in C programming with output matching the bottom examples For this problem you w
ID: 3594988 • Letter: I
Question
in C programming with output matching the bottom examples
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
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
output should match the 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.
Requirements
Use doubles to store real numbers
Print all doubles to 2 decimal points
Restrictions
No global variables may be used
Your main function may only declare variables and call other functions
(0,0) (0-1)Explanation / Answer
********************************************************************
The sample input and output match as given in the question.
********************************************************************
#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 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.
*/
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The working of each function has been given in the description, kindly look into the code. Each method has been described with its working. If you have any queries, kindly comment.
Kindly rate the answer if you find it useful. All The Best. :)
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