hw

#define _USE_MATH_DEFINES
#include <stdio.h>
#include <math.h>

const double M = 1.0;
const double G = 1.0;

typedef struct  {
    double x;
    double y;
    double vx;
    double vy;
} planet;

void start(planet *const a, double x0, double y0, double vx0, double vy0){
    a->x = x0;
    a->y = y0;
    a->vx = vx0;
    a->vy = vy0;
}

double f(const planet *const a, int i){
    if(i==0)
        return a->vx;
    if(i==1)
        return a->vy;
    if(i==2)
        return -G*M*a->x/pow(a->x*a->x+a->y*a->y, 1.5);
    if(i==3)
        return -G*M*a->y/pow(a->x*a->x+a->y*a->y, 1.5);
}

double* get(planet *const a, int i){
    if(i==0)
        return &(a->x);
    if(i==1)
        return &(a->y);
    if(i==2)
        return &(a->vx);
    if(i==3)
        return &(a->vy);
}

void set_k(const planet *const a, double *k){
    for(int i = 0; i<4; i++)
        k[i] = f(a, i);
}

void next(planet *const old_planet, planet *const new_planet, double dt){
    double k1[4];
    double k2[4];
    double k3[4];
    double k4[4];
    *new_planet=*old_planet;
    set_k(new_planet, k1);

    for(int i = 0; i<4; i++)
        *get(new_planet, i) = *get(old_planet, i)+dt*k1[i]/2;
    set_k(new_planet, k2);

    for(int i = 0; i<4; i++)
        *get(new_planet, i) = *get(old_planet, i)+dt*k2[i]/2;
    set_k(new_planet, k3);

    for(int i = 0; i<4; i++)
        *get(new_planet, i) = *get(old_planet, i)+dt*k3[i];
    set_k(new_planet, k4);

    for(int i = 0; i<4; i++)
        *get(new_planet, i) = *get(old_planet, i)+dt/6*(k1[i]+2*k2[i]+2*k3[i]+k4[i]);

}

void print_planet(const planet *const a){
    printf("%.10f %.10f\n", a->x, a->y);
}

int main(){
    planet a;
    start(&a, 1, 0, 0, 1);
    double T = 2*M_PI;
    int n = 1000;
    double dt = T/n;
    planet old;
    for(int i = 0; i<n; i++){
        old = a;
        next(&old, &a, dt);
    }
    print_planet(&a);
}