4MO Lab1_

#include<bits/stdc++.h>

#define INF 1000010000
#define nl '\n'
#define pb push_back
#define ppb pop_back
#define mp make_pair
#define fi first
#define se second
#define pii pair<int,int>
#define pdd pair<double,double>
#define all(c) (c).begin(), (c).end()
#define SORT(c) sort(all(c))
#define sz(c) (c).size()
#define rep(i,n) for( int i = 0; i < n; ++i )
#define repi(i,n) for( int i = 1 ; i <= n; ++i )
#define repn(i,n) for( int i = n - 1 ; i >= 0 ; --i )
#define repf(j,i,n) for( int j = i ; j < n ; ++j )
#define die(s) {std::cout << s << nl;}
#define dier(s) {std::cout << s; return 0;}
#define vi vector<int>
typedef long long ll;

#define eps 1e-8
#define M_E 2.71828182845904523536

using namespace std;
vi pows = {11 , 0 , 0 , 5 , -7 , 1};
double k_exp = -1.;
double k_pow_exp = -1.;
// y = x^5-7x^4+5x^3+11-e^(-x)
// y' = 5x^4-28x^3+15x^2+e^(-x)
//plot https://i.gyazo.com/26c1d22f6ba983c17251fb73a9b56082.png
//solutions https://i.gyazo.com/232259e4f577671ffbaaf72e625ab487.png

inline double f(double x){
    double res = 0;
    double tmp = 1;
    rep(i , sz(pows)){
        res += tmp * (double)pows[i];
        tmp *= x;
    }
    res += k_exp * pow(M_E , k_pow_exp * x);
    return res;
}

inline double dfdx(double x){
    double res = 0;
    double tmp = 1;
    rep(i , sz(pows) - 1){
        res += tmp * (i + 1) * (double)pows[i + 1];
        tmp *= x;
    }
    res += k_exp * k_pow_exp * pow(M_E , k_pow_exp * x);
    return res;
}

inline void solve1(){
    double l = -1000.;
    double r = 1000.;
    int i = 0;
    do{
        ++i;
        double mb = 0.5 * (l + r);
        if(abs(f(mb)) < eps){
            cout << "x: " << mb << " f(x):" << f(mb)<< " iteration:" << i << nl;
            return;
        }
        if(f(l) * f(mb) < 0)r = mb;
        else l = mb;
    }while(abs(l - r) > eps);
    cout << "x: " << l << " f(x):" << f(l)<< " iteration:" << i << nl;
}

inline void solve2(){
    double x = 1.;
    double t = x - f(x)/dfdx(x);
    int i = 0;
    do{
        x = t;
        t = t - f(t)/dfdx(t);
        ++i;
    }while(abs(t - x) > eps);
    cout << "x: " << t << " f(x):" << f(t)<< " iteration:" << i << nl;
}


inline void solve3(){
    double x = 10.;
    double a = 0.0002;//1 /(2 * dfdx(x));
    double t = x - f(x)/dfdx(x);
    int i = 0;
    do{
        t = x;
        x = x - a * f(x);
        ++i;
    }while(abs(t - x) > eps);
    cout << "x: " << x << " f(x):" << f(x)<< " iteration:" << i << nl;
}

int main() {
//  ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.precision(10);
    cout.setf(ios::fixed);

    solve1();
    solve2();
    solve3();
    system("pause");
    return 0;
}