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

            if(i+j<=n){
                distinctpaths++;
            }
        }
    }   
           cout<<distinctpaths;  
       }

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 tdp (int i, int n, int jumps[]) {
    int j;
    int count=0;
    while (j>=1 && j<=jumps[i]) {
    tdp(i+j, n, jumps [n-j]);
    count ++;
    }
    return count;
}
int main() {
    int n;
    cin>>n;
    int jumps [n];
    for (int i=0; i<n; i++) {
        cin>>jumps [i];
    }
    cout<< tdp (0, n, jumps)<<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;
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;
    }
};
unsigned int ways(int idx, int n, int jumps[], Memo & memo)
{
    
    if (memo.has(idx)) 
    {
    return memo.get(idx);
    }
    else
    {
        if(idx == n)
        {
            memo.add(idx,1);
            return 1;
        }   
        int way_s=0;
        for(int i =1; i<=jumps[idx]; i++)
        {
            if(idx + i<=n)
            {   
                way_s += ways(idx+i,n,jumps,memo);
            }
            else
            break;
        }
        memo.add(idx,way_s);
        return way_s;
    }
}
int main()
{
    int n;
    cin>>n;
    int jumps[n];
    for(int i =0; i<n ; i++)
    {
        cin>>jumps[i];
    }
    Memo memo;
    cout<< ways(0,n,jumps,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: 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;
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 recursive(int n,int jumps)
{
   for(i=0;i<n;i++)
   {
      recursive(n-1,jumps[])
   }
}
int main()
{
    int n;
    cin>>n;
    int i;
    int jumps[n];
    for(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>



int main() {

    int n ;
    cin >> n; 

    int jumps[n];
    int magicalpath[n] ;

    for (int i = 0 ; i < jumps.length();i++) {
          jumps[i] = (n-1)-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 noofways(int jump[],int n){
    if(n==0){return 0;}
    for(int i=0;i<n;i++){
        cin>>jump[i];
    }
}
int main(){
    int n;
    cin>>n;
    int jump[n];
      

    
}
})

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 jumps(int jum[],int o,int p){
    int h;int y=o+1;
    if(p==o){return 0;}
    else if(jum[o]==1){return 0;}
    for(int u=0;u<jum[o];u++){
        h=h+jumps(jum,y+u,p);
    }

}
int main(){
    int n;
    cin>>n;int j;
    int jump[n];
    for(int k=0;k<n;k++){
        cin>>jump[k];
    if(jump[k]==1){j++;}}
if(j==n){cout<<1;}
else cout<<jumps(jump,1,n);
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>
#include<vector>
#include<cmath>
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 now(int n,vector<int> jump,int p)
{   int step;
if(p==n)
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);

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

cout<<now(n,jumps,0);







}










































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;
   }
};

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 paths(int jumps [],int d,int a){
    if(a>d) return 0;
    if(a==d) return 1;
    for(int i=a;i<=d;i++){
        if(jumps[i]==2) return paths(jumps,d,a+2);
        if(jumps[i]==3) return paths(jumps,d,a+3);
        if(jumps[i]==4) return paths(jumps,d,a+4);
        if(jumps[i]==5) return paths(jumps,d,a+5);
        if(jumps[i]==6) return paths(jumps,d,a+6);
        if(jumps[i]==7) return paths(jumps,d,a+7);
    }
    return paths(jumps,d,a+1);

}

int main(){
    int n;
    int jumps[50];
    cin >> n;
    int d=n-1;
    for(int i=0;i<n;i++) cin >> jumps[i];
    cout << paths(jumps,d,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 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 namespace std;
int distpath(int n,int jumps[]){
    int count=1;
    for(int i=0;i<n;i++){
        if(i+jumps[i]<=n-1){
            count=count+jumps[i]-1;
        }

    }
    return count;
}
int main(){
    int n;
    cin>>n;
    int jumps[n];
    for(int i=0;i<n;i++){
        cin>>jumps[i];
    }
    cout<<distpath(n,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: 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 recurse(int jumps[],int n,int i)
    {
        int newi;
        if(i==n-1) return 1;
        if(i>n-1) return 0;
       
        for (int x=i+1; x<=i+jumps[i]; x++)
        {
            newi=x;
            return recurse(jumps, n, newi);
        }
    }    

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

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

    k=recurse(jumps,n,0);
    
    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