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 || (k==n-1 && n%2==0)) 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: 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 a,int b){
    if(a<b) return 0;
    else if(a==0 || b==0) return 0;
    else if(a==1 && b==1) return 1;
    else if(a==2 && b==1) return 2;
    else {
        int x=count(a-1,b)+count(a-2,b-1);
        return x;}
}
int main(){
    int a,b;
    cin>>a>>b;
    int v=count(a,b);
    cout<<v;
}

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 binary(int m ,int n){
    if(m/2+1<n){return 0 ;}
    else if(m==2 && n==1){return 2 ;}
    else if(m==2 && n==0){return 1 ;}
    else if(m==2 && n==2){return 0 ;}
    else if(m==1 && n==0){return 1 ;}
    else if(m==1 && n==1){return 1 ;}
    else {return binary(m-1,n)+binary(m-2,n-1) ;}
}
int main(){
    int n,k ;
    cin >> n >> k ;
    cout << binary(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>
//#include <vector>
using namespace std;
/**void sort (vector <int>& a)
{
    //cout << "??";
    for (int l=0; l < a.size(); l++)
    {
        for (int k=0; k < a.size()-1; k++)
        {
            cout << "?";
            if (a[k]>a[k+1]) {swap(a[k],a[k+1]);cout<<'*';}
            //cout << a[k] << " " << a[k+1] << endl;
        }
        //for (int x: a) cout << x;
        //cout << endl;
    } 
}
int sum (vector<int> x)
{
    int s;
    for (int y: x) s+=y;
    return s;
}

void sort (vector<vector <int>>& a)
{
    for (int l=0; l < a.size(); l++)
    {
        for (int k=0; k < a.size()-1; k++)
        {
            if (sum(a[k])>sum(a[k+1])) swap(a[k],a[k+1]);
        }
    } 
}
int main(void)
{
    vector <int> a = {1,2,3,0};
    for (int x: a) cout << x ;
    sort(a);
    for (int x: a) cout << x;
    vector <vector<int>> mat = {{0,1},{0,0}};
    cout << sum(mat[1]);
    swap(mat[0],mat[1]);
    cout << mat[0][1];
}**/
int B (int n,int k)
{
    if(k==1) return n;
    if(k>(n-k+1)) return 0;
    if (k==(n-k+1)) return 1;
    //return 69;
    return (B(n-1,k)+B(n-2,k-1));
}
int main(void)
{
    int n,k;
    cin >> n >> k;
    cout << B(n,k);
}
//98 88,77 78,

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 main {

    int n,k;
    cin >> n;
    cin>>n ;
    cin>> 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 binarycount(int n,int k){
    if(k==1){
        return n-(2*k)+2;
    }
    else if(n==k){
        return 0;
    }
    return binarycount(n-1,k) + binarycount(n-2,k-1);
}

int main(){
    int n,k;
    cin >> n >> k;
    cout << binarycount(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: 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(intn,intk,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)+
       return countBinaryStrings(n-1,k-1,0);}

    int main(){
        int n=4,k=2;
        int result countBinaryStrings(n,k,0);

        cout<<"number of validstrings":<<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 fact(int n){
    if (n<=0){
        return 1;
    }
    return n* fact(n-1);
}
int main(){
    int n ,k;
    cin >> n >> k;
    if ((n+1)/2 <= k){
       cout << fact(n-k+1)/(fact(k))*(fact(n-(k+k)+1));
        
    }
}

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 binarySearch(int n,int k){
    int count = 0;
    if(n < 0 || k < 0){
        return count;
    }

    
    while(n > 0 || k > 0){
        binarySearch(n-1,k) + binarySearch(n-2,k-1);
        count++;
        n--;
        k--;
    }
    return count;
}

int main(){
    int n,k;
    cin >> n >> k;
    int sum = binarySearch(n,k);
    cout << sum;
    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 B(int n, int k){

    if(n < k) return 0;

    else if(n <= 1 || k <= 0) return 1;

    else return B(n-1,k) + B(n-2,k-1);
}
int main(){
    int n,m;
    cin >> n >> m;
    cout << B(n,m);
}

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==1&& k==1)
    return 1;
    if (k==0 && n==0)
    return 1;
    if (n<=k)
        return 0;
    
    else
    return (B(n-1,k)+B(n-2,k-1));
}
int main(){
    int x,y;
    cin >>x>>y;
    cout << B(x,y);
}

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=1 && k=1) return 1;
    
B(n,k) = B(n-1,k) + B(n-2,k-1)
}
int main(){
    int n , k;
    cin>>n>>k;
    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