CodeGraderBench/CodeGraderBench huggingface dataset:
Problem: You are given a game consisting of n positions arranged in a line from index 0 to n-1. From each position i, you are given a number jumps[i] which represents how far you are allowed to jump forward from that position.

Your task is to compute how many valid ways exist to reach the last position starting from position 0, following the rules below.

Rules

1. You start from position 0.
2. From position i, you may move to any position j such that:
   j > i and j - i <= jumps[i].
3. You may only move forward.
4. A path is considered valid if you can reach the last position (n-1) using the allowed jumps.

The program uses a recursive function to count all such valid paths.



Input Format

- An integer n representing the number of positions.
- n integers representing the array jumps, where jumps[i] indicates the maximum jump length from position i.



Output Format

- Print the total number of valid ways to reach the last position starting from index 0.



Constraints

- 1 <= n <= 1000  
- 0 <= jumps[i] <= n  



Explanation

The recursive function works backward and checks whether a position can reach the end based on the jump limits. If a position can reach the target, it contributes to the total count of paths.

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

int paths(int arr[], int n){
// int total_paths:
// {for int i=0; i<n; i++}
}

int main(){
    int n;
    cin>>n;
    int jumps[n];
    for (int i=0; i<n; i++)
    {
        cin>>jumps[i];
    }
    return 0;
}

Grading criterion: Memoization: The code may vary (used the code provided by the instructor or completely implemented by students)
Rating A: Correctly uses memoization by storing and retrieving results for each index and avoiding redundant recursive calls
Rating B: Some issue with memoization

Rating C: Memoization not used

Rating D: Major issiue
Assigned grade: D
Problem: You are given a game consisting of n positions arranged in a line from index 0 to n-1. From each position i, you are given a number jumps[i] which represents how far you are allowed to jump forward from that position.

Your task is to compute how many valid ways exist to reach the last position starting from position 0, following the rules below.

Rules

1. You start from position 0.
2. From position i, you may move to any position j such that:
   j > i and j - i <= jumps[i].
3. You may only move forward.
4. A path is considered valid if you can reach the last position (n-1) using the allowed jumps.

The program uses a recursive function to count all such valid paths.



Input Format

- An integer n representing the number of positions.
- n integers representing the array jumps, where jumps[i] indicates the maximum jump length from position i.



Output Format

- Print the total number of valid ways to reach the last position starting from index 0.



Constraints

- 1 <= n <= 1000  
- 0 <= jumps[i] <= n  



Explanation

The recursive function works backward and checks whether a position can reach the end based on the jump limits. If a position can reach the target, it contributes to the total count of paths.

Student submission:
#include <iostream>
#include <vector>
#include <string>

using namespace std;

struct Memo {
   static const int NMAX = 100;
   bool filled[NMAX] = {};
   int memo[NMAX];
   bool has(unsigned i) { return filled[i]; }
   int get(unsigned i) { return memo[i]; }
   void add(unsigned i, int val) {
       memo[i] = val;
       filled[i] = true;
   }
};

int& counter(int i, int& count, int* a, int n){
    int p=i;
    int j= a[i];
    for (int k=1; k<=j; k++){
        a= &a[p++];
        if (i==(n-1)) {(count++);}
        else{
            counter(i+k, count, a, n);
        }
    }
    return count;
}

int main(){
    Memo m;
    int n;
    cin >> n; int a[n], count=0;
    for (int& i: a) cin >> i;
    counter(0, count, a, n);
    cout << count;
}

Grading criterion: Memoization: The code may vary (used the code provided by the instructor or completely implemented by students)
Rating A: Correctly uses memoization by storing and retrieving results for each index and avoiding redundant recursive calls
Rating B: Some issue with memoization

Rating C: Memoization not used

Rating D: Major issiue
Assigned grade: D
Problem: You are given a game consisting of n positions arranged in a line from index 0 to n-1. From each position i, you are given a number jumps[i] which represents how far you are allowed to jump forward from that position.

Your task is to compute how many valid ways exist to reach the last position starting from position 0, following the rules below.

Rules

1. You start from position 0.
2. From position i, you may move to any position j such that:
   j > i and j - i <= jumps[i].
3. You may only move forward.
4. A path is considered valid if you can reach the last position (n-1) using the allowed jumps.

The program uses a recursive function to count all such valid paths.



Input Format

- An integer n representing the number of positions.
- n integers representing the array jumps, where jumps[i] indicates the maximum jump length from position i.



Output Format

- Print the total number of valid ways to reach the last position starting from index 0.



Constraints

- 1 <= n <= 1000  
- 0 <= jumps[i] <= n  



Explanation

The recursive function works backward and checks whether a position can reach the end based on the jump limits. If a position can reach the target, it contributes to the total count of paths.

Student submission:
#include<iostream>
using namespace std;
int calc(int arr[],int n,int k=0){
    cin>>n;
    int count;
    for(int i=0;i<n;i++){
        cin>>arr[i];
    };
    if (k=n-1){
        return 1;
    }; // base case;
   

if (arr[k]+k>n-1) {k=k+1 ;
return (calc(arr[],n,k)+1);
}
else {
    return calc(arr[],n,k+1)+calc(arr[],n,k) ;
};
};
 
int main(){
    int n;
    cin>>n;
    int arr[n];
  cout<<calc(arr[],n);

}

Grading criterion: Memoization: The code may vary (used the code provided by the instructor or completely implemented by students)
Rating A: Correctly uses memoization by storing and retrieving results for each index and avoiding redundant recursive calls
Rating B: Some issue with memoization

Rating C: Memoization not used

Rating D: Major issiue
Assigned grade: B
Problem: You are given a game consisting of n positions arranged in a line from index 0 to n-1. From each position i, you are given a number jumps[i] which represents how far you are allowed to jump forward from that position.

Your task is to compute how many valid ways exist to reach the last position starting from position 0, following the rules below.

Rules

1. You start from position 0.
2. From position i, you may move to any position j such that:
   j > i and j - i <= jumps[i].
3. You may only move forward.
4. A path is considered valid if you can reach the last position (n-1) using the allowed jumps.

The program uses a recursive function to count all such valid paths.



Input Format

- An integer n representing the number of positions.
- n integers representing the array jumps, where jumps[i] indicates the maximum jump length from position i.



Output Format

- Print the total number of valid ways to reach the last position starting from index 0.



Constraints

- 1 <= n <= 1000  
- 0 <= jumps[i] <= n  



Explanation

The recursive function works backward and checks whether a position can reach the end based on the jump limits. If a position can reach the target, it contributes to the total count of paths.

Student submission:
#include<simplecpp>

int fxn (int jumps[], int i , int j, int n ){
        if( ){
            return -1 ;
        }

    return fxn ( int jumps[], int i , int j, int n);
    sum++ ;
}

main_program {
int sum = 0, n;
int jumps[n];
cin >> n;
for (int k=0;k<n;k++){
cin >> jumps[k];}
int i=0,j=n-1;

cout<<sum ;






}




for (int i=0, int j=n-1 ;   j+i < n , j <= jumps[i]    ;     ) {
    for()




if (i==j){break;}

}

Grading criterion: Memoization: The code may vary (used the code provided by the instructor or completely implemented by students)
Rating A: Correctly uses memoization by storing and retrieving results for each index and avoiding redundant recursive calls
Rating B: Some issue with memoization

Rating C: Memoization not used

Rating D: Major issiue
Assigned grade: D
Problem: You are given a game consisting of n positions arranged in a line from index 0 to n-1. From each position i, you are given a number jumps[i] which represents how far you are allowed to jump forward from that position.

Your task is to compute how many valid ways exist to reach the last position starting from position 0, following the rules below.

Rules

1. You start from position 0.
2. From position i, you may move to any position j such that:
   j > i and j - i <= jumps[i].
3. You may only move forward.
4. A path is considered valid if you can reach the last position (n-1) using the allowed jumps.

The program uses a recursive function to count all such valid paths.



Input Format

- An integer n representing the number of positions.
- n integers representing the array jumps, where jumps[i] indicates the maximum jump length from position i.



Output Format

- Print the total number of valid ways to reach the last position starting from index 0.



Constraints

- 1 <= n <= 1000  
- 0 <= jumps[i] <= n  



Explanation

The recursive function works backward and checks whether a position can reach the end based on the jump limits. If a position can reach the target, it contributes to the total count of paths.

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

struct Memo {
   static const int NMAX = 100;
   bool filled[NMAX] = {};
   int memo[NMAX];
   bool has(unsigned i) { return filled[i]; }
   int get(unsigned i) { return memo[i]; }
   void add(unsigned i, int val) {
       memo[i] = val;
       filled[i] = true;
   }
};


int path(int arr[],int n,int p,Memo& memo){
    if (memo.has(p))return memo.get(p);
    int sum=0;
  if(p==1)return 1;
  else if (p<1)return 0;

for(int j=1;j<=arr[n-p];++j){
    sum=sum+path(arr,n,p-j,memo);
}
memo.add(p,sum);
return sum;
}



int main(){
    int n;
    cin>>n;
    int jumps[100];
    for(int i=0;i<n;++i){
        cin>>jumps[i];
    }
   Memo memo;
  cout<< path(jumps,n,n,memo);
   
}

Grading criterion: Memoization: The code may vary (used the code provided by the instructor or completely implemented by students)
Rating A: Correctly uses memoization by storing and retrieving results for each index and avoiding redundant recursive calls
Rating B: Some issue with memoization

Rating C: Memoization not used

Rating D: Major issiue
Assigned grade: A
Problem: You are given a game consisting of n positions arranged in a line from index 0 to n-1. From each position i, you are given a number jumps[i] which represents how far you are allowed to jump forward from that position.

Your task is to compute how many valid ways exist to reach the last position starting from position 0, following the rules below.

Rules

1. You start from position 0.
2. From position i, you may move to any position j such that:
   j > i and j - i <= jumps[i].
3. You may only move forward.
4. A path is considered valid if you can reach the last position (n-1) using the allowed jumps.

The program uses a recursive function to count all such valid paths.



Input Format

- An integer n representing the number of positions.
- n integers representing the array jumps, where jumps[i] indicates the maximum jump length from position i.



Output Format

- Print the total number of valid ways to reach the last position starting from index 0.



Constraints

- 1 <= n <= 1000  
- 0 <= jumps[i] <= n  



Explanation

The recursive function works backward and checks whether a position can reach the end based on the jump limits. If a position can reach the target, it contributes to the total count of paths.

Student submission:
#include<iostream>
using namespace std;
int tp(int n, int jumps[], int p){
    
    int path=0;
    int i=p;
for(int k=jumps[i];k>0;k--){
    i=i+k;
    if(i==n){path++;}
    else {tp((n-i), jumps,i);}
}

}



int main(){
    int n;
    cin>> n;
    int jumps[n];
    int p=0;
    for(int i=0; i<n; i++){
        cin>> jumps[i];
    }
    cout<< tp(n,jumps,p);


}

Grading criterion: Memoization: The code may vary (used the code provided by the instructor or completely implemented by students)
Rating A: Correctly uses memoization by storing and retrieving results for each index and avoiding redundant recursive calls
Rating B: Some issue with memoization

Rating C: Memoization not used

Rating D: Major issiue
Assigned grade: B
Problem: You are given a game consisting of n positions arranged in a line from index 0 to n-1. From each position i, you are given a number jumps[i] which represents how far you are allowed to jump forward from that position.

Your task is to compute how many valid ways exist to reach the last position starting from position 0, following the rules below.

Rules

1. You start from position 0.
2. From position i, you may move to any position j such that:
   j > i and j - i <= jumps[i].
3. You may only move forward.
4. A path is considered valid if you can reach the last position (n-1) using the allowed jumps.

The program uses a recursive function to count all such valid paths.



Input Format

- An integer n representing the number of positions.
- n integers representing the array jumps, where jumps[i] indicates the maximum jump length from position i.



Output Format

- Print the total number of valid ways to reach the last position starting from index 0.



Constraints

- 1 <= n <= 1000  
- 0 <= jumps[i] <= n  



Explanation

The recursive function works backward and checks whether a position can reach the end based on the jump limits. If a position can reach the target, it contributes to the total count of paths.

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

struct Memo {
   static const int NMAX = 100;
   bool filled[NMAX] = {};
   int memo[NMAX];
   bool has(unsigned i) { return filled[i]; }
   int get(unsigned i) { return memo[i]; }
   void add(unsigned i, int val) {
       memo[i] = val;
       filled[i] = true;
   }
};

int numOfDistinctPaths(int n,int *jumps){
    int totalWays = 0;
    if(n==1){
        totalWays = 1;
    }
    for(int i=n;i>=1;i--){

            totalWays = totalWays + numOfDistinctPaths(n-jumps[n-i+1],jumps);

    }
    return totalWays;
}

int main(){
    int n;
    cin >> n;
    int jumps[n];
    for(int i=0;i<n;i++){
        cin >> jumps[i];
    }
    cout << numOfDistinctPaths(n, jumps);
    return 0;
}

Grading criterion: Memoization: The code may vary (used the code provided by the instructor or completely implemented by students)
Rating A: Correctly uses memoization by storing and retrieving results for each index and avoiding redundant recursive calls
Rating B: Some issue with memoization

Rating C: Memoization not used

Rating D: Major issiue
Assigned grade: C
Problem: You are given a game consisting of n positions arranged in a line from index 0 to n-1. From each position i, you are given a number jumps[i] which represents how far you are allowed to jump forward from that position.

Your task is to compute how many valid ways exist to reach the last position starting from position 0, following the rules below.

Rules

1. You start from position 0.
2. From position i, you may move to any position j such that:
   j > i and j - i <= jumps[i].
3. You may only move forward.
4. A path is considered valid if you can reach the last position (n-1) using the allowed jumps.

The program uses a recursive function to count all such valid paths.



Input Format

- An integer n representing the number of positions.
- n integers representing the array jumps, where jumps[i] indicates the maximum jump length from position i.



Output Format

- Print the total number of valid ways to reach the last position starting from index 0.



Constraints

- 1 <= n <= 1000  
- 0 <= jumps[i] <= n  



Explanation

The recursive function works backward and checks whether a position can reach the end based on the jump limits. If a position can reach the target, it contributes to the total count of paths.

Student submission:
#include<iostream>
using namespace std;
int jumpss(int n,int A[]){
       if(n==1)return 1;
    if(A[n-1]<n){return jumpss(n-1,A)+jumpss(n-(A[n-1]),A);}
    else return jumpss(n-1,A);
}
int main(){
    int n;cin>>n;
    int A[n];int a;
    for(int i=n-1;i>=0;i--){
        cin>>a;
        A[i]=a;
    }
    cout<<jumpss(n,A);
}

Grading criterion: Memoization: The code may vary (used the code provided by the instructor or completely implemented by students)
Rating A: Correctly uses memoization by storing and retrieving results for each index and avoiding redundant recursive calls
Rating B: Some issue with memoization

Rating C: Memoization not used

Rating D: Major issiue
Assigned grade: C
Problem: You are given a game consisting of n positions arranged in a line from index 0 to n-1. From each position i, you are given a number jumps[i] which represents how far you are allowed to jump forward from that position.

Your task is to compute how many valid ways exist to reach the last position starting from position 0, following the rules below.

Rules

1. You start from position 0.
2. From position i, you may move to any position j such that:
   j > i and j - i <= jumps[i].
3. You may only move forward.
4. A path is considered valid if you can reach the last position (n-1) using the allowed jumps.

The program uses a recursive function to count all such valid paths.



Input Format

- An integer n representing the number of positions.
- n integers representing the array jumps, where jumps[i] indicates the maximum jump length from position i.



Output Format

- Print the total number of valid ways to reach the last position starting from index 0.



Constraints

- 1 <= n <= 1000  
- 0 <= jumps[i] <= n  



Explanation

The recursive function works backward and checks whether a position can reach the end based on the jump limits. If a position can reach the target, it contributes to the total count of paths.

Student submission:
#include<iostream>
 using namespace std;
 int n;
 int count;
 int ways(int a)
   {
    if(a==(n-1))
     {
        return count++;
     }
    for(int i=1;i<=a;i++)
      {
        count=ways(i);
      }
   }
  int main()
    {
        cin>>n;
        int A[n];
        for(int i=0;i<n;i++)
          {
            cin>>A[i];
          }
        count=ways(A[0]);      
        cout<<count;  
    }

Grading criterion: Memoization: The code may vary (used the code provided by the instructor or completely implemented by students)
Rating A: Correctly uses memoization by storing and retrieving results for each index and avoiding redundant recursive calls
Rating B: Some issue with memoization

Rating C: Memoization not used

Rating D: Major issiue
Assigned grade: C
Problem: You are given a game consisting of n positions arranged in a line from index 0 to n-1. From each position i, you are given a number jumps[i] which represents how far you are allowed to jump forward from that position.

Your task is to compute how many valid ways exist to reach the last position starting from position 0, following the rules below.

Rules

1. You start from position 0.
2. From position i, you may move to any position j such that:
   j > i and j - i <= jumps[i].
3. You may only move forward.
4. A path is considered valid if you can reach the last position (n-1) using the allowed jumps.

The program uses a recursive function to count all such valid paths.



Input Format

- An integer n representing the number of positions.
- n integers representing the array jumps, where jumps[i] indicates the maximum jump length from position i.



Output Format

- Print the total number of valid ways to reach the last position starting from index 0.



Constraints

- 1 <= n <= 1000  
- 0 <= jumps[i] <= n  



Explanation

The recursive function works backward and checks whether a position can reach the end based on the jump limits. If a position can reach the target, it contributes to the total count of paths.

Student submission:
#include<iostream>
using namespace std;
int totalpaths(int i,int jumps[]){
    if(i==(n-1)){
        return 0;
    }
    if(i==(n-2)){
        return 1;
    }


}
int main(){
    int n;
    cin>>n;
    int jumps[n];
}

Grading criterion: Memoization: The code may vary (used the code provided by the instructor or completely implemented by students)
Rating A: Correctly uses memoization by storing and retrieving results for each index and avoiding redundant recursive calls
Rating B: Some issue with memoization

Rating C: Memoization not used

Rating D: Major issiue
Assigned grade: D
Problem: You are given a game consisting of n positions arranged in a line from index 0 to n-1. From each position i, you are given a number jumps[i] which represents how far you are allowed to jump forward from that position.

Your task is to compute how many valid ways exist to reach the last position starting from position 0, following the rules below.

Rules

1. You start from position 0.
2. From position i, you may move to any position j such that:
   j > i and j - i <= jumps[i].
3. You may only move forward.
4. A path is considered valid if you can reach the last position (n-1) using the allowed jumps.

The program uses a recursive function to count all such valid paths.



Input Format

- An integer n representing the number of positions.
- n integers representing the array jumps, where jumps[i] indicates the maximum jump length from position i.



Output Format

- Print the total number of valid ways to reach the last position starting from index 0.



Constraints

- 1 <= n <= 1000  
- 0 <= jumps[i] <= n  



Explanation

The recursive function works backward and checks whether a position can reach the end based on the jump limits. If a position can reach the target, it contributes to the total count of paths.

Student submission:
#include<iostream>
using namespace std;
int main()
{
    int ways=0;
    int count=0;
    int n;
    cin>>n;
    int jumps[n];
    for(int i=0;i<n;i++)
    {
        cin>>jumps[i];
    }
    for(int p=1;p<8;p++)
    {
    for(int j=0;j<n;j++)
    {
            if(jumps[j]==p)count++;
        }
        if(count==0) ways++;
    }
}

Grading criterion: Memoization: The code may vary (used the code provided by the instructor or completely implemented by students)
Rating A: Correctly uses memoization by storing and retrieving results for each index and avoiding redundant recursive calls
Rating B: Some issue with memoization

Rating C: Memoization not used

Rating D: Major issiue
Assigned grade: D