CodeGraderBench/CodeGraderBench huggingface dataset:
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

Student submission:
#include<iostream>
using namespace std;
int res =0;
int counting(int n,int k){
    if(n==1){return 1;}
    if(k==1){return n;}
    
    res=counting(n-1,k)+counting(n,k-1);
    return res;
}



int main(){
    int n;cin>>n;
    int k;cin>>k;
    cout<<counting(n,k);

}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

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

int count(int n,int k){
    if(n==1){
        return 1;
    }
    if(k==1){
        return n;
    }
    return count(n-1,k)+count(n,k-1);
}

int main(){
    int n,k;
    cin >> n >> k;
    cout << count(n,k);
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

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

int seq(int n, int k){
    if(k=1){
        return n;
    }
    if(n=k){
        return 1;
    }
    return seq(n-1, k) + seq(n-1, k-1);
}

int main(){
    int n, k;
    cin>>n>>k;
    cout<<seq(n+k-1, k-1);
    return 0;
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

Student submission:
#include<iostream>
using namespace std;
int main(){
int n,k;
cin>>n>>k;
int combination(int n, int k) {
if(k == 0 || k == n) return 1;
return (combination(n-1,k-1) + combination(n-1,k));
}
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: B
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

Student submission:
#include<iostream>
using namespace std;
int count(int n, int k){
    if (n == 1){
        return 1;
    }
    if (k == 1){
        return n;
    }
    return count(n-1,k) + count(n, k-1);
}

int main(){
    int n, k;
    std::cin>>n>>k;
    std::cout << count(n,k);
    return 0;
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

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

int C(int n, int k){
    if(n==1) return 1;
    if(k==1) return n;
    if(k==0) return 0;
    return C(n-1,k) + C(n, k-1);
}

int main(){
    int n, k;
    cin >> n>>k;
    cout << C(n,k);
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

Student submission:
#include<iostream>
using namespace std;
int num(int n, int k){
    if(n==1)
    return 1;
    if (k==1)
    return n;
    return num(n-1,k)+num(n,k-1);
}
int main(){
    int n,k;
    cin>>n>>k;
    int ans=num(n,k);
    cout<<ans;
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

Student submission:
#include <iostream>
using namespace std;
int fn(int a,int b){
if ( a==1 )
    {return 1;}
else if (b==1)
    {return a;}
return (fn(a-1,b)+fn(a,b-1));
};
int main(){
int n,k;
cin>>n>>k;
cout << fn(n,k);


}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

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

int seq(int n, int k) {
    if (n == 1) {
        return 1;
    }
    if (k == 1) {
        return n;
    }
    return (seq(n-1,k) + seq(n,k-1));
}

int main() {
    int n, k;
    cin >> n >> k;
    cout << seq(n,k);
    return 0;
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

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

int sequence(int n, int k) {

    if(n==1) {
        return 1;
    }
    if(k==0) {
        return 1;
    }

    return sequence((n-1),k) + sequence(n,(k-1));
}

int main() {
    int n,k;
    cin>>n>>k;
    cout<<sequence(n,k)<<endl;
    return 0;
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

Student submission:
#include <iostream>
using namespace std;
int count(int n,int k){
    if(k==0 || n==0) return 0;
    if(n==1) return 1;
    if(k==1) return n;
    else return count(n-1,k)+count(n,k-1);
}
int main(){
    int a,b;
    cin>>a>>b;
    cout<<count(a,b);
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

Student submission:
#include<isostream>
namespace std;
int z = o ;
int p = 1 ; 
int q = 1 ; 
int r = 1 ;
int totalnumber(int n, k)( 
    for ( i=1 , i <= n , i+=)(
        for( j=k, j>=1 , j--) (
            for ( m=0 , m<= k, m++)(
            r=+1
            if( r>0)( 
                cout<< " r";
                return;
            )
        )
    )
    
)
int main (){ 
    int n, k ;
    cin>> n,k;
    totalnumber(n,k)
    cout<< r;
    return;

}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: C
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

Student submission:
#include<iostream>
using namespace std;
int C(int n,int k){
    if(n==1) return 1;
    if(n>1&&k==1) return n;

    return C(n-1,k)+C(n,k-1);
}
int main(){
    int n,k;
    cin>>n>>k;
    cout<<C(n,k);
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

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

int CNK(int n, int k){
    int out = 0;
    if(n == 1){
        out += 1;
        return out;
    }
    if(k==1){
        out += n;
        return out;
    }
    return CNK(n-1,k) + CNK(n,k-1); 
}

int main(){
    int n, k;
    cin>>n>>k;
    cout<<CNK(n,k);
    return 0;
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A
Problem: Write a C++ program to calculate the number of possible sequences that can be formed under certain conditions using recursion. The program should define a recursive function 'combination(int n, int k)' which calculates the total number of ways to arrange 'n' and 'k' such that the count follows a specific recursive relationship.

Code must fulfil these requirements:
A. Input: Accept two integers, 'n' and 'k', from the user

B. Recursive Function Definition: Define a recursive function 'int combination(int n, int k)' that follows the rules below:

C. Base Cases:
    1. If 'n == 1' and 'k >= 1', return '1'
       (Only one way to arrange if one element is available but multiple positions exist.)
    2. If 'k == 1' and 'n >= k', return 'n'
       (If there’s only one position, the number of ways equals the number of elements available.)
    3. If either 'n < 0' or 'k < 0', return '0'
       (Negative values are invalid)

D. Recursive Relation: combination(n, k) = combination(n - 1, k) + combination(n, k - 1)

E. Function Call and Output

Student submission:
#include<iostream>
using namespace std;
int countSequences(int N,int K)
{
    if(N!=0 && K==0)
    return 1;
    else if(N==0)
    return 0;
    else
    return countSequences(N-1,K)+ countSequences(N,K-1);
}
int main()
{
    int n,k;
    cin>>n>>k;
    int ans=countSequences(n,k);
    cout<<ans;
}

Grading criterion: Implementation of the Recursive Relationship
Rating A: Correctly implements the recursive call as defined in the hint. 

Rating B: some issue
Rating C: major issue
Rating D: 0
Assigned grade: A