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;
double Babylonian_sqrt(double S, double eps)
{
double x0=S, x=(x0+S/x0)/2;
while(fabs(x-x0)>eps)
{
x0=x;
x=(x0+S/x0)/2;

}
return x0;
}
int main()
{
double S, eps;
cin>>S>>eps;
double sqrt=Babylonian_sqrt(S, eps);
sqrt=(floor(sqrt*100000))/100000.0;
cout<<fixed; cout.precision(5);
cout<<sqrt;
}

Grading criterion: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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 <iostream>
#include <cmath>
#include <iomanip>
using namespace std;

float babsqrt(float s, float x, float e){
	float g = (x + s/x)/2;
	if(abs(g-x) <= e)return x;
	else return babsqrt(s, g, e);
}

int main(){
		
	float s, e; cin>>s>>e;

	cout<<fixed;
	cout<<setprecision(5);

	cout<<babsqrt(s, 1, e);

	return 0;
}

Grading criterion: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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<iostream>
#include<cmath>
using namespace std;

float SquareRoot(float S,float epsilon)
                {
                 float x_0 = 2.5;
                 float x_1 = ((x_0+S/x_0))/2;
                 while(fabs(x_1-x_0)>=epsilon)
                      {
                       x_0 = x_1;
                       x_1 = (x_0 + S/x_0)/2;
                       }
                 return x_1;
                 }
int main()
{
 float S,epsilon;
 cin>>S>>epsilon;
 float root = SquareRoot(S,epsilon);
 cout<<fixed;
 cout.precision(5);
 cout<<root;

}

Grading criterion: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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>
#include<cmath>
double f(double x)
{int S;
cin >> S;

return x+S/x/2;}

main_program{
double xL;
cin >> xL;


double epsilon=0.00001;

bool flagR;

  while(flagR-xL>epsilon)
  {
  flagR=f(xL)>0;
	  
	  
  }
cout << xL;


}

Grading criterion: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
Assigned grade: D
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 sqroot(double s, double eps) 
{
double x0=1;
double xl=0;
double xn = (x0+ (s*(1.00000)/x0))*(1.00000) / (2.00000);
double next=0; 

while (fabs(xn-next) >= eps) 
{
next = xl;
xl = ((xn+s*(1.00000)/xn)*(1.00000) )/ (2.00000);
xn=xl;
}
cout << fixed; 
cout.precision(5);
cout << xl;
}

int main () 
{
	double s; cin >>s;
	double eps; cin >> eps;
sqroot (s,eps);
}

Grading criterion: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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<iostream>
using namespace std;
double  squareroot(double S) {
double x0=1,x2=100,x1;
cin>>S;double epsilon;
while (abs(x2-x0)>epsilon){
x1=(x0+S/x0)/2;
x2=x0;x0=x1;
}
return x0;	
}
int main(){
double S,epsilon;cin>>S>>epsilon;		  
cout<<fixed;
cout.precision(5);
	cout<<squareroot(S);
}

Grading criterion: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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;

float root (float s, float eps){
float pre=1;
float cur=(1+s)/2.0;
	while ((cur-pre)>=eps||(cur-pre)<=(-eps)){
	pre=cur;
	cur=(pre+(s/pre))/2.0;
	}
return pre-0.00001;
}

int main(void){
float s,eps;
cin>>s>>eps;
cout<<fixed;
cout.precision(5);
cout<<root(s,eps);
}

Grading criterion: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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<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: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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 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: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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<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: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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 <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: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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<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: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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 <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: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
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<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: Whether babylonian method is correctly implemented
Rating A: fully correct
Rating B: Almost correct
Rating C: tried in right somewhat direction
Rating D: totally wrong
Assigned grade: B