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 path(int j[],int n,int d,int w=0,int idx=0){
    if(d==0) return (w+1);
    for(int i=idx;i<n;i++)
    { for(int p=i+1;p<=i+j[i];p++)
        { if((idx+p)<=(n-1))
            {int s=d-p;
            int id=idx+p;
            w=path(j,n,s,w,id);
        }
    }

}
return w;
}
int main(){
    int n;
    cin>>n;
    int jump[10];
    for(int i=0;i<n;i++)
    {
        cin>>jump[i];
    }
    int ways=path(jump,n,n-1);
    cout<<ways;
}

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
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>
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 func(int k,int a[]){
    int b=0;
    int x=;
    return for(int x;<a[x];i++){

        b=b+func(int k-i;)
    }

}
int main(){

    
}

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
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 std::cin; using std::cout; using std::endl;


int main(){
    int n;
    int sum=0;
    cin>>n;
    int jumps[50]={};
    for(int k=0;k<n;k++){
        cin>>jumps[k];
    }
    for(int i=0;i<n;i++){
        
    }
    cout<<sum;
}

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
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,sum=0;

struct Memo{};

void func(int i,int jumps[]){
    int steps=n-i;
    int k=0;
    int b=i+1;
    int c=i+jumps[i];
    if(i<n){
        func(i+1,jumps);
        k++;
    }
    if(i+b<=n&&i<n){
        for(int j=b;j<=c&&j!=1&&(i+j)<=n;j++){
            
        func(i+j,jumps);
        k++;
    }
    }
    sum=sum+k;

}

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

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
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;

void path(int jumps[],int i,int target,int& sum){
    if(i==target){
        ++sum;
        return;
    }
    
    if(i>target)
    {
      return;
      }

    int possible=jumps[i];

    for(int j=1;j<=possible &&i+j<=target+1;j++){
    path(jumps,i+j,target,sum);
    }
    

}


int main(){
    int n;cin>>n;
    int jumps[n],sum=0;
    for(int i=0;i<n;i++)
    cin>>jumps[n];
    path(jumps,0,n-1,sum);
    cout<<sum<<endl;
}

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
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>
int main(){
    using std::cin;
    using std::cout;
    using std::endl;

    int n;
cin >> n;
int jumps[n];
for (int i=0;i<n;i++){
    cin >> jumps[i];
}
int j=n;
int abc[j];
abc[j]=0;
abc[0]=1;     //base case
int sum;
for (int i=n-1;i>=0;i--){
    if (i + jumps[i] >= n-1){
        abc[j] = abc[j]+abc[i]; //for recurssion of function 
    } 
    n--;
}
    


cout << sum << endl;
}

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
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 noofdistinctpaths(int jumps[],int n,int i){
    if(i==n-1){
        return 1;
    }
    if(i>n-1){
        return 0;
    }
    for(int j=i+1;j<n && jumps[i]>1;jumps[i]--){

        return noofdistinctpaths(jumps,n,j);
    } 



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



}

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
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 func(int n, int jumps[], int x, Memo& memo){
    if(x==n-1)return 1;
    int s=0;
    for(int i=1;i<=jumps[x] && i+x<n;i++){
        if(memo.has(x+i))
            s+=memo.get(x+i);
        else
            s+=func(n,jumps,x+i,memo);
    }
    memo.add(x,s);
    return s;
}

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

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
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;
   }
};
void recur(int i,int j,int X[],int& count){
    if(i==j){
        count++;
        return;
    }
    else{
        for(int k=1;k<=X[i];k++){
            if(i+k<=j)
                recur(i+k,j,X,count);
            else{
                break;
            }
        }
    }
}
int main(){
    int n;
    cin>>n;
    int X[n];
    for(int i=0;i<n;i++){
        cin>>X[i];
    }
    int k=0;
    int& count=k;
    recur(0,n-1,X,count);
    cout<<k;
}

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
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;
int main(){
int n;
cin>>n;
unsigned int jumps[n];
for(int i=0;i<n;i++)
cin>>jumps[i];
int m=n;
    for(int i=0;i<n-1;i++){
        for(int j=i+1;j<n;j++){
        if(jumps[i]==jumps[j])
        m=m-1;
    }
}
cout<<m;
}

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
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 main(){
    int N;
    cin >> N;
    int jumps[N];
    for(int i=0; i<N; i++){
        cin >> jumps[i];
    }
}

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
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 main(){
    int n;
    cin>>n;
    if(n>=2&&<=50);

    int jumps[i];

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

   for(int i=0;i<n;++i){
    for(int j=0;i<n;i++){
        if(1<=j<=jumps[i]&&i+j<=n){
            j++;
        }  

    cout<<j;  

    
   
}

Grading criterion: Recursion call
Rating A: Correctly sets up the recursive call, with valid parameters and accumulates paths for all valid jumps

Rating B: Some issue
Rating C: Major issue
Rating D: 0
Assigned grade: C