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>
#include<vector>
using namespace std;
struct Memo{
    bool filled[50]={};
    unsigned long long int A[50]={};
    bool has(int i){
        if(filled [i]){return true;}
        else {return false;}

    }
    unsigned long long int get(int i){
        if (filled[i]){return A[i];}
        else return 0;
    }
    void add(int i,unsigned long long int n){
        if(filled[i]){return;}
        else{filled[i]=true;A[i]=n;}
    } 
};
unsigned long long int find(int n,const vector<int> jumps,Memo& memo){
if(n==0){return 1;}
if(memo.has(n)){return memo.get(n);}
else{
    unsigned long long int sum=0;
    for(int i=0;i<n;i++){
        if(jumps[i]>=(n-i)){
            sum+=find(i,jumps,memo);
        }
    }
    memo.add(n,sum);
    return sum;
}
    }


int main(){
    int n;cin>>n;vector<int> jumps;
    for(int i=0;i<n;i++){
        int x;cin>>x;cin.ignore();jumps.push_back(x);
    }
     Memo memo;
    cout<<find(n-1,jumps,memo)<<endl; 
}

Grading criterion: Base condition
Rating A: Correctly handles the base conditions and returns 1 and 0 appropriately

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>
using namespace std;
int tnodp(int a){
    
}
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 main(){
    int n;
    cin>>n;
    int jumps[n];
    for(int i=0;i<n;i++){
    cin>>jumps[i];
    cout<<tnodp(n)<<endl;
    cout<<jumps[n-1];
}
}

Grading criterion: Base condition
Rating A: Correctly handles the base conditions and returns 1 and 0 appropriately

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>
#include<iostream>
#include<vector>

int now (int n;vector<int>jump;intp){
    int step
    if (p=n-1){
        return 1 ;
    }
    if (p=n-2){
        return 2;
    }
    step = now(n,jump,p+1);
    return step;
}
   

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

Grading criterion: Base condition
Rating A: Correctly handles the base conditions and returns 1 and 0 appropriately

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 rec(int a,int ar[],int copy,int i=0){
    if(a==0)
    return -1;
    int num=ar[i++];
    for(int i=1;i<=num;i++){
        if(i+a>=copy+2)
        return 0;
        return 1+rec(a-i,ar,copy,i);
    }
}
int main(){
    Memo obj;
    int n;
    cin>>n;
    int copy=n;
    int jumps[n];
    for(int i=0;i<n;i++){
        cin>>jumps[i];
    }
    cout<<rec(n,jumps,copy);
}

Grading criterion: Base condition
Rating A: Correctly handles the base conditions and returns 1 and 0 appropriately

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;
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 dispath(int jumps[],int n,int ways,int i){
    if(i==n){
        return 0;
    }
    if(i<n){
        for(int k=(i+1);k<(i+jumps[i]);k++){
        return dispath(jumps,n,ways+1,k);
        }
    }
    return ways+2;
}
int main(){
    int n;
    cin>>n;
    int jumps[n];
    for(int i=0;i<n;i++){
        cin>>jumps[i];
    }
    cout<<dispath(jumps,n,0,0);
}

Grading criterion: Base condition
Rating A: Correctly handles the base conditions and returns 1 and 0 appropriately

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>
using namespace std;

int main(){    
    int n;
    cin>>n;
    int jump[n];
    for(int i=0; i<n; i++){
        cin>>jump[i];
    }
    int count=0;
    for(int i=0; i<n; i++){
        for(int j=i; j<n; j++){
            if(i+jump[i]<(n-1-i)){
                count++;
            }
        }
    }
    cout<<count;
}

Grading criterion: Base condition
Rating A: Correctly handles the base conditions and returns 1 and 0 appropriately

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 ways=0;
int calcways(int n, int jumps[]);
int n;
int main(){
    
    cin>>n;
    int jumps[n];
    cin>>jumps[n];
    for(int i=0;i<n;i++){
        int inp;
        cin>>inp;
        jumps[i]=inp;
    }
    
    cout<<calcways(n, jumps)-1;
  
    

    
}

int calcways(int m, int jumps[]){
    if (m==0){
        return ways;
    }
    for(int i=0;i<m;i++){
        if(m-1-(jumps[i])>=0){
            ways++;
            ways=ways+calcways(i+1, jumps);

        }
    }
    
        
    

}

Grading criterion: Base condition
Rating A: Correctly handles the base conditions and returns 1 and 0 appropriately

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 numofways(int a);

int main(){
    int n;
    cin>>n
    int a[n];
    for(int i=0;i<n; i++)
    {
        cin>>a[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 ways(int pos,int arr[],int n){
    if(pos==(n-1)) return 1;
    int total;
    for(int i=pos;i<=pos+arr[pos];i++){
        total+= ways(i,arr,n);
    }
    return total;


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

}

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;
    int jumps[n];
    for(int i=0;i<n;i++)
     cin >> jumps[i];
     int d=0;
       for(int i=0;i<n;i++) {
       if(a[i]=n)
       d++;
     }
        for(int i=0;i<n;i++) {
            for(int j=1;)
        }

     

}

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 f(int n, int i , int jumps[]){
    if(i=n-2){
        return 1;
    }
    int my;
    if(jumps[i] > n-1-i){
      my = (n-1-i)*(n-i)/2 ;
    }
    else my = jumps[i] ;
    return f(n,i,jumps) = f(n,i+1,jumps) +  my;
}
int main(){
    int n;
    cin >> n;
    int jumps[n];
    for(int i=0;i<n;i++){
        cin >> jumps[i];
    }
return f(n,0,jumps) ;
}

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;

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