CodeGraderBench/CodeGraderBench huggingface dataset:
Problem: college X telephone exchange office has been struggling with a problem that the phone system is getting mixed up and connecting callers to wrong numbers. The users dial a 4 digit number, and the telephone exchange needs to extend it to an 8 digit number by prefixing it with 2159 or 2576, according to certain rules (see below). However, it has been noticed that  when a user dials a 4-digit number, an old system which can handle only 8-digit numbers arbitrarily encodes it into two 4-digit numbers whose sum is the dialed number.

You’ve been appointed to create a solution that will automatically translate the two 4-digit numbers received from the system into the correct 8-digit phone number. 
Write a C++ program that accepts two non-negative integers as input from the user, adds them to get a 4-digit number xxxx (the number originally dialed), and prints out 2159xxxx or 2576xxxx, according to the following rules. Certain dialed numbers are invalid, and in those cases the output should simply say “invalid.”
first digit of the dialed number xxxx	prefix	Output
1xxx/3xxx/4xxx	2159	2159xxxx
5xxx/7xxx/8xxx	2576	2576xxxx
0xxxx/2xxx/6xxx/9xxx		invalid

Input Format Two positive integers separated by a space.

Output Format An 8-digit number, or invalid

Assumptions on Input
●	0 <= m <= 9999 (m may omit leading zeros).
●	0 <= n <= 9999 (n may omit leading zeros).
●	0 <= m + n <= 9999.

Student submission:
#include<simplecpp>

main_program{
    int inp1, inp2;
    int dialednum;
    cin>>inp1>>inp2;
    dialednum=inp1+inp2;

    if (dialednum/1000==1 || dialednum/1000==3 || dialednum/1000==4){
        cout<<"2159"<<dialednum<<endl;
        
    } 
    else if (dialednum/1000==5 || dialednum/1000==7 || dialednum/1000==8){

        cout<<"2576"<<dialednum<<endl;
    }
    else{
        cout<<"invalid"<<endl;
    }
    


}

Grading criterion: Output
Rating A: correctly prints the output
Rating B: Some issue
Rating C: Major issue
Rating D: 0
Assigned grade: A
Problem: college X telephone exchange office has been struggling with a problem that the phone system is getting mixed up and connecting callers to wrong numbers. The users dial a 4 digit number, and the telephone exchange needs to extend it to an 8 digit number by prefixing it with 2159 or 2576, according to certain rules (see below). However, it has been noticed that  when a user dials a 4-digit number, an old system which can handle only 8-digit numbers arbitrarily encodes it into two 4-digit numbers whose sum is the dialed number.

You’ve been appointed to create a solution that will automatically translate the two 4-digit numbers received from the system into the correct 8-digit phone number. 
Write a C++ program that accepts two non-negative integers as input from the user, adds them to get a 4-digit number xxxx (the number originally dialed), and prints out 2159xxxx or 2576xxxx, according to the following rules. Certain dialed numbers are invalid, and in those cases the output should simply say “invalid.”
first digit of the dialed number xxxx	prefix	Output
1xxx/3xxx/4xxx	2159	2159xxxx
5xxx/7xxx/8xxx	2576	2576xxxx
0xxxx/2xxx/6xxx/9xxx		invalid

Input Format Two positive integers separated by a space.

Output Format An 8-digit number, or invalid

Assumptions on Input
●	0 <= m <= 9999 (m may omit leading zeros).
●	0 <= n <= 9999 (n may omit leading zeros).
●	0 <= m + n <= 9999.

Student submission:
#include <simplecpp>
main_program{
    int m,n;
    cin>>m;
    cin>>n;
    int sum,mod;
    sum=m+n;
    mod=sum/1000;
    if(mod==1 || mod==3 || mod==4){
        cout<<"2159"<<sum;
    }
    else if(mod==5 || mod==7 || mod==8){
        cout<<"2576"<<sum;
    }
    else{
        cout<<"invalid";
    }
    
}

Grading criterion: Output
Rating A: correctly prints the output
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);
}

Grading criterion: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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

    return count(n-1, k)+ count (n, k-1);

}

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

Grading criterion: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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 main() {
    vector<int> b,c,d;
    b ={1,2}
    c ={1, b[0]+ b[1],2(b[0]+b[1])}
    d ={1,c[0]+c[1], c[0]+c[1]+c[2],2(c[0]+c[1]+c[2])}
    cin>> n >> k;
    if(n=1){
        cout<<1 <<endl;
    if(n=2){
        cout << b[0]+b[1]<< endl;
    if (n=3){
        cout << c[0]+c[1]+c[2]<< endl;
    if (n=4){
        cout << d[0]+d[1]+d[2]+d[3]<< endl;
    }    
    }    
    }    
    }
    return 0;
}

Grading criterion: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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;
    cin>>n>>k;
    cout<<count(n,k);
    return 0;
}

Grading criterion: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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){
    int sum,a=0,b=0,c=0,total;
    if (n==1&&k==1)return 1;
    else if(n==1&&k!=1)return 1;
    else if(n!=1&&k==1)return n;
    else return count(n-1,k)+count(n,k-1);
    }

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

Grading criterion: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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

int main(){
    int n;
    cin >> n;
    int k ;
    cin>> k;
     if(k<0 || k> n)
     cout<< "invalid";
     else
     cout<< p(n,k);
    }

Grading criterion: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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 p){
    if(n==1 || k==1){
        p+=1;
    }
    return (c(n-1,k,p)+c(n,k-1,p));
    return p;

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

Grading criterion: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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

}

int main(){
    int n,k;
    cin>>n>>k;

    cout<<seq(n,k);
    return 0;
}

Grading criterion: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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

return sum;
}

int main(){
    int n, k;
    cin >> n >> k;
    int result= nonD(n,k);
    cout << "result" << endl;
    return 0;
}

Grading criterion: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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)==0) return 1;
    if ((n-1)<0) return 0;
    if ((k-1)==0) return 2;
    if ((k-1)<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: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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

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

}

Grading criterion: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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

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

Grading criterion: Declarations of variable, taking input, and final output
Rating A: Correctly declares and reads two integers as input and cout for final output

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