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Inputting an equation and evaluating it

MarcheCabaret (1)
Hello everyone,

I'm trying to calculate numeric integrals with Monte Carlo Method. Briefly, it's a method to calculate integrals with random numbers. My assignment is to calculate multiple integrals (maximum 3) with the help of these method.

Algorithm:
1)Input number of multiple integrals (It can be 1,2 or 3)

2)Input a function (It can be f(x),f(x,y),f(x,y,z))

3)Input upper and lower limits (Depending on number of integrals. If user inputs
3 in 1st step, he/she must input 6 limits for three integrals)

4)Input number of experiments (This is related with Monte Carlo Method, a high number decreases the error between analytic solution and numerical solution)

5)Output

So the thing is I've coded all steps except the 2. Because I don't know how to input an equation from keyboard and evaluate it with limits of integral. I've tried to make it string but then it doesn't do the calculations. When I tried to double or int, then compiler doesn't know what is * or - means. If you give me an idea, I'd be appreciated.


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// Monte Carlo Method for evaluating integrals

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

double Random(){
	return rand()/(RAND_MAX+1.0);
}

int main(){
	int degree;
	double upperx,lowerx,uppery,lowery,upperz,lowerz,n,s=0;
	string function;
	cout << "Input your degree(1,2,3): " << endl;
	cin >> degree;
	
	if(degree==1){
		cout << "Input your function: " << endl;
		cin >> function; // How to input an equation?
		cout << "Input upper limit of x: " << endl;
		cin >> upperx;
		cout << "Input lower limit of x: " << endl;
		cin >> lowerx;
		cout << "Input n: " << endl;
		cin >> n;
		for(int i=1; i<=n; i++){
			double x = lowerx + (upperx-lowerx)*Random();
			s+=function; // How to calculate x values in an equation and sum the results?
		}
		double mean = s/n;
		double integ = (upperx-lowerx)*mean;
		cout << integ;
	}
	
	else if (degree==2){
		cout << "Input your function: " << endl;
		cin >> function; // How to input an equation?
		cout << "Input upper limit of x: " << endl;
		cin >> upperx;
		cout << "Input lower limit of x: " << endl;
		cin >> lowerx;
		cout << "Input upper limit of y: " << endl;
		cin >> uppery;
		cout << "Input lower limit of y: " << endl;
		cin >> lowery;
		cout << "Input n: " << endl;
		cin >> n;
		for(int i=1; i<=n; i++){
			double x = lowerx + (upperx-lowerx)*Random();
			double y = lowery + (uppery-lowery)*Random();
			s+=function; // How to calculate x and y values in an equation and sum the results?
		}
		double mean = s/n;
		double integ = (upperx-lowerx)*(uppery-lowery)*mean;
		cout << integ;
	}
	
	else if (degree==3){
		cout << "Input your function: " << endl;
		cin >> function; // How to input an equation?
		cout << "Input upper limit of x: " << endl;
		cin >> upperx;
		cout << "Input lower limit of x: " << endl;
		cin >> lowerx;
		cout << "Input upper limit of y: " << endl;
		cin >> uppery;
		cout << "Input lower limit of y: " << endl;
		cin >> lowery;
		cout << "Input upper limit of z: " << endl;
		cin >> upperz;
		cout << "Input lower limit of z: " << endl;
		cin >> lowerz;
		cout << "Input n: " << endl;
		cin >> n;
		for(int i=1; i<=n; i++){
			double x = lowerx + (upperx-lowerx)*Random();
			double y = lowery + (uppery-lowery)*Random();
			double z = lowerz + (upperz-lowerz)*Random();
			s+=function; // How to calculate x, y and z values in an equation and sum the results?
		}
		double mean = s/n;
		double integ = (upperx-lowerx)*(uppery-lowery)*(upperz-lowerz)*mean;
		cout << integ;
	}
	else cout << "Please put a number between 1 and 3!" << endl;
}
keskiverto (10402)
The searchword is probably "expression parser".

For example: https://github.com/bamos/cpp-expression-parser


The parser would create a data structure (most likely a binary tree) from a string. The data structure will have a "evaluate" method.

As example: "2 + 3 * 5" converts into
  +
 / \
2   *
   / \
  3   5

Both nodes and leaves of such tree could be related types: runtime polymorphism.
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