CodeGraderBench/CodeGraderBench huggingface dataset:
Problem: Write a C++ program to count the number of binary strings (strings containing only '0' and '1') of length 'n' that contain exactly 'k' pairs of consecutive 1s. You must deduce the logical stopping points (base cases) for your recursion by considering the physical constraints of binary strings. For example, consider what happens when 'k' is 0, what the maximum number of consecutive pairs could possibly be in a string of length 'n', or if it is physically possible to have 1 pair in a string of length 1.

Code Requirements:

1. Input:
Read two integers 'n' and 'k' from the user.

'n' is the length of the binary string.

'k' is the number of consecutive pairs of 1s required.

2. Recursive Function & Base Cases:
Define a recursive function Bin(int n, int k) that returns the number of valid binary strings. Do not use arbitrary or hardcoded base cases. You must logically deduce and implement the correct base cases based on the physical constraints described in the context above.

3. Recursive Relation:
The function must follow this specific recursive relationship:
Bin(n, k) = Bin(n-1, k) + Bin(n-2, k-1)

4. Function Call:
Call the recursive function from the main() function and print the result.

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

int recurse(int n, int k){
    if( k == 0 && n != 0){
        return 1;
    }
    if( n == k ){
        if (n == 1 || n == 0){
            return 1;
        }else {
            return 0;
        }
    }
    return recurse(n-1,k) + recurse(n-2,k-1);
}

int main(){
    int n = 0, k = 0;
    cin >> n >> k;
    cout << recurse(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 count the number of binary strings (strings containing only '0' and '1') of length 'n' that contain exactly 'k' pairs of consecutive 1s. You must deduce the logical stopping points (base cases) for your recursion by considering the physical constraints of binary strings. For example, consider what happens when 'k' is 0, what the maximum number of consecutive pairs could possibly be in a string of length 'n', or if it is physically possible to have 1 pair in a string of length 1.

Code Requirements:

1. Input:
Read two integers 'n' and 'k' from the user.

'n' is the length of the binary string.

'k' is the number of consecutive pairs of 1s required.

2. Recursive Function & Base Cases:
Define a recursive function Bin(int n, int k) that returns the number of valid binary strings. Do not use arbitrary or hardcoded base cases. You must logically deduce and implement the correct base cases based on the physical constraints described in the context above.

3. Recursive Relation:
The function must follow this specific recursive relationship:
Bin(n, k) = Bin(n-1, k) + Bin(n-2, k-1)

4. Function Call:
Call the recursive function from the main() function and print the result.

Student submission:
#include<iostream>
using namespace std;
int CountBinaryStrings( int n,int k,int prev){
if (k<0) return 0;
if (n==0)  return (k==0) ? 1:0;

if(prev==1) return CountBinaryStrings(n-1,k,0);
return CountBinaryStrings(n-1,k,0) + CountBinaryStrings(n-1,k-1,1);

}
int main(){
int n,k;
cin>>n,k;
int result= CountBinaryStrings(n,k,0);
cout<< result<<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: B
Problem: Write a C++ program to count the number of binary strings (strings containing only '0' and '1') of length 'n' that contain exactly 'k' pairs of consecutive 1s. You must deduce the logical stopping points (base cases) for your recursion by considering the physical constraints of binary strings. For example, consider what happens when 'k' is 0, what the maximum number of consecutive pairs could possibly be in a string of length 'n', or if it is physically possible to have 1 pair in a string of length 1.

Code Requirements:

1. Input:
Read two integers 'n' and 'k' from the user.

'n' is the length of the binary string.

'k' is the number of consecutive pairs of 1s required.

2. Recursive Function & Base Cases:
Define a recursive function Bin(int n, int k) that returns the number of valid binary strings. Do not use arbitrary or hardcoded base cases. You must logically deduce and implement the correct base cases based on the physical constraints described in the context above.

3. Recursive Relation:
The function must follow this specific recursive relationship:
Bin(n, k) = Bin(n-1, k) + Bin(n-2, k-1)

4. Function Call:
Call the recursive function from the main() function and print the result.

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

int n {

if(n < 0) return -1; 

if(n == 0) return 1;

return n *(n-1);
}

int main() {

int n;

cin >> n;

int ans =n

ans == -1 ? cout << "Not defined" : 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: C
Problem: Write a C++ program to count the number of binary strings (strings containing only '0' and '1') of length 'n' that contain exactly 'k' pairs of consecutive 1s. You must deduce the logical stopping points (base cases) for your recursion by considering the physical constraints of binary strings. For example, consider what happens when 'k' is 0, what the maximum number of consecutive pairs could possibly be in a string of length 'n', or if it is physically possible to have 1 pair in a string of length 1.

Code Requirements:

1. Input:
Read two integers 'n' and 'k' from the user.

'n' is the length of the binary string.

'k' is the number of consecutive pairs of 1s required.

2. Recursive Function & Base Cases:
Define a recursive function Bin(int n, int k) that returns the number of valid binary strings. Do not use arbitrary or hardcoded base cases. You must logically deduce and implement the correct base cases based on the physical constraints described in the context above.

3. Recursive Relation:
The function must follow this specific recursive relationship:
Bin(n, k) = Bin(n-1, k) + Bin(n-2, k-1)

4. Function Call:
Call the recursive function from the main() function and print the result.

Student submission:
#include<iostream>
using namespace std;
int binary(int n,int k)
{
    if(k==0) return 1;
    if(k==1) return n;
    if(n==k && k!=1 && k!=0) return 0;
    else return (binary(n-1,k)+binary(n-2,k-1));
}
int main()
{
    int n,k;
    cin>>n>>k;
    cout<<binary(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 count the number of binary strings (strings containing only '0' and '1') of length 'n' that contain exactly 'k' pairs of consecutive 1s. You must deduce the logical stopping points (base cases) for your recursion by considering the physical constraints of binary strings. For example, consider what happens when 'k' is 0, what the maximum number of consecutive pairs could possibly be in a string of length 'n', or if it is physically possible to have 1 pair in a string of length 1.

Code Requirements:

1. Input:
Read two integers 'n' and 'k' from the user.

'n' is the length of the binary string.

'k' is the number of consecutive pairs of 1s required.

2. Recursive Function & Base Cases:
Define a recursive function Bin(int n, int k) that returns the number of valid binary strings. Do not use arbitrary or hardcoded base cases. You must logically deduce and implement the correct base cases based on the physical constraints described in the context above.

3. Recursive Relation:
The function must follow this specific recursive relationship:
Bin(n, k) = Bin(n-1, k) + Bin(n-2, k-1)

4. Function Call:
Call the recursive function from the main() function and print the result.

Student submission:
#include<simple.cpp>
main_program{
    int age ;
    cin<< age ;
    if (age>=18){cout <<"you can fail"<<endl;}
    else{cout<< "you can't fail"<<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 count the number of binary strings (strings containing only '0' and '1') of length 'n' that contain exactly 'k' pairs of consecutive 1s. You must deduce the logical stopping points (base cases) for your recursion by considering the physical constraints of binary strings. For example, consider what happens when 'k' is 0, what the maximum number of consecutive pairs could possibly be in a string of length 'n', or if it is physically possible to have 1 pair in a string of length 1.

Code Requirements:

1. Input:
Read two integers 'n' and 'k' from the user.

'n' is the length of the binary string.

'k' is the number of consecutive pairs of 1s required.

2. Recursive Function & Base Cases:
Define a recursive function Bin(int n, int k) that returns the number of valid binary strings. Do not use arbitrary or hardcoded base cases. You must logically deduce and implement the correct base cases based on the physical constraints described in the context above.

3. Recursive Relation:
The function must follow this specific recursive relationship:
Bin(n, k) = Bin(n-1, k) + Bin(n-2, k-1)

4. Function Call:
Call the recursive function from the main() function and print the result.

Student submission:
#include<iostream>
using namespace std;
int B(int n, int k){
    if (n<0) return 0;
    if(n==0 && k==0) return 1;
    if (n==2 && k==2) return 0;
    if(n==1 && k==1) return 1;
    return (B(n-1, k)+B(n-2, k-1));
}
int main(){
    int n, k;
    cin>>n>>k;
    cout<<B(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 count the number of binary strings (strings containing only '0' and '1') of length 'n' that contain exactly 'k' pairs of consecutive 1s. You must deduce the logical stopping points (base cases) for your recursion by considering the physical constraints of binary strings. For example, consider what happens when 'k' is 0, what the maximum number of consecutive pairs could possibly be in a string of length 'n', or if it is physically possible to have 1 pair in a string of length 1.

Code Requirements:

1. Input:
Read two integers 'n' and 'k' from the user.

'n' is the length of the binary string.

'k' is the number of consecutive pairs of 1s required.

2. Recursive Function & Base Cases:
Define a recursive function Bin(int n, int k) that returns the number of valid binary strings. Do not use arbitrary or hardcoded base cases. You must logically deduce and implement the correct base cases based on the physical constraints described in the context above.

3. Recursive Relation:
The function must follow this specific recursive relationship:
Bin(n, k) = Bin(n-1, k) + Bin(n-2, k-1)

4. Function Call:
Call the recursive function from the main() function and print the result.

Student submission:
#include<iostream>
using namespace std;
int B(int n, int k){
    if(n==k && k!=1){
        return 0;
    }
    else if(k==1){
        return n;
    }
    return (B(n-1,k)+ B(n-2,k-1));
}
int main(){
    int n,k;
    cin>>n>>k;
    int b=0;
    b=B(n,k);
    cout<<b<<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 count the number of binary strings (strings containing only '0' and '1') of length 'n' that contain exactly 'k' pairs of consecutive 1s. You must deduce the logical stopping points (base cases) for your recursion by considering the physical constraints of binary strings. For example, consider what happens when 'k' is 0, what the maximum number of consecutive pairs could possibly be in a string of length 'n', or if it is physically possible to have 1 pair in a string of length 1.

Code Requirements:

1. Input:
Read two integers 'n' and 'k' from the user.

'n' is the length of the binary string.

'k' is the number of consecutive pairs of 1s required.

2. Recursive Function & Base Cases:
Define a recursive function Bin(int n, int k) that returns the number of valid binary strings. Do not use arbitrary or hardcoded base cases. You must logically deduce and implement the correct base cases based on the physical constraints described in the context above.

3. Recursive Relation:
The function must follow this specific recursive relationship:
Bin(n, k) = Bin(n-1, k) + Bin(n-2, k-1)

4. Function Call:
Call the recursive function from the main() function and print the result.

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

int B(int n,int k)
{
    if(n<0)
    return 0;
    if(n<k)
    return 0;
    
    if(n==1 & k==1)
    {
        return 1;
    }
    if(n==0 & k==0)
    {
        return 1;
    }
   return(B(n-1,k)+B(n-2,k-1));

}
int main()
{
    int n,k;
    cin>>n;
    cin>>k;
    cout<<B(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: 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 a,b;
    cout<<"enter initial 4 digit numbers 1st telephone:";
    cin>>a;
    cout<<"enter initial 4 digit number 2nd telephone:";
    cin>>b;
    cout<<"updated numbers";
    cout<<a<<"2129";
    cout<<b<<"2576";


}

Grading criterion: Declaration of variables
Rating A: correct declaration of variables
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>

int main(){
    int m,n;
    cin>>m;
    cin>>n;
    int s=m+n;
    int firstd = (s/1000);
    if((firstd==0 )|| (firstd==2)||(firstd==6)||(firstd==9))
     {cout<<"invalid";}
    else if((firstd==1)||(firstd==3)||(firstd==4)) {
            cout<<"2159"<<s<<endl;}
      else if((firstd==5)||(firstd==7)||(firstd==8)) {
        cout<<"2576"<<s<<endl;}
         

    }

Grading criterion: Declaration of variables
Rating A: correct declaration of variables
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 num1,num2;
        cin>>num1>>num2;
        int sum;
        sum=num1+num2;
        if(sum<1000){
            cout<<"invalid";
        }
        if(sum>=1000 && sum<2000){
            cout<<"2159"<<sum;
        }
        if(sum>=2000 && sum<3000){
            cout<<"invalid";
        }
        if(sum>=3000 && sum<4000){
            cout<<"2159"<<sum;
        }
        if(sum>=4000 && sum<5000){
            cout<<"2159"<<sum;
        }
        if(sum>=5000 && sum<6000){
            cout<<"2576"<<sum;
        }
        if(sum>=6000 && sum<7000){
            cout<<"invalid";
        }
        if(sum>=7000 && sum<8000){
            cout<<"2576"<<sum;
        }
        if(sum>=8000 && sum<9000){
            cout<<"invalid";
        }
        
}

Grading criterion: Declaration of variables
Rating A: correct declaration of variables
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 n1,n2,sum;
    cin>>n1>>n2;
    sum=n1+n2;
    if(sum>=0 && sum<=999)
    {cout<<"invalid";}
    else if(sum>=2000 && sum<=2999)
    { cout<<"invalid";}
    else if(sum>=6000 && sum<=6999) {
        cout<<"invalid";
    }
    else if(sum>=9000) {
        cout<<"invalid";
    } 
    else if(sum>1000 && sum<=1999) 
        { cout<<"2159"<<sum;}  
        else if(sum>=3000 && sum<=4999) {cout<<"2159"<<sum;}
        else if(sum>5000 && sum<=5999) {cout<<"2576"<<sum;}
        else if(sum>=7000 && sum<=8999){cout<<"2576"<<sum;}
        
}

Grading criterion: Declaration of variables
Rating A: correct declaration of variables
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 ; int n;
    cin>>m;
    cout<<" ";
    cin>>n;
    int number=m+n;
    int firstdig=number/1000;
    if(firstdig==1||firstdig==3||firstdig==4)
    cout<<"2159"<<number<<endl;
    else if(firstdig==5||firstdig==7||firstdig==8)
    cout<<"2576"<<number<<endl;
    else if (firstdig==0||firstdig==2||firstdig==6||firstdig==9)
    cout<<"invalid"<<endl;
}

Grading criterion: Declaration of variables
Rating A: correct declaration of variables
Rating B: Some issue
Rating C: Major issue
Rating D: 0
Assigned grade: A