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 B(int n, int k){
    if(n<k){
        return 0;
    }
    if((n==1 && k==1) || (n==0 && k==0)){
        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: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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 std::cout;
using std::cin;
using std::endl;

int B(int n, int k);

int main() {
    int n = 0, k = 0;
    cin >> n >> k;

    int total = B(n, k);

    cout << total << endl;

    return 0;
}

int B(int n, int k) {
    // base case
    if(n == 0) {
        return 0;
    }

    if(n == 1) {
        if(k > 1) {
            return 0;
        }
        else {
            return 1;
        }
    }
    
    if(n == 2) {
        if( k > 2) {
            return 0;
        }
        if(k == 2) {
            return 0;
        }
        if(k == 1) {
            return 2;
        }
        if(k == 0) {
            return 1;
        }
    }

    // use 1, implies next must be zero
    // B(n - 2, k - 1)

    // don't use 1
    // B(n - 1, k)

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

Grading criterion: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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 recurse(int n, int k){
    int count=0,result =0;
    if(n<k) return 0;
    if(n==1 && k==1) return 1;
    if(n==2 && k==1) return 1;
    while(n>k){
        result = recurse(n-1,k) + recurse(n-2,k-1);
        count++;
    }
    return count;
}
int main(){
    int n,k;
    cin>>n>>k;
    cout<<recurse(n,k);
}

Grading criterion: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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>
int rec(int n, int k)
{
    if(k>n)
      return 0;
    else if(k==1)
      return n;
    else if(k==0)
      return 1;
    else if(k==n && k>1)
      return 0;
    else
      return rec(n-1,k) + rec(n-2,k-1);
}
int main()
{
    int n,k;
    std::cin >> n >> k;
    std::cout << rec(n,k) << std::endl;
}

Grading criterion: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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 findpossible(int a, int k) {
if(n < 2*k-1) return 0; //Base case
else if (n = k) return 0;
else if (n )


return n, findPossible(n, k));
}

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

Grading criterion: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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 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: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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



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

Grading criterion: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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 count_binary(int n,int k, int count){
    if(k>n || k<0)return 0;
    if(n<0)return 0;
    if(n==1||n==0)return 1;

    count+= count_binary(n-1,k,count)+count_binary(n-2,k-1,count);
    return count;
}

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

Grading criterion: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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) {
    int N ;
    if (n==0 || k==0) {
        B(0,0) == 0;
    }
    N = B(n-1, k)+ B(n-2, k-1);
    return N;
}
int main() {
    int n, k;
    cin >> n >> k;
    cout << B(n,k) << endl;
}

Grading criterion: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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

    }
    if ( n ==1 ) { 
         return 1 ; 
    }
    if ( k ==0 ) { 
        return 1 ; 
    }
     if ( k > (n+1)/2) { 
        return 0  ; 
    }

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


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

Grading criterion: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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 count=0;
int B(int n, int k){
    if (k>n) return 0;
    if (k=n==0) return 0;
    if (k=n){
     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: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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 Binarycomb(int p, int q)
{
    if(p-q==0&&(p!=1&&q!=1))
    {
        return 0;
    }
    if(p!=0&&q==0)
    {
        return 1;
    }
    if(p==1&&q==1)
    {
        return 1;
    }
    if(p==0)
    {
        return 0;
    }
    if(p%2==0)
    {
        if(q>(p/2))
        {
            return 0;
        }
        if(q=(p/2))
        {
            return 1;
        }
    }
    else if(p%2!=0)
    {
        if(q>((p/2)+1))
        {
            return 0;
        }
    }
        return ((Binarycomb(p-1,q))+ (Binarycomb(p-2,q-1)));
}

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

Grading criterion: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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 (k>n || k<0) return 0;
    if (n==1 || n==0) 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: Calls the funcion from the main and prints the result
Rating A: Correctly calls the function from the main

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