Check if the given number K is enough to reach the end of an array

Given an array arr[] of n elements and a number K. The task is to determine if it is possible to reach the end of the array by doing the below operations:

Traverse the given array and,

  • If any element is found to be non-prime then decrement the value of K by 1.
  • If any element is prime then refill the value of K to its initial value.

If it is possible to reach the end of array with (K > 0), then print YES otherwise print NO.



Examples:

Input : K = 2   ,  arr[]={ 6, 3, 4, 5, 6} ;
Output : Yes
Explanation :
 1- arr[0] is not prime, so K = K-1 = 1
 2- arr[1] is prime so K will be refilled to its 
    initial value. Therefore,  K = 2.
 3- arr[2] is not prime.
    Therefore,  K = 2-1 = 1
 4- arr[3] is prime so K will be refilled to its 
    initial value. Therefore,  K = 2.
 5- arr[4] is not prime.
    Therefore,  K = 2-1 = 1
 6- Since the end of the array is reached with K>=0
    So output is YES

Input :  n=6 , k=3;
         arr[]={ 1, 2, 10, 4, 6, 8};
Output : No

Recommended: Please solve it on “PRACTICE “first , before moving on to the solution.

Simple Approach:

  • Traverse each element of the array and Check if the value of current element is prime or not.
  • If it is Prime then refill the power of K else decrement by 1.
  • If it is possible to reach the end of the array with (K > 0) then print “YES” otherwise “NO”.

Below is the implementation of the above approach:

C++

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// C++ program to check if it is possible
// to reach the end of the array
#include <iostream>
using namespace std;
  
// Function To check number is prime or not
bool is_Prime( int num ) 
{
    // because 1 is not prime 
    if(num == 1)
    return false;
      
    for(int i=2 ; i*i <= num ; i++ )
    {
        if( num % i == 0 )
        return false;
    }
      
return true
}
  
// Function to check whether it is possible
// to reach the end of the array or not     
bool isReachable( int arr[] , int n , int k)
{   
    // store initial value of K
    int x = k ;
              
    for(int i=0 ; i < n ; i++ )
    {
        // Call is_prime function to
        // check if a number is prime. 
        if( is_Prime(arr[i]) )
        {
            // Refill K to initial value
            k = x;
        }                 
        else
        {
            // Decrement k by 1
            k-- ;                 
        }
  
      
        if( k <= 0 && i < (n-1) && (!is_Prime(arr[i+1])) )
            return false ;
    }
              
    return true ;
}
  
// Driver Code
int main()
{
    int arr[] = { 6, 3, 4, 5, 6};
    int n = sizeof(arr)/sizeof(arr[0]) ;
    int k = 2 ;
  
          
    isReachable( arr , n , k ) ? cout << "Yes" << endl : 
                                    cout << "No" << endl ; 
          
    return 0 ;

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Java

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// Java program to check if 
// it is possible to reach
// the end of the array
import java.io.*;
import java.util.*;
import java.lang.*;
  
class GFG
{
      
// Function To check 
// number is prime or not
static boolean is_Prime(int num) 
{
    // because 1 is not prime 
    if(num == 1)
    return false;
      
    for(int i = 2 ;
            i * i <= num ; i++ )
    {
        if(num % i == 0)
        return false;
    }
      
return true
}
  
// Function to check whether 
// it is possible to reach
// the end of the array or not     
static boolean isReachable(int arr[] , 
                           int n , int k)
    // store initial value of K
    int x = k ;
              
    for(int i = 0 ; i < n ; i++ )
    {
        // Call is_prime function to
        // check if a number is prime. 
        if(is_Prime(arr[i]))
        {
            // Refill K to 
            // initial value
            k = x;
        }                 
        else
        {
            // Decrement k by 1
            k-- ;                 
        }
  
      
        if(k <= 0 && i < (n - 1) && 
          (is_Prime(arr[i + 1]) != true))
            return false ;
    }
              
    return true ;
}
  
// Driver Code
public static void main(String args[])
{
    int arr[] = new int[]{ 6, 3, 4, 5, 6};
    int n = arr.length;
    int k = 2 ;
  
    if(isReachable(arr, n, k) == true)
        System.out.print("Yes" + "\n");
     else
        System.out.print("No" + "\n"); 
}

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Python3

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# Python 3 program to check if it is 
# possible to reach the end of the array
from math import sqrt
  
# Function To check number is prime or not
def is_Prime(num):
      
    # because 1 is not prime 
    if(num == 1):
        return False
    k = int(sqrt(num)) + 1
  
    for i in range(2, k, 1):
        if(num % i == 0):
            return False
              
    return True
  
# Function to check whether it is possible
# to reach the end of the array or not 
def isReachable(arr, n , k):
      
    # store initial value of K
    x = k
              
    for i in range(0, n, 1):
          
        # Call is_prime function to
        # check if a number is prime. 
        if( is_Prime(arr[i])):
              
            # Refill K to initial value
            k = x     
        else:
              
            # Decrement k by 1
            k -= 1        
      
        if(k <= 0 and i < (n - 1) and 
          (is_Prime(arr[i + 1])) == False):
            return False
              
    return True
  
# Driver Code
if __name__ == '__main__':
    arr = [6, 3, 4, 5, 6]
    n = len(arr)
    k = 2
  
    if (isReachable( arr , n , k )):
        print("Yes")
    else:
        print("No")
  
# This code is contributed by
# Sahil_Shelangia

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C#

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// C# program to check if 
// it is possible to reach
// the end of the array
using System;
  
class GFG
{
      
// Function To check 
// number is prime or not
static bool is_Prime(int num) 
{
    // because 1 is not prime 
    if(num == 1)
    return false;
      
    for(int i = 2 ;
            i * i <= num ; i++ )
    {
        if(num % i == 0)
        return false;
    }
      
return true
}
  
// Function to check whether 
// it is possible to reach
// the end of the array or not 
static bool isReachable(int []arr , 
                        int n , int k)
    // store initial 
    // value of K
    int x = k ;
              
    for(int i = 0 ; i < n ; i++ )
    {
        // Call is_prime function 
        // to check if a number 
        // is prime. 
        if(is_Prime(arr[i]))
        {
            // Refill K to 
            // initial value
            k = x;
        }             
        else
        {
            // Decrement k by 1
            k-- ;             
        }
  
      
        if(k <= 0 && i < (n - 1) && 
        (is_Prime(arr[i + 1]) != true))
            return false ;
    }
              
    return true ;
}
  
// Driver Code
public static void Main()
{
    int []arr = new int[]{ 6, 3, 4, 5, 6};
    int n = arr.Length;
    int k = 2 ;
  
    if(isReachable(arr, n, k) == true)
        Console.WriteLine("Yes" + "\n");
    else
        Console.WriteLine("No" + "\n"); 
}
  
// This code is contributed by vt_m

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PHP

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<?php
// PHP program to check if it is possible
// to reach the end of the array
  
// Function To check number 
// is prime or not
function is_Prime($num
{
    // because 1 is not prime 
    if($num == 1)
    return false;
      
    for($i = 2 ; ($i * $i) <= $num ; $i++ )
    {
        if($num % $i == 0)
        return false;
    }
      
    return true; 
}
  
// Function to check whether it is possible
// to reach the end of the array or not 
function isReachable($arr , $n , $k)
    // store initial value of K
    $x = $k ;
              
    for($i = 0 ; $i < $n ; $i++)
    {
        // Call is_prime function to
        // check if a number is prime. 
        if(is_Prime($arr[$i]))
        {
            // Refill K to initial value
            $k = $x;
        }             
        else
        {
            // Decrement k by 1
            $k-- ;             
        }
  
      
        if($k <= 0 && $i < ($n - 1) &&
            (!is_Prime($arr[$i + 1])))
            return false ;
    }
              
    return true ;
}
  
// Driver Code
$arr = array(6, 3, 4, 5, 6);
$n = sizeof($arr);
$k = 2;
  
if(isReachable( $arr , $n , $k ))
    echo "Yes";
else
    echo "No"
      
// This code is contributed 
// by Sach_Code
?>

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Output:

Yes

Time complexity: O(N(sqrt N))

Efficient Approach: The above approach can be optimized by using Sieve of Eratosthenes to check if a number is prime or not.

Below is the implementation of the efficient approach:

C++

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// CPP program to check if it is possible
// to reach the end of the array
#include <iostream>
#define MAX 1000000
using namespace std;
  
// Function for Sieve of Eratosthenes
void SieveOfEratosthenes( int sieve[], int max ) 
{   
    for(int i=0; i<max; i++)
        sieve[i] = 1;
          
    for(int i=2 ; i*i <= max ; i++ )
    {
        if( sieve[i] == 1 )
        {
            for( int j=i*2 ; j <= max ; j+=i )
                sieve[ j ] = 0;
        }
    }
}
  
// Function to check if it is possible to
// reach end of the array     
bool isReachable( int arr[] , int n , int sieve[] , int k)
{   
    // store initial value of K
    int x = k; 
      
    for(int i=0 ; i < n ; i++ )
    {   
        if( sieve[arr[i]] )
        {   
            // Refill K to initial value
            k = x;
        }                 
         else
        {
            // Decrement k by 1
            k -= 1;                 
        }
  
          
        if((k <= 0) && (i < (n-1)) && 
                        (sieve[arr[i+1]] == 0))
        {
            return false ;   
        }               
    }
              
    return true ;
}
  
// Driver Code
int main()
{
    int arr[] = {6, 3, 4, 5, 6};
      
    int sieve[MAX];
      
    int n = sizeof(arr)/sizeof(arr[0]) ;
      
    int k = 2;
          
  
    SieveOfEratosthenes(sieve, MAX) ; 
  
    isReachable( arr , n , sieve , k ) ? cout << "Yes" << endl :
                                            cout << "No" << endl ; 
  
    return 0 ;

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Java

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// Java program to check if it is possible
// to reach the end of the array
class GFG 
{
  
    static int MAX = 1000000;
  
    // Function for Sieve of Eratosthenes
    static void SieveOfEratosthenes(int sieve[], int max) 
    {
        for (int i = 0; i < max; i++) 
        {
            sieve[i] = 1;
        }
  
        for (int i = 2; i * i < max; i++) 
        {
            if (sieve[i] == 1)
            {
                for (int j = i * 2; j < max; j += i) 
                {
                    sieve[j] = 0;
                }
            }
        }
    }
  
    // Function to check if it is possible to
    // reach end of the array     
    static boolean isReachable(int arr[], int n, 
                                int sieve[], int k) 
    {
        // store initial value of K
        int x = k;
  
        for (int i = 0; i < n; i++) 
        {
            if (sieve[arr[i]] == 1
            {
                // Refill K to initial value
                k = x;
            
            else
            {
                // Decrement k by 1
                k -= 1;
            }
  
            if ((k <= 0) && (i < (n - 1))
                    && (sieve[arr[i + 1]] == 0)) 
            {
                return false;
            }
        }
  
        return true;
    }
  
    // Driver Code
    public static void main(String[] args) 
    {
        int arr[] = {6, 3, 4, 5, 6};
        int[] sieve = new int[MAX];
        int n = arr.length;
        int k = 2;
  
        SieveOfEratosthenes(sieve, MAX);
  
        if (isReachable(arr, n, sieve, k)) 
        {
            System.out.println("Yes");
        
        else
        {
            System.out.println("No");
        }
    }
}
  
/* This code contributed by PrinciRaj1992 */

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C#

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// C# program to check if it is possible
// to reach the end of the array
using System;
  
class GFG
{
    static int MAX = 1000000;
  
    // Function for Sieve of Eratosthenes
    static void SieveOfEratosthenes(int []sieve, int max) 
    {
        for (int i = 0; i < max; i++) 
        {
            sieve[i] = 1;
        }
  
        for (int i = 2; i * i < max; i++) 
        {
            if (sieve[i] == 1)
            {
                for (int j = i * 2; j < max; j += i) 
                {
                    sieve[j] = 0;
                }
            }
        }
    }
  
    // Function to check if it is possible to
    // reach end of the array 
    static bool isReachable(int []arr, int n, 
                                int []sieve, int k) 
    {
        // store initial value of K
        int x = k;
  
        for (int i = 0; i < n; i++) 
        {
            if (sieve[arr[i]] == 1) 
            {
                // Refill K to initial value
                k = x;
            
            else
            {
                // Decrement k by 1
                k -= 1;
            }
  
            if ((k <= 0) && (i < (n - 1))
                    && (sieve[arr[i + 1]] == 0)) 
            {
                return false;
            }
        }
  
        return true;
    }
  
    // Driver Code
    static public void Main ()
    {
        int []arr = {6, 3, 4, 5, 6};
        int[] sieve = new int[MAX];
        int n = arr.Length;
        int k = 2;
  
        SieveOfEratosthenes(sieve, MAX);
  
        if (isReachable(arr, n, sieve, k)) 
        {
            Console.WriteLine("Yes");
        
        else
        {
            Console.WriteLine("No");
        }
    }
}
  
/* This code contributed by ajit. */

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Output:

Yes

Time complexity: O(?Max * loglog(Max)) + O(n)



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