CodeGraderBench/CodeGraderBench huggingface dataset:
Problem: ​
Assume you are given blocks of size 1, 2 and 3. Write a C++ program to recursively count the number of ways in which a tower of size n can be built with these blocks, such that exactly k of the blocks are of size 1.

 

Example: If n = 4 and k = 2, then there are three possible ways in which the tower can be built. If L1, L2, L3 represent the lego blocks of sizes 1, 2, 3 respectively, then the tower of size 4 can be built using the following block arrangements:

 

L1, L1, L2

L1, L2, L1

L2, L1, L1

 

HINT: If T(n, k) represents the number of ways in which a tower of size n can be built with exactly k 1-sized blocks, then T(n, k) can be recursively written as:

 

T(n,k) = T(n-1, k-1) + T(n-2, k) + T(n-3, k)

where

T(n-1, k-1) represents the number of ways in which a size 1 block is used first, i.e., the number of ways to build a tower of size (n-1) containing exactly (k-1) blocks of size 1.
T(n-2, k) represents the number of ways in which a size 2 block is used first, i.e., the number of ways to build a tower of size (n-2) containing exactly k blocks of size 1.
T(n-3, k) represents the number of ways in which a size 3 block is used first, i.e., the number of ways to build a tower of size (n-3) containing exactly k blocks of size 1.
Use this recurrence formula to implement the recursive function. Think carefully about the base cases.

 

Note: 

You need to solve this question using recursion only. 
Solutions using any other approach will not be considered and any testcases that pass will be negated i.e. will be given a 0. 
 

Input Format

A line containing two positive integers n and k, separated by a space
 

Output Format

An integer representing the count of valid ways to build a tower.
 

Assumptions on Input

Assume that the value of n entered by the user will be between 1 and 15, both inclusive
Assume that the value of k entered by the user will be between 1 and 10, both inclusive
If it is not possible to construct a tower, return 0.

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

int n_towers(int n, int k)
{
 if (n < k || n < 0 || k < 0)
 {
  return 0;
 }
 else if (n == k || (k == 0 && n > 1))
 {
  return 1;
 }

 return (n_towers(n-1, k-1) + n_towers(n-2, k) + n_towers(n-3, k));
}

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

 cout << n_towers(n, k) << 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: A
Problem: ​
Assume you are given blocks of size 1, 2 and 3. Write a C++ program to recursively count the number of ways in which a tower of size n can be built with these blocks, such that exactly k of the blocks are of size 1.

 

Example: If n = 4 and k = 2, then there are three possible ways in which the tower can be built. If L1, L2, L3 represent the lego blocks of sizes 1, 2, 3 respectively, then the tower of size 4 can be built using the following block arrangements:

 

L1, L1, L2

L1, L2, L1

L2, L1, L1

 

HINT: If T(n, k) represents the number of ways in which a tower of size n can be built with exactly k 1-sized blocks, then T(n, k) can be recursively written as:

 

T(n,k) = T(n-1, k-1) + T(n-2, k) + T(n-3, k)

where

T(n-1, k-1) represents the number of ways in which a size 1 block is used first, i.e., the number of ways to build a tower of size (n-1) containing exactly (k-1) blocks of size 1.
T(n-2, k) represents the number of ways in which a size 2 block is used first, i.e., the number of ways to build a tower of size (n-2) containing exactly k blocks of size 1.
T(n-3, k) represents the number of ways in which a size 3 block is used first, i.e., the number of ways to build a tower of size (n-3) containing exactly k blocks of size 1.
Use this recurrence formula to implement the recursive function. Think carefully about the base cases.

 

Note: 

You need to solve this question using recursion only. 
Solutions using any other approach will not be considered and any testcases that pass will be negated i.e. will be given a 0. 
 

Input Format

A line containing two positive integers n and k, separated by a space
 

Output Format

An integer representing the count of valid ways to build a tower.
 

Assumptions on Input

Assume that the value of n entered by the user will be between 1 and 15, both inclusive
Assume that the value of k entered by the user will be between 1 and 10, both inclusive
If it is not possible to construct a tower, return 0.

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

int T(int n, int k){
 if(n == 1 && k == 1){
    return 1;
 }
 else if(n==3 && k==0){
    return 1;

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

 }
 else if(n==2 && k==0){
    return 1;
 }
 else if(n<k){
    return 0;
 }
 else if(n<=0){
    return 0;
 }
 else if( n> k+5 ){
    return 0;
 } else if( n > 0 && k== -1 ){
    return 0;
 }
 else { return T(n-1,k-1)+ T(n-2,k) + T(n-3,k);
 }
}

int main(){
int n,k;
cin >> n>>k;
cout<< T(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: ​
Assume you are given blocks of size 1, 2 and 3. Write a C++ program to recursively count the number of ways in which a tower of size n can be built with these blocks, such that exactly k of the blocks are of size 1.

 

Example: If n = 4 and k = 2, then there are three possible ways in which the tower can be built. If L1, L2, L3 represent the lego blocks of sizes 1, 2, 3 respectively, then the tower of size 4 can be built using the following block arrangements:

 

L1, L1, L2

L1, L2, L1

L2, L1, L1

 

HINT: If T(n, k) represents the number of ways in which a tower of size n can be built with exactly k 1-sized blocks, then T(n, k) can be recursively written as:

 

T(n,k) = T(n-1, k-1) + T(n-2, k) + T(n-3, k)

where

T(n-1, k-1) represents the number of ways in which a size 1 block is used first, i.e., the number of ways to build a tower of size (n-1) containing exactly (k-1) blocks of size 1.
T(n-2, k) represents the number of ways in which a size 2 block is used first, i.e., the number of ways to build a tower of size (n-2) containing exactly k blocks of size 1.
T(n-3, k) represents the number of ways in which a size 3 block is used first, i.e., the number of ways to build a tower of size (n-3) containing exactly k blocks of size 1.
Use this recurrence formula to implement the recursive function. Think carefully about the base cases.

 

Note: 

You need to solve this question using recursion only. 
Solutions using any other approach will not be considered and any testcases that pass will be negated i.e. will be given a 0. 
 

Input Format

A line containing two positive integers n and k, separated by a space
 

Output Format

An integer representing the count of valid ways to build a tower.
 

Assumptions on Input

Assume that the value of n entered by the user will be between 1 and 15, both inclusive
Assume that the value of k entered by the user will be between 1 and 10, both inclusive
If it is not possible to construct a tower, return 0.

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

int T(int n, int k){
    if (k<=0 || n<=0 ) return 0;
    if (n<=k){ return 1;}
    if((n-k)==1) return 0;
    return T(n-1,k-1)+T(n-2,k)+T(n-3,k);
}

int main(){
    int n,k;
    cin >> n >> k;
    cout << T(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: ​
Assume you are given blocks of size 1, 2 and 3. Write a C++ program to recursively count the number of ways in which a tower of size n can be built with these blocks, such that exactly k of the blocks are of size 1.

 

Example: If n = 4 and k = 2, then there are three possible ways in which the tower can be built. If L1, L2, L3 represent the lego blocks of sizes 1, 2, 3 respectively, then the tower of size 4 can be built using the following block arrangements:

 

L1, L1, L2

L1, L2, L1

L2, L1, L1

 

HINT: If T(n, k) represents the number of ways in which a tower of size n can be built with exactly k 1-sized blocks, then T(n, k) can be recursively written as:

 

T(n,k) = T(n-1, k-1) + T(n-2, k) + T(n-3, k)

where

T(n-1, k-1) represents the number of ways in which a size 1 block is used first, i.e., the number of ways to build a tower of size (n-1) containing exactly (k-1) blocks of size 1.
T(n-2, k) represents the number of ways in which a size 2 block is used first, i.e., the number of ways to build a tower of size (n-2) containing exactly k blocks of size 1.
T(n-3, k) represents the number of ways in which a size 3 block is used first, i.e., the number of ways to build a tower of size (n-3) containing exactly k blocks of size 1.
Use this recurrence formula to implement the recursive function. Think carefully about the base cases.

 

Note: 

You need to solve this question using recursion only. 
Solutions using any other approach will not be considered and any testcases that pass will be negated i.e. will be given a 0. 
 

Input Format

A line containing two positive integers n and k, separated by a space
 

Output Format

An integer representing the count of valid ways to build a tower.
 

Assumptions on Input

Assume that the value of n entered by the user will be between 1 and 15, both inclusive
Assume that the value of k entered by the user will be between 1 and 10, both inclusive
If it is not possible to construct a tower, return 0.

Student submission:
#include <iostream>
using namespace std;
int tower(int n,int k){
    if ((n==k) && (n!=0)) {return 1;}
    if ((n<=0) || (k<0) || (n<k)) {return 0;}
    if ((n==2||n==3) && (k==0)) {return 1;}
    return tower(n-1,k-1)+tower(n-2,k)+tower(n-3,k);
}
int main(){
    int n;int k; cin>>n>>k;
    cout<<tower(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: ​
Assume you are given blocks of size 1, 2 and 3. Write a C++ program to recursively count the number of ways in which a tower of size n can be built with these blocks, such that exactly k of the blocks are of size 1.

 

Example: If n = 4 and k = 2, then there are three possible ways in which the tower can be built. If L1, L2, L3 represent the lego blocks of sizes 1, 2, 3 respectively, then the tower of size 4 can be built using the following block arrangements:

 

L1, L1, L2

L1, L2, L1

L2, L1, L1

 

HINT: If T(n, k) represents the number of ways in which a tower of size n can be built with exactly k 1-sized blocks, then T(n, k) can be recursively written as:

 

T(n,k) = T(n-1, k-1) + T(n-2, k) + T(n-3, k)

where

T(n-1, k-1) represents the number of ways in which a size 1 block is used first, i.e., the number of ways to build a tower of size (n-1) containing exactly (k-1) blocks of size 1.
T(n-2, k) represents the number of ways in which a size 2 block is used first, i.e., the number of ways to build a tower of size (n-2) containing exactly k blocks of size 1.
T(n-3, k) represents the number of ways in which a size 3 block is used first, i.e., the number of ways to build a tower of size (n-3) containing exactly k blocks of size 1.
Use this recurrence formula to implement the recursive function. Think carefully about the base cases.

 

Note: 

You need to solve this question using recursion only. 
Solutions using any other approach will not be considered and any testcases that pass will be negated i.e. will be given a 0. 
 

Input Format

A line containing two positive integers n and k, separated by a space
 

Output Format

An integer representing the count of valid ways to build a tower.
 

Assumptions on Input

Assume that the value of n entered by the user will be between 1 and 15, both inclusive
Assume that the value of k entered by the user will be between 1 and 10, both inclusive
If it is not possible to construct a tower, return 0.

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

int tower (int n, int k) {
    if (n < k || k == n-1 || k<0) return 0;
    if (n == 1 || n == 2 || n==k) return 1;
    if (n == 3) {
        if(k == 1) return 2;
        if (k == 0) return 1;
    } 
    else return tower (n-1, k-1) + tower (n-2, k) + tower (n-3,k);
}

int main () {
    int n,k;
    cin >> n >> k;
    cout << tower (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: ​
Assume you are given blocks of size 1, 2 and 3. Write a C++ program to recursively count the number of ways in which a tower of size n can be built with these blocks, such that exactly k of the blocks are of size 1.

 

Example: If n = 4 and k = 2, then there are three possible ways in which the tower can be built. If L1, L2, L3 represent the lego blocks of sizes 1, 2, 3 respectively, then the tower of size 4 can be built using the following block arrangements:

 

L1, L1, L2

L1, L2, L1

L2, L1, L1

 

HINT: If T(n, k) represents the number of ways in which a tower of size n can be built with exactly k 1-sized blocks, then T(n, k) can be recursively written as:

 

T(n,k) = T(n-1, k-1) + T(n-2, k) + T(n-3, k)

where

T(n-1, k-1) represents the number of ways in which a size 1 block is used first, i.e., the number of ways to build a tower of size (n-1) containing exactly (k-1) blocks of size 1.
T(n-2, k) represents the number of ways in which a size 2 block is used first, i.e., the number of ways to build a tower of size (n-2) containing exactly k blocks of size 1.
T(n-3, k) represents the number of ways in which a size 3 block is used first, i.e., the number of ways to build a tower of size (n-3) containing exactly k blocks of size 1.
Use this recurrence formula to implement the recursive function. Think carefully about the base cases.

 

Note: 

You need to solve this question using recursion only. 
Solutions using any other approach will not be considered and any testcases that pass will be negated i.e. will be given a 0. 
 

Input Format

A line containing two positive integers n and k, separated by a space
 

Output Format

An integer representing the count of valid ways to build a tower.
 

Assumptions on Input

Assume that the value of n entered by the user will be between 1 and 15, both inclusive
Assume that the value of k entered by the user will be between 1 and 10, both inclusive
If it is not possible to construct a tower, return 0.

Student submission:
int T(int n, int k){
    if(n<k) return 0;
    if(n==k) return 1;
    return T(n-1,k-1)+ T(n-2,k)+ T(n-3,k);
}

main_program{
     int n,k;
     cin>>n>>"">>k;
     cout<< T(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: ​
Assume you are given blocks of size 1, 2 and 3. Write a C++ program to recursively count the number of ways in which a tower of size n can be built with these blocks, such that exactly k of the blocks are of size 1.

 

Example: If n = 4 and k = 2, then there are three possible ways in which the tower can be built. If L1, L2, L3 represent the lego blocks of sizes 1, 2, 3 respectively, then the tower of size 4 can be built using the following block arrangements:

 

L1, L1, L2

L1, L2, L1

L2, L1, L1

 

HINT: If T(n, k) represents the number of ways in which a tower of size n can be built with exactly k 1-sized blocks, then T(n, k) can be recursively written as:

 

T(n,k) = T(n-1, k-1) + T(n-2, k) + T(n-3, k)

where

T(n-1, k-1) represents the number of ways in which a size 1 block is used first, i.e., the number of ways to build a tower of size (n-1) containing exactly (k-1) blocks of size 1.
T(n-2, k) represents the number of ways in which a size 2 block is used first, i.e., the number of ways to build a tower of size (n-2) containing exactly k blocks of size 1.
T(n-3, k) represents the number of ways in which a size 3 block is used first, i.e., the number of ways to build a tower of size (n-3) containing exactly k blocks of size 1.
Use this recurrence formula to implement the recursive function. Think carefully about the base cases.

 

Note: 

You need to solve this question using recursion only. 
Solutions using any other approach will not be considered and any testcases that pass will be negated i.e. will be given a 0. 
 

Input Format

A line containing two positive integers n and k, separated by a space
 

Output Format

An integer representing the count of valid ways to build a tower.
 

Assumptions on Input

Assume that the value of n entered by the user will be between 1 and 15, both inclusive
Assume that the value of k entered by the user will be between 1 and 10, both inclusive
If it is not possible to construct a tower, return 0.

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

int tower(int n, int k){
    if(n==k)
        return 1;
    if(n<k || n == k+1 || k<0)
        return 0;
    return tower(n-1,k-1) + tower(n-2,k) + tower(n-3,k);
}

int main(){
    int n,k;
    cin >> n >> k;
    int num = tower(n,k);
    cout << num;
    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: ​
Assume you are given blocks of size 1, 2 and 3. Write a C++ program to recursively count the number of ways in which a tower of size n can be built with these blocks, such that exactly k of the blocks are of size 1.

 

Example: If n = 4 and k = 2, then there are three possible ways in which the tower can be built. If L1, L2, L3 represent the lego blocks of sizes 1, 2, 3 respectively, then the tower of size 4 can be built using the following block arrangements:

 

L1, L1, L2

L1, L2, L1

L2, L1, L1

 

HINT: If T(n, k) represents the number of ways in which a tower of size n can be built with exactly k 1-sized blocks, then T(n, k) can be recursively written as:

 

T(n,k) = T(n-1, k-1) + T(n-2, k) + T(n-3, k)

where

T(n-1, k-1) represents the number of ways in which a size 1 block is used first, i.e., the number of ways to build a tower of size (n-1) containing exactly (k-1) blocks of size 1.
T(n-2, k) represents the number of ways in which a size 2 block is used first, i.e., the number of ways to build a tower of size (n-2) containing exactly k blocks of size 1.
T(n-3, k) represents the number of ways in which a size 3 block is used first, i.e., the number of ways to build a tower of size (n-3) containing exactly k blocks of size 1.
Use this recurrence formula to implement the recursive function. Think carefully about the base cases.

 

Note: 

You need to solve this question using recursion only. 
Solutions using any other approach will not be considered and any testcases that pass will be negated i.e. will be given a 0. 
 

Input Format

A line containing two positive integers n and k, separated by a space
 

Output Format

An integer representing the count of valid ways to build a tower.
 

Assumptions on Input

Assume that the value of n entered by the user will be between 1 and 15, both inclusive
Assume that the value of k entered by the user will be between 1 and 10, both inclusive
If it is not possible to construct a tower, return 0.

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

int t(int n,int k) {
        //base cases
        if(n<=0) return 0;
        if(n==1 && k == 1) return 1;
        else if (n==1) return 0;
        if (n==2 && (k == 0 || k == 2)) return 1;
        else if (n==2)  return 0;
        if (n==3 && (k == 1)) return 2;
        if (n == 3 && k == 3) return 1;
        else if (n==3) return 0;
        return (t(n-1,k-1) + t(n-2,k) + t(n-3,k));
}
int main(){
        int n,k;
        cin >> n >> k;
        cout << t(n,k) << 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: B
Problem: ​
Assume you are given blocks of size 1, 2 and 3. Write a C++ program to recursively count the number of ways in which a tower of size n can be built with these blocks, such that exactly k of the blocks are of size 1.

 

Example: If n = 4 and k = 2, then there are three possible ways in which the tower can be built. If L1, L2, L3 represent the lego blocks of sizes 1, 2, 3 respectively, then the tower of size 4 can be built using the following block arrangements:

 

L1, L1, L2

L1, L2, L1

L2, L1, L1

 

HINT: If T(n, k) represents the number of ways in which a tower of size n can be built with exactly k 1-sized blocks, then T(n, k) can be recursively written as:

 

T(n,k) = T(n-1, k-1) + T(n-2, k) + T(n-3, k)

where

T(n-1, k-1) represents the number of ways in which a size 1 block is used first, i.e., the number of ways to build a tower of size (n-1) containing exactly (k-1) blocks of size 1.
T(n-2, k) represents the number of ways in which a size 2 block is used first, i.e., the number of ways to build a tower of size (n-2) containing exactly k blocks of size 1.
T(n-3, k) represents the number of ways in which a size 3 block is used first, i.e., the number of ways to build a tower of size (n-3) containing exactly k blocks of size 1.
Use this recurrence formula to implement the recursive function. Think carefully about the base cases.

 

Note: 

You need to solve this question using recursion only. 
Solutions using any other approach will not be considered and any testcases that pass will be negated i.e. will be given a 0. 
 

Input Format

A line containing two positive integers n and k, separated by a space
 

Output Format

An integer representing the count of valid ways to build a tower.
 

Assumptions on Input

Assume that the value of n entered by the user will be between 1 and 15, both inclusive
Assume that the value of k entered by the user will be between 1 and 10, both inclusive
If it is not possible to construct a tower, return 0.

Student submission:
#include<iostream>
using namespace std;
int waystotower(int n, int k){
    if(n<3|| k<1){
        return 0;

}else{
return waystotower(n-1, k-1)+ waystotower(n-2, k)+ waystotower(n-3, k);
}
}



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