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

int main(){
    int n, k;
    cin >> n;
    cin >> k;
    return count(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>
#include <vector>
using namespace std;
int C(vector <int> vec, int n, int k){
    if(k==0) return 1;
    if(n==1) return 1;
    return C(vec,n-1, k) + C(vec,n, k-1);
}
int main(){
    int n,k;
    cin>>n>>k;
    vector <int> vec;
    for(int i=0; i<n; i++) vec.push_back(i+1);
    cout<<C(vec, 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 combination(int n,int k) {
    
    if(n==1&&k==1){
       int combination(n,k)=1;
    }
    while(n>1&& k>1) {
       int combination(n,k)=int combination(n-1,k)+int combination(n,k-1);
        n=n-1;
        k=k-1;
    }
    return combination(n,k);
}

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

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<simplecpp>
main_program;
int combination (int n,int k){
    if (k==0 || k==n) return 1;
   
   {return (combination (n-1,k)+combination (n,k-1))} ;
}

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==0) return 0;
    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:
int findcount(int k,n){
    count=(n-1, k) + C(n, k-1)

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

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 count(int n , int k);
int main(){
    int n,k;
    std::cin >> n >> k;
    
}
int x=0;
int count(int n , int k){
    
    if(n>1){
        
        count(n-1,k);
        

    }
    if(k>1){
        
        count(n,k-1);
    }
    else{
        return 1;
    }
}

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 combination(int n, int k){
    if(n==1 && k>=1){
        return 1;
    }
    if(k==1 && n>=k){
        return n;
    }
    if(n<0 || k<0){
        return 0;
    }
    return (combination(n-1,k) + combination(n,k-1));
}

int main(){
    int n,k;
    cin>>n>>k;
    cout<<combination(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 couseq(int n,int k int a=0){

    if(n<1 && k<2) {
        couseq()
        a+=1;
    }
    couseq(n,k)=couseq((n-1),k)+ couseq(n,(k-1));
    return a;
    
}
int main(){
    int n,k,a=0;
    int length;
    cin>> 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: 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 countseq(int n,int k){
    if (k==0) return 0;
    if (n==1) return 1;
    if (k==1) return n;
   
    return countseq(n-1,k)+countseq(n,k-1);
}

int main(){
    int n; int k;
    cin>>n; cin>>k;
    cout<<countseq(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 noofways(int n,int k){
    if(n==0) return 0;
    if(n==1 || k==0 )return 1;
    return noofways(n-1,k) + noofways(n,k-1);
}
int main(){
    int n,k;
    cin>>n>>k;
    cout<<noofways(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 countingsequences(int n , int k){
    if (n==1) return 1;
    if (k==0) return 1;
    if (n==0) return 1;
    return ( countingsequences(n-1, k) + countingsequences(n, k-1) );
}


int main(){
    int n,k;
    cin>>n>>k;
    cout<<countingsequences(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 countSeq(int n,int k){
    if(n==1){
        return 1;
    }
    if(k==1){
        return n;
    }
    return countSeq(n-1,k)+ countSeq(n,k-1);
}
int main(){
    int n,k;
    cin>>n>>k;
    cout<<countSeq(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 <simplecpp>
int int factorial(int a) {
if(a <= 1) return 1;
else return a*factorial(a-1);
}

int c (int n , int k )
{ int num = factorial(n);
   int dino = factorial(n-1)*factorial(k);
   num/dino= c(n-1 , k ) + c(n,k-1)
}
main_program {
    int n,k;
    cin>> n,k ;
    int result = c (n,k)
    cout << result;
}

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>
#include <vector>

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);
    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