i = 0; i < NP; i++)
{
Individual &ind = pop[i];
int r1, r2, r3;
do
{
r1 = rand() % NP;
} while (r1 == i);
do
{
r2 = rand() % NP;
} while (r2 == i || r2 == r1);
do
{
r3 = rand() % NP;
} while (r3 == i || r3 == r1 || r3 == r2);
for (int j = 0; j < dim; j++)
{
double r = rand() / double(RAND_MAX);
if (r < CR)
{
ind.x[j] = pop[r1].x[j] + F * (pop[r2].x[j] - pop[r3].x[j]);
}
}
ind.fitness = func(ind.x);
}
}
void crossover(vector<Individual> &pop, int dim)
{
for (int i = 0; i < NP; i++)
{
Individual &ind = pop[i];
vector<double> x_new(dim);
for (int j = 0; j < dim; j++)
{
double r = rand() / double(RAND_MAX);
if (r < CR)
{
x_new[j] = ind.x[j];
}
else
{
x_new[j] = pop[rand() % NP].x[j];
}
}
double f_new = func(x_new);
if (f_new < ind.fitness)
{
ind.x = x_new;
ind.fitness = f_new;
}
}
}
bool cmp(Individual &a, Individual &b)
{
return a.fitness < b.fitness;
}
void select(vector<Individual> &pop)
{
sort(pop.begin(), pop.end(), cmp);
pop.resize(NP);
}
double run()
{
vector<Individual> pop;
init_population(pop, DIM);
for (int g = 0; g < MAX_GEN; g++)
{
mutation(pop, DIM);
crossover(pop, DIM);
select(pop);
}
return pop[0].fitness;
}
int main()
{
vector<double> x = {0, 1, 3, 4, 6, 7, 9, 10};
double y[] = {0, 1.2, 2.8, 3.5, 4.2, 4.8, 6.4, 7.2};
for (int i = 0; i < x.size() - 1; i++)
{
cout << "[" << x[i] << ", " << x[i + 1] << "]: ";
for (int j = 0; j < 10; j++)
{
double t = x[i] + (x[i + 1] - x[i]) * j / 9.0;
cout << y[i] + (y[i + 1] - y[i]) * j / 9.0 << " ";
}
cout << endl;
}
cout << "拟合误差:" << run() << endl;
return 0;
}
```
该程序拟合的是一组分段连续线性数据。数据由 x 和 y 两个数组组成,其中 x 表示每个线性段的起始点,y 表示每个线性段的斜率和截距。程序使用差分进化算法来拟合这组数据,通过最小化拟合误差来求解每个线性段的斜率和截距。
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