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;
void squrt(double S,double epsilon){
double arr[1000];
arr[0]=1;
for(int i=1;i<1000;i++){
arr[i]=(arr[i-1]+(S/arr[i-1]))/2;
}
for(int k=0;k<1000;k++){
if(abs(arr[k+1]-arr[k])<epsilon){
cout<<fixed;
cout.precision(5);
cout<<arr[k];
break;
}
}
}
int main(){
double S,epsilon;
cin>>S>>epsilon;
squrt(S,epsilon);
}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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 s){
return (x+(s/x))/2;}
int main(){
double s,x1;
double x=1;
double epsilon;
cin>>s>>epsilon;
x1=f(x,s);
while(fabs(x-x1)>epsilon){
x=x1;
x1=f(x1,s);}
cout<<fixed;
cout.precision(5);
cout<<x;
return 0;}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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 sq(double s,double eps){
double x=1;
while(fabs((x+s/x)/2-x)>eps){
x=(x+s/x)/2;
}
	return x;
}
int main(){
	double s,eps;
	cin>>s>>eps;
	cout<<fixed;
	cout.precision(5);
	cout<<sq(s,eps);
}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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;

float absVal (float x){
	if (x>=0){
		return x;
	}
	return -1*x;
}

float root (float s, float epsilon){
	float x0 = 1, x1 = (1+s)/2;

	for (; absVal(x0 - x1) >= epsilon;){
		x0 = x1;
		x1 = (x0+(s/x0))/2;
	}
	return x1;
}

int main(){
	float s = 0, epsilon = 0;

	cin >> s >> epsilon;

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

	cout << root(s, epsilon);

	return 0;
}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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 S,double epsilon){
double  b;
double a=0;
b=1;
while (abs(b-a)>epsilon){
a=b;
b=(a+S/a)/2;
}
return b;
}

int main (){
double S,epsilon;
cin>>S>>epsilon;
cout<<fixed;
cout.precision(5);
cout<<f(S,epsilon);
}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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;
float ans(float a, float b, float c){
	float d = (c + a/c)/2;
	while((abs(d-c)>b)){
		c=d;
		d = (c + a/c)/2;
	}
	return d;
	}

int main(){
float S, e;
cin>>S>>e;
float d = S/2;
float sqrt = ans(S,e,d);
cout.fixed;
cout.precision(6);
cout << sqrt;

}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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 square_root(int S, double epsilon){
float x0;
double x1;
double x2;
x0=sqrt(S);
int x=floor(x0);
x1=x;
x2=(x1+S/x1)/2;
while (abs(x2-x1)>=epsilon)
{x1=x2;
x2=(x1+S/x1)/2;}
return x2;
}
int main(){
int S;
double epsilon;
cin >> S >> epsilon;
double ans;
ans = square_root(S,epsilon);
cout << ans;
}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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;
int main(){
double eps;
double s;
cin>>s;cin>>eps;
double x0=4.0;
double x1=(x0+(s/x0))/2.0;
double x2=(x1+(s/x1))/2.0;
while(abs(x2-x1)>=eps){x1=x2;
x2=(x1+(s/x1))/2.0;
}cout.fixed;
cout.precision(6);
cout<<x2;
}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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;

int main()
{
	int n,x1=0,x2=1;
	cin >> n;
	double sn=0,re=0;
	double psi=3.35989;
	for(int i=1;i<n;i++)
	{
		int temp =x2;
		x2=x1+x2;
		x1=temp;
		sn+=1.0/x1;
	}
	re=(psi-sn)/psi;
	cout << fixed;
	cout.precision(5);
	cout << sn << "\n" << re;
}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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 sqr(double s,double eps){
double x=2,y=1;
while(fabs(y-x) > eps){
x=y;
y = double(x + double(s)/double(x))/double(2);
}
return y;
}
int main(){
double s,eps;
cin>>s>>eps;
cout<<fixed;
cout.precision(5);
cout<<sqr(s,eps);

}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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 squareroot(double S)
{
 double x0=1;double x1=(S+10);
 double eps;cin >> eps;
 while(fabs(x1-x0)>=eps)
  {
   double temp;
   temp=x0;
   x0=x1;
   x1=(temp+(S/temp))/2;
  }
 return x1;
}
int main()
{
 double S; cin >> S;
 cout << squareroot(S);

}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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;
int main(){
double s,epsilon;
cin>>s>>epsilon ;
double a=s/2 ,b,c,d ;
b=(a+(s/a))/2;
c=(b+(s/b))/2;
do{
b=c;
d=(c+(s/c))/2;
c=d;
}while(c-b>epsilon);
cout<<fixed;
cout.precision(5);
cout <<(c+(s/c))/2;
}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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 root(double S,double eps){
if(S>0){
double x=2.33456,t;
double y=(x+S/x)/2;
if(y-x>0)t=y-x;
else  t=x-y;
while(t>eps){x=y;y=(x+S/x)/2;
if(y-x>0)t=y-x;
else t=x-y;};
return x;};
}
int main(){
double a,aps;
cin>>a>>aps;
cout<<fixed;
cout.precision(5);
cout<<root(a,aps);
}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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 myroot(double s, double e)
{double x0=4.00000, x1, y;

do {	x1=(x0+s/x0)/2;
	y=x0;
	x0=x1;
}while (fabs(y-x1)>=e);

return y;
}

int main()
{double e, s;
cin>>s>>e;
cout<<fixed;
cout.precision(5);
cout<<myroot(s, e);
return 0;
}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C
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;

long double babylonian(long double S, long double eps){
	long double x0=S,x1=(x0+S/x0)/2;
	do{
		x0 = x1;
		x1 = (x0 + S/x0)/2;
	}while(fabs(x1-x0)>eps);
	return x0;
}

int main(){
	long double S,eps;
	cin >> S >> eps;
	cout<<fixed;
	cout.precision(5);
	cout << babylonian(S,eps);
}

Grading criterion: Quality and number of comments
Rating A: Well Commented
Rating B: Ok Commented
Rating C: Poor or no comments
Rating D: 0
Assigned grade: C