/*
 * highorder.cpp
 *
 *  Created on: 21.01.2014
 *      Author: trifon
 */

#include <iostream>
#include <cmath>
using namespace std;

double sum(int n, double(*f)(double), int(*next)(int)) {
	double s = 0;
	for(int i = 1; i <= n; i = next(i))
		s += f(i);
	return s;
}

double product(int a, int b) {
	double p = 1;
	for(int i = a; i <= b; i++)
		p *= i*i;
	return p;
}



int plus1(int i) { return i + 1; }
int mult2(int i) { return i * 2; }

typedef int (*next_function)(int);
typedef double (*term_function)(double);
typedef double (*operation)(double,double);

double accumulate (operation op,
					double base_value,
 					double a, double b,
					term_function f,
					next_function next)  {
	double s = base_value;
	for(int i = a; i <= b; i = next(i))
		s = op(s, f(i));
	return s;
}

double mult(double x, double y) { return x * y; }
double pl(double x, double y) { return x + y; }
double square(double x) { return x * x; }

double X;
double const_fun(double i) {
	return X;
}

double power(double x, int n) {
	X = x;
	return accumulate(mult, 1, 1, n, const_fun, plus1);
}

double id(double x) { return x; }

double fact(int n) {
	return accumulate(mult, 1, 1, n, id, plus1);
}

double exp_term(double i) {
	return power(X, i) / fact(i);
}

double my_exp(double x, int n) {
	X = x;
	return accumulate(pl, 0, 0, n, exp_term, plus1);
}

// цяло число
//int choose_function;

// функция, която връща цяло число
//int choose_function(int n);

// указател към функция
//double (*choose_function)(double);

// функция, която връща указател към функция
//double (*choose_function)(double)(int n) {
	// ужас!!!
//}

// по-добре
term_function choose_function(int n) {
	switch(n) {
	case 1: return sin;
	case 2: return cos;
	case 3: return exp;
	case 4: return log;
	}
}

term_function F;

double derive_result(double x) {
	const double DELTA = 1E-5;
	return (F(x + DELTA) - F(x)) / DELTA;
}

term_function derive(term_function f) {
	F = f;
	return derive_result;
}

void choosetest() {
	cout << "Изберете функция: ";
	int n; cin >> n;
	term_function f = choose_function(n);
	cout << "Въведете число: ";
	double x; cin >> x;
	cout << "f(x) = " << f(x) << endl;
}

int main() {
	cout << sum(4, sin, plus1) << endl;
	cout << accumulate(pl, 0, 1, 4, sin, plus1) << endl;
	cout << sum(4, cos, mult2) << endl;
	cout << accumulate(pl, 0, 1, 4, cos, mult2) << endl;
	cout << product(5, 7) << endl;
	cout << accumulate(mult, 1, 5, 7, square, plus1) << endl;
	cout << power(2, 5) << endl;
	cout << fact(5) << endl;
	cout << my_exp(1, 10) << endl;
	//choosetest();
	term_function fp = derive(square);
	cout << fp(5) << endl;
	cout << derive(square)(5) << endl;
	cout << derive(sin)(5) << ' ' << cos(5) << endl;
	return 0;
}