CodeGraderBench/CodeGraderBench huggingface dataset:
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<iostream>
#include<cmath>
using namespace std;

int main(){
double s,x1,x2,eps;
cin>>s>>eps;
x1=s/2;
x2=(x1+(s/x1))/2;
while(fabs(x2-x1)>eps){
x1=x2;
x2=(x1+(s/x1))/2;
}
cout<<fixed;
cout.precision(5);
cout<<x2;

return 0;
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<iostream>
using namespace std;

double sqrt(double x, double eps)
{double a=1;
while(abs((a+x/a)/2-a)>eps)
{a=(a+x/a)/2;
}
return a;
}
int main()
{double x,eps;
cin>>x>>eps;
cout<<fixed;
cout.precision(5);
cout<<sqrt(x,eps);
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: A
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<simplecpp>
double squro(double s){
double x1,x0,eps=0.001;
cout<<"enter the initial guess";cin>>x0;
x1=(x0+s/x0)/2;
while(x0-x1>eps){
x0=x1;
x1=(x0+s/x0)/2;}
return x1;}

main_program{
int a;double y;
cin>>a;
y=squro(a);
cout<<y;}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<iostream>
#include<cmath>
using namespace std;
float sqrt(float S,float eps){
	float a=1,b=(a+S/a)*0.5;
	while (fabs(b-a)>eps){
		a=b;
		b=(a+S/a)*0.5;
	}
	return b;
}
int main(){
	float S,eps;
	cin>>S>>eps;
	float r=sqrt(S,eps);
	cout<<fixed;
	cout.precision(5);
	cout<<r;
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<iostream>
#include<cmath>
using namespace std;
double f(double x,double e){
	double a,y;a=1;y=(a+x/a)/2;
	while(fabs(a-y)>=e){
	a=y;
	y=(a+x/a)/2;
	}
	return a;
}
int main(){
double x,e;
cin>>x>>e;
cout<<fixed;
cout.precision(5);
cout<<f(x,e);
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include <iostream>
#include <cmath>
using namespace std;
int main (){
	double S;
	
	cin >> S;
	double X = S/2, x2, eps;
	cin >> eps;
	cout << fixed;
	cout.precision(5);
	while (fabs(X-x2)>eps)
	{ 
		X=(X+S/X)/2;
		x2=(X+S/X)/2;
	}
	
	 cout << X;
	
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<iostream>
#include<cmath>
using namespace std;
double root(double S, double eps)
{  double x=1,y;
   y=(S+1)/2;
   while(fabs(y-x)>eps)
   {  x=y;
      y=(y+S/y)/2;
   }
   return y;
}
int main()
{  double S,eps;
   cin >> S >> eps;
   cout << fixed;
   cout.precision(5);
   cout << root(S,eps);
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<iostream>
#include<cmath>
using namespace std;
float f(float x,float eps){
	float x0, x1;
	x0 =  x/2;
	x1= (x0 + x/x0)/2;
	while(fabs(x1 - x0) > eps)
	{
		x0 = x1;
		x1 = (x1 + x/x1)/2;
	}
	return x1;
}
int main(){ 
	float s;
	cin >> s;
	float eps = 0.000001;
	float x;
	x = f(s,eps);
	cout << fixed;
	cout.precision(5);
	if(s == 0)
		cout << 0;
	else
		cout << x;
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<iostream>
using namespace std;
void  sqrt(float s,float epsilon){
int x0;
float xi;

for(int i=0;i<=100;i++){
x0=1;
int j=i+1;
float xj=(xi+(float)s/(float)xi)*0.5;
if(xj-xi<epsilon) cout<<xj;

}
}
int main()
{
 int s;
float epsilon;
cin>>s>>epsilon;
sqrt(s,epsilon);



}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<iostream>
#include<cmath>
using namespace std;

double sqrt(double n, double eps){
double x=n;
double xp=n/2;
while(fabs(x-xp)>eps){
xp=x;
x=double((x+n/x)/2);
}
return x;
}

int main(){

double n,eps;
cin >> n >> eps;
cout<<fixed;
cout.precision(5);
cout << sqrt(n,eps);
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include <iostream>
#include <cmath>
using namespace std;

double sqroot(double s, double epsilon){

double x=5.0,y=1.0,z=1.0;
for( ;fabs(x-z)>epsilon;x=y){

y= (x+s/x)/2.0;
z=x;

}

return y;
}
int main(){

double s,epsilon;
cin>>s>>epsilon;

double x= sqroot( s, epsilon);

cout<<fixed;
cout.precision(5);

cout<<x;
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<iostream>
#include<cmath>
using namespace std;


double sqrt(double s,double eps,double x0){
double x1;
x1=((x0+(s/x0))/2);
while(abs(x1-x0)>eps)
	{
x0=x1;
x1=((x1+(s/x1))/2);
	}
return x1;
}

int main(){
double s,eps,x0=3;
cin>>s>>eps;
cout << fixed;
cout.precision(5);
cout<<sqrt(s);
return 0;
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include <iostream>
#include <cmath>
using namespace std;

double sqrt(double s,double x0,double epsilon){
	double x1 = (x0+(s/x0))/2;
	if(abs(x1-x0)<epsilon){
		return x1;
	}
	else{
		return sqrt(s,x1,epsilon);
	}
}


int main(){
	double input,epsilon;
	cin>>input>>epsilon;
	cout<<fixed;
	cout.precision(5);
	cout<<sqrt(input,10,epsilon);
	return 0;
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<iostream>
#include<cmath>
using namespace std;
void sqrt(double a,double b){

long long int n= 1000000;
double epsilon=0.00001;
double x[n+100];

x[0]=b;
x[1]=(b+(a/b))/2;
epsilon=0.01000;
int r;

for(int i=1;i<n;i++){
x[i+1]=(x[i]+a/(x[i]))/2;
if( x[i+1]-x[i]<0.00001)
{int r=i;
cout<<fixed;
cout.precision(5);
cout<<x[r];break;
}
}
}
int main(){
double x0,S;
double epsilon=0.01;

cin>>S>>x0;
sqrt(S,x0);
return 0;
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B
Problem: An iterative method, called the Babylonian method, for finding square roots, was known to the ancient Babylonians (1500 BC) and Greeks (100 AD) long before Newton invented his general procedure. Here's how it works. Suppose you are given any positive number S. To find the square root of S, do the following: Make an initial guess. Guess any positive number x0.Improve the guess. Apply the formula x1 = (x0 + S / x0) / 2. The number x1 is a better approximation to sqrt(S).Iterate until convergence. Apply the formula xn+1 = (xn + S / xn) / 2 until the process converges. Convergence is achieved when the absolute difference between xn+1  and xn falls below some user specified epsilon.Your job is to write a C++ program containing a function that determines the approximate square root of the number S (taken as input) up to some desired precision epsilon. To get credit, you must write a function.

Input Format - S should be greater than 0. Epsilon should be small in value. 
Output Format - Print the value of the square root up to 5 decimal places.  

Constraints
S > 0, 
epsilon <= 0.01.

Student submission:
#include<iostream>
#include<cmath>
using namespace std;
float f(float S,float epsilon){
float x0=1.0;
float x1;
x1=((x0+(S/x0))/2.0);
while(fabs(x1-x0)>epsilon){
x0=x1;
x1=((x0+(S/x0))/2.0);
}
return x1;
}
int main(){
float S,epsilon;
cin>>S;
cin>>epsilon;
cout<<fixed;
cout.precision(5);
cout<<f(S,epsilon);
}

Grading criterion: Use of function beyond what was instructed or any other nice quality.
Rating A: Some extra nice qualities
Rating B: Nothing Extra
Rating C: 0
Rating D: 0
Assigned grade: B