Please, using C language, not C+or C++. Thanks. Files to submit: pi.c Time it to
ID: 3600849 • Letter: P
Question
Please, using C language, not C+or C++. Thanks.
Files to submit: pi.c
Time it took Matthew to Complete: 20 mins
Requriements
Program must compile with both -Wall and -Werror options enabled
Submit only the files requested
Use doubles to store real numbers
Print all doubles to 2 decimal points unless stated otherwise
Restrictions
No global variables may be used
Your main function may only declare variables and call other functions
Description
For this problem you will be implementing a Monte Carlo method for the estimation of pi. Imagine that you have a circle of radius 1 whose center is at (0,0) surrounded by a square with sides of length 2 as pictured below
If we randomly choose points within the square the probability of a point being inside the circle is proportional to the area of the square that it occupies. This means that
The probability for pi can be approximiated by picking a large number of points between [-1, 1] and counting the number that are inside the circle. The number of points inside the circle divided by the the total number of points picked is the probability of being inside the circle
Report your answer to 3 digits after the decimal place
Assumptions
Input will not always be valid
If invalid input is received your program should continue to ask for more input until a valid value is entered
White space after desired input is allowed
You will probably want to wait until after we cover how to do this in class before handling it
Valid values for inputs
Seed: an integer
Number iterations: an integer greater than 0
Randomness
In order to match the outputs on Mimir you will need to make calls to rand in the exact order that I do
First generate a random number between [-1, 1] for the x axis
Then generate a random number between [-1,1] for the y axis
You should the following expression for generating a random double between LO and HI
LO + ((double) rand()) / (((double) RAND_MAX) / (HI - LO))
Hint it would be a good idea to make the above expression into a function
Numbers that fall exactly on the edge of the circle are considered to be inside the circle
Examples
Example 1
Enter the seed for the random number generator: 4
Enter the number of iterations to run: 10
The value of pi is 3.200.
Example 2
Enter the seed for the random number generator: -7
Enter the number of iterations to run: 2
The value of pi is 4.000.
Example 3
Enter the seed for the random number generator: -7
Enter the number of iterations to run: 10000
The value of pi is 3.144.
Example 4
Enter the seed for the random number generator: 3.45
Enter the seed for the random number generator: why
Enter the seed for the random number generator: 12
Enter the number of iterations to run: cat
Enter the number of iterations to run: -1
Enter the number of iterations to run: 3.141
Enter the number of iterations to run: 75
The value of pi is 3.147.
Explanation / Answer
Here,
the input Function is called by the main() and is called till a correct input is given.
Once the inputs are received :double calculatePI(int seed, int iterations)
is called with uses seed and the iterations. In x and y double generateRandom(int seed)
values are generated randomly. Then using 2 point formula we find the if the distance is
less than the radius 1, the point is inside the circle else iy=t is outside the circle.
double probability = (double)(inside / total);
Here inside is points found inside the circle and we calculate probability.
and then return pi as:double PI = 4 * probability;
Comments have been provided for each step.
The outputs have also been provided.
Kindly see the code below. If you have any queries. Kindly comment.
*******************************************************************
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
//Function to generate random numbers
double generateRandom(int seed) {
int LO=-1;
int HI=1;
double r = LO + ((double) rand()) / (((double) RAND_MAX) / (HI - LO));
return r;
}
//Function to take input and validate
int input(int *b){
char input[100] = "";
double x;
int num;
char str[20] = "";
int assignment[5] = {0};
double tolerance = 1e-12;
fgets(input, 100, stdin);
if (sscanf(input, "%lf", &x) == 1) {
num = (int)x;
if (fabs(x - num)/x > tolerance ) {
return -1;
} else {
*b=1;
return num;
}
} else if (sscanf(input, "%s", str) == 1) {
return -1;
} else {
return -1;
}
}
//Function to calculate PI
double calculatePI(int seed, int iterations) {
double total=iterations;
double inside=0;
double x,y;
for(int i=1;i<=iterations;i++) {
x=generateRandom(seed);//Generate randomNumbers for x
y=generateRandom(seed);//Generate randomNumbers for y
//printf("The value of x is %f ",x);
//printf("The value of y is %f ",y);
double res = sqrt((x*x)+(y*y));//Finding if the point is inside the circle
//printf("The value of res is %f ",res);
if(res<=1)//checking the point inside or outside the circle
inside++;
}
//printf("The value of inside is %d ",inside);
double probability = (double)(inside / total);//calculating probability
//printf("The value of probability is %f ",probability);
double PI = 4 * probability;
return PI;//Value of PI
}
int main()
{
srand(time(NULL));
int seed = 0;
int result = 0;
while(result==0){
printf("Enter the seed for the random number generator: ");
seed=input(&result);
}
int iterations = -1;
while(iterations<0){
printf("Enter the number of iterations to run: ");
iterations=input(&result);
}
printf("The value of pi is %.3f.",calculatePI(seed,iterations));
return 0;
}
****************************************************************************
Sample output:
/*
Sample Input/Output:
Example 1
Enter the seed for the random number generator: 4
Enter the number of iterations to run: 10
The value of pi is 3.200.
Example 2
Enter the seed for the random number generator: -7
Enter the number of iterations to run: 2
The value of pi is 4.000.
Example 3
Enter the seed for the random number generator: -7
Enter the number of iterations to run: 10000
The value of pi is 3.144.
Example 4
Enter the seed for the random number generator: 3.45
Enter the seed for the random number generator: why
Enter the seed for the random number generator: 12
Enter the number of iterations to run: cat
Enter the number of iterations to run: -1
Enter the number of iterations to run: 3.141
Enter the number of iterations to run: 75
The value of pi is 3.147.
*/
****************************************************************************
I hope this helps you.
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All the best :)