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;
void ways(int jumps[],int n,int pos,int *count){
    if(pos==n-1)
    {
        (*count)++;
    }
    if(pos<n){
        for(int k=1;k<=jumps[pos];k++)
        {
            if((pos+k)<n)
            {
                ways(jumps,n,pos+k,count);
            }
        }
    }
}
int main(){
    int n;
    cin>>n;
    int jumps[n];
    //maximum jumps from ith position
    for(int i=0;i<n;i++){
        cin>>jumps[i];
    }
    int count=0;
    ways(jumps,n,0,&count);
    cout<<count;
    
}

Grading criterion: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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 disPath(int arr[], int n, int index){
    if(n==0) return 0;
    if(n==1) return 1;
    for(int i=1; i<=arr[index]; i++){
        if((index+i)<n-1){
        return index+ disPath(arr, n, index+1);
        }
    }
}
int main(){
    int n, jumps[50];
    cin >> n;
    for(int i=0; i<n; i++){
        cin >> jumps[i];
    }
    int ans=disPath(jumps, n, 0);
    cout<< ans;
}

Grading criterion: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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;
   }
};
Memo mem;

int steps(int arr[100],int n,int ic=0){
    
    if(ic==n-1)return 1;
    if(ic>n-1)return 0;
    int m=0;
    int i=1;
    for(;i<=arr[ic] && i+ic<=n-1;i++){
        if(mem.has(i+ic)){
        m=m+mem.get(i+ic);
        }
        else
        m=m+steps(arr,n,ic+i);
    }
    mem.add(i+ic,m);
    return m;
    
}

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

Grading criterion: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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;
   }
};

int totalDistinctPaths(int jumps[],int n,Memo& memo,int pos) {
    if(memo.has(pos)) {
        return memo.get(pos);
    }
    int j = 0
    int paths = 0;
    for(int i=0;i<)
    paths = totalDistinctPaths(int jumps[],n,memo,pos+j)
    memo.add(n,paths);
    return paths;
}

int main() {
    Memo memo;
    int pos = 0;
    int n; cin >> n;
    int jumps[50];
    for(int i=0;i<n;i++) {
        cin >> jumps[i];
    }
    cout << totalDistinctPaths(jumps,n,memo,pos);
}

Grading criterion: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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 jumps[n] ;

    int i , j ;

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

    }
    
    i+j <= n ;
    
}

Grading criterion: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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

}
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: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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 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: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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>
#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: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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 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: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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<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: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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;
   }
};


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: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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 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: Declaration of variables and array
Rating A: correctly declares the variable n and array/vector

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