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 fact(int a){
    if(a<=1) return 1;
    return a*fact(a-1);
}

int C(int n,int k){
    return fact(n)/(fact(k)*fact(n-k));
}
int countSequence(int n,int k){
    
    if(n==1 && k==1) return 1;
    if(k==1) return n;
    if(n==1) return 1;
    C(n, k) = C(n-1, k) + C(n, k-1);
    return C(n, k);
}
int main(){
    int n;
    int k;
    cin>>n>>k;
   cout<< countSequence(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: 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(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 seq(int n, int k){
    if((n<=0)||(k<=0)){
        return 0;
    }
    if(n==1){
        return 1;
    }
    if((k==1)&&(n!=1)){
        return n;
    }

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

int main(){
    int n,k;
    cin>>n>>k;
    int a= seq(n,k);
    cout<<a<<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: 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 countSequence(int n,int k){
    if(n==1) return 1;
    if(k==1) return n;
    return countSequence(n-1,k)+countSequence(n,k-1);
}
int main(){
    int n,k;
    cin>>n>>k;
    cout<<countSequence(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 numberofpair(int n,int k){
    int t;
    if(n<=1 && k<=1){ return 0 ;}
    if(n>=2 && k==1){return n;}
    if(n==1 && k>=2){return 1;}
    if(n==2 && k==2){ return 3 ;}

    else {
        t=numberofpair(n-1,k)+numberofpair(n,k-1);
        return t;}

}

int main(){

unsigned int n,k;
cin>>n>>k;
cout<< numberofpair(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 C(int n, int k) {
    if (n==1) return 1;
    if (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) << 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: 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){
    int a = 1;
    if (n==1&k==0) return (1);
    if (n<0 & k < 0) return 0;
    if (n>=0 & k>=0){
    return sequence(n-1,k) + sequence(n,k-1);
    }
}
int main (){
    int n , k;
    cin >> n;
    cin>>k;
    cout << sequence(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 counting(int n,int m){
    if((n>0) && (m == 0)){
        return 1;
    }
    if((n == 0) && (m>0)){
        return 0;
    }
    return (counting(n-1,m) + counting(n,m-1));
}
int main() {
    int n,m;
    cin>> n>> m;
    cout<<counting(n,m)<<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: 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;
    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>
#include<vector>
using namespace std;

int countseq(vector<int>seq,int n,int k){
    for(int i=0;i<k;i++){
    seq.push_back(n);
    }

countseq(seq, n-1, k);

}

int main(){
    vector<int> seq;
    int n,k;
    cin>>n>>k;
    countseq(seq, n, k);

    //for(int i=0;i<seq.size();i++){
       // cout<<seq[i];
    }

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 CountingSequences( int n, int k) {
    if (n==1 || k==0) return 1;
    else return (CountingSequences(n-1,k) + CountingSequences(n,k-1));
}
int main() {
    int n, k;
    cin >> n >> k;
    cout << CountingSequences(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: 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 || k<0) return 0;
if (k==0) return 0;
if (n==1) return k;
else 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 C(int n,int k;){
      int count;
      if(n<k){return count;}
    if(k==0){return count;}
    int i ;
    int j;
    for(i=1;i<=n;i++){
        for(j=1;j<=k,j++){
while(j>=i){count+=1}
        }
        
    }
C(n-1,k)+C(n,k-1);
return count;

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