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 p(int n,int k){
    if(n-k+1<=1)return 1;
    if(n-2*k+1<=1)return 1;
    if(k<=1) return 1;
    if(n-k+1<k)return 0;
    return ((n-k+1)*p(n-k+1-1,k))/((((n-(2*k)+1)*p(n-(2*k)+1-1,k)))*(k*p(k-1,k)));
}
int main(){
   int n,k;
   cin>>n>>k;
   cout<<p(n,k);
   

}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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 countBinarystring(int n,int k,int prev){
    if(k<0) return 0;
    if (n==0) return (k==0) ? 1:0;

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

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

}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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 count (int n, int k){
    if (n==k && n!=1) return 0;
    if (n==k && n==1) return 1;
    if (n==k && n==0) return 1;
    return count(n-1,k) + count(n-2,k-1);
}
int main ()
{
    int n, k;
    cin >> n >> k;
    cout << count (n,k);
    return 0;
}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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 bin(int n, int k){
    if (n<0 || k<0 || k>(n/2)+1){
        return 0;
    }
    if(n==k && n>1 && k>1 ){
        return 0;
    }

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

    

     return bin(n-1,k)+ bin(n-2,k-1); 
}

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

    return 0;
}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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(k==0 && n==0){
        return 1;
    }
    if(k==1 && n==1){
        return 1;
    }
    if(n<k){
        return 0;
    }
    return b(n-1,k)+b(n-2,k-1);

}

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

}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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 count(int n,int k){
    if(k>=n && n!=1 && k!=0){
        return 0;
    }
    else if(n<3 && k!=1 ){
    return 1;
    }
    if(n==1 && k==1){
        return 1;
    }
    return count(n-1,k)+count(n-2,k-1);
}
int main(){
    int n,k;
    cin>>n>>k;
    cout<<count(n,k);
}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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 CountBinary(int n, int k){
    if(n==1){
        return 1;
    }
    if(n==2 && k==1){
        return 2;
    }
    if(n==2 && k==0){
        return 1;
    }
    if(k==1){
        return n;
    }
    if(k==0){
        return 1;
    }
    if(k>n){
        return 0;
    }
    if(k==n &&k!=1 && k!=0){
        return 0;
    }
     return CountBinary(n-1,k)+CountBinary(n-2,k-1);

}
int main(){
    int n,k;
    cin>>n>>k;
    int cb=CountBinary(n,k);
    cout<<cb;
}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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 ;
    else if (k==0) return 1;
    else if(n==1 && k ==1) return 1;
    else if (n ==0 && k==0) return 0;

    return B(n-1, k) + B(n-2, k-1);
}

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

    cout << (B(n,k));
}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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 Count(int n, int k){
    int count;
    if(n == 0 || k == 0){
        return 1;
    }
    if (k == 1 && n == 1) return 1;
    if (n == k){
        return 0;
    }
    count = Count(n-1,k) + Count(n-2,k-1);
    return count;
}
int main(){
    int n, k;
    cin>> n >> k;
    cout << Count(n,k);
}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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>
#include<vector>
#include<string>
using namespace std;

int countbinary(int n, int k){
    if(n%2==0 && k>n/2) return 0;
    if(n%2!=0 && k>(n+1)/2)return 0;
    if(n==1 && k==1)return 1;
    if(n==2 && k==1)return 2;
    if(n==2 && k==2)return 0;

return countbinary(n-1,k)+countbinary(n-2, k-1);
}

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

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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 count(int n,int k){
    if(k>n) return 0;
        if (n==2 && k==0) return 0;
        if(n==2 && k==1) return 2;
        if(n==1 && k==0) return 0;
        if(n==1 && k==1) return 1;
        else{
            return count(n-1,k)+count(n-2,k-1);
        }
    }
int main(){
    int n,k;
    cin>>n>>k;
    
    cout<<count(n,k)<<endl;
}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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 b(int n,int k)
{
    if(n==2)
    {
        return 2;
    }
    else if(k<=2)
    return (b(n-1,k)+b(n-2,k-1));
}
int main()
{
    int n,k;
    cin>>n>>k;
    cout<<b(n,k);
}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

Rating B: some issue
Rating C: major isssue
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 numberOfBinaryString(int n, int k){
    if(k>n || n==0) return 0;
    if(k==0) return 1;
    if(k==1) return n;

    return numberOfBinaryString(n-1,k) + numberOfBinaryString(n-2,k-1);
}

int main(){

    int n,k;
    cin>>n>>k;

    cout<<numberOfBinaryString(n,k);

    return 0;
}

Grading criterion: Base Case Identification
Rating A: Correctly returns 0 or 1 when n or k become 0 or when the function reaches conditions where constructing the string isn’t possible of length n with k 1's

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