Can't fix errors in monte carlo program - c++

Question

I'm trying to write a program that simulates darts being thrown at a standard curve. Whenever I get close to debugging the entire thing something else pops up. So far I am getting a lot of errors like:
Error: variable is not declared in this scope
Also there's an error I have no idea how to fix which has to do with C++ comparing pointers and integers
I'm pretty new to C++ so any pointers would be greatly appreciated.
Here's what I got so far.
note: errors are on lines 67, 70, 72, and 75.
#include <iostream>
#include <cstdlib>
#include <cmath>
using namespace std;
double seed(int darts, int x);
int main ()
{
int darts, x_max;
double area;
char again = 'y';
char giveDarts;
while (again == 'y' || again == 'Y');
cout << "Run program (y/n)?";
cin >> giveDarts;
switch (giveDarts) {
case 'y':
case 'Y':
cout << "Enter the ammount of darts to be thrown: "; //since we are simulating DARTS I will use the varible darts instead of "NumberOfSamples"
cin >> darts;
srand(darts);
default:
break;
}
cout << "Enter maximum value of x: ";
cin >> x_max;
while (x_max < 0);
cout << "Please enter a positive value of x: ";
cin >> x_max;
cout << endl;
srand(time(NULL));
area = seed(darts, x_max);
cout << "Estimate of area under curve is: " << area << endl;
cout << "Go again? ";
cin >> again;
return 0;
}
double seed(int darts, int x_max)
{
int i, num_darts=0; //num_darts instead of SamplesInsideArea.
double area;
for(i=1; i<=darts; i++) // for loop
{
double x, y;
double pi = 3.14;
double n (double t);
return 1/sqrt(2*pi)*exp(-pow(t,2)/2); //error:'t' was not declared in this scope
x = rand() / static_cast<double>(RAND_MAX);
y = rand() / static_cast<double>(RAND_MAX);
n(0) = (x*x_max + y*y_max); //error: y_max was not declared in this scope
if(num_darts <= n) //error: ISO C++ forbids comparison between pointer and integer
num_darts++;
area*n(0)+0.5 = static_cast<double>(num_darts)/darts; //error: invalid Ivalue in assignment.
}
return area;
}

Answer 1

This line:
double n (double t);
is prototyping a function n that takes one parameter double t. This is causing two of the errors:
error: 't' was not declared in this scope (because function prototypes don't declare variables)
error: ISO C++ forbids comparison between pointer and integer (because n is a pointer to a function)
Did you mean this to be a function prototype? If not, what did you mean?
The error error: y_max was not declared in this scope is straight-forward. y_max isn't declared anywhere.
This line:
area*n(0)+0.5 = static_cast<double>(num_darts)/darts; //error: invalid Ivalue in assignment.
The error error: invalid Ivalue in assignment is because you can't assign a value to an expression. What did you intend to do here?
Additionally, there are some other problems:
This line:
while (again == 'y' || again == 'Y');
will cause your program to go into an infinite loop, since you set again = 'y' just before it, and the semicolon tells the compiler this:
while (again == 'y' || again == 'Y')
{
// do nothing
}
To fix this, remove the semicolon and put braces around the code that needs to be inside the while loop. The same issue exists later too (while (x_max < 0);).
Someone else pointed out this one:
return 1/sqrt(2*pi)*exp(-pow(t,2)/2);
which occurs in the middle of the function. This will cause that function to finish immediately and return the calculated value. Is this what you intended? The code after this line will never run.
More problems:
This code doesn't handle the N/n case. The program will not stop when you type 'n', and will probably crash.
switch (giveDarts) {
case 'y':
case 'Y':
cout << "Enter the ammount of darts to be thrown: "; //since we are simulating DARTS I will use the varible darts instead of "NumberOfSamples"
cin >> darts;
srand(darts);
default:
break;
}
cout << "Enter maximum value of x: ";
Use braces to control loops, not whitespace. Instead of this:
while (x_max < 0);
cout << "Please enter a positive value of x: ";
cin >> x_max;
cout << endl;
You want this:
while (x_max < 0)
{
cout << "Please enter a positive value of x: ";
cin >> x_max;
cout << endl;
}
This line:
area*n(0)+0.5 = static_cast<double>(num_darts)/darts;
If you're trying to set area, this needs to be in the form:
area = static_cast<double>(num_darts)/darts; // n(0)+0.5 goes where??

Answer 2

When you are first learning to program C++, I suggest that you declare and define all of your functions at the global level. This means that lines like double n (double t); should never appear inside any braces. So to fix part of the problem with your code, move these two lines of code:
double n (double t);
return 1/sqrt(2*pi)*exp(-pow(t,2)/2);
outside of the seed() function and make a few minor modifications so it looks like this:
double n (double t) {
return 1/sqrt(2*pi)*exp(-pow(t,2)/2)
}
This should help you in the right direction. (Just be sure that pi is declared either as a global constant.)