Maximum Number of Contiguous Prime Numbers in an Array in C++

We are given with an array of prime numbers, arranged in random order. The size of the array is N. The goal is to find the longest sequence of contiguous prime numbers in the array.

Prime number is the one which has only two factors, 1 and the number itself. 1,2,3,5,7,11,13….are prime numbers whereas 4,6,8,9,10….20 are non-prime. Every non-prime number has more than 2 factors. Let’s understand with examples.

Input − Arr[] = { 1,3,5,2,6,7,13,4,9,10

Output − 3

Explanation − The prime numbers in the above array are 3,5,2,7,13. The numbers that are contiguous are 3,5,2 and 7,13. Longest sequence has 3 numbers. So the answer is 4.

Input − Arr[] = { 5,7,17,27,31,21,41 }.

Output − 3

Explanation − The prime numbers in the above array are 5,7,17,31,41. The numbers that are contiguous are 5,7,17. Longest sequence has 3 numbers. So the answer is 3.

Approach used in the below program is as follows

• The integer array Arr[] is used to store the prime and non-prime numbers.

• Function isprime(int num) is used to check whether the num is prime or not. If it is prime then it must have no factor till it’s half is reached.

• For prime numbers isprime() returns 1 else it returns 0.

• Function primeSubarray(int arr[], int n) takes two input parameters. The array of numbers itself, its size. Returns the size of the longest sequence of contiguous prime numbers.

• Traverse the numbers in arr[] from start. If arr[i] is non-prime ( isprime(arr[i])==0 ). Then change the count of contiguous prime numbers as 0.

• If it is prime, then increment the count of prime numbers. (It will start from 0 again if nonprime is encountered)

• Check if the count is maximum so far, if yes store it’s value in maxC.

• Return the maxC as result.

Example

 Live Demo

#include <iostream>
#include <stdio.h>
int isprime(int num){
   if (num <= 1)
      return 0;
   for (int i = 2; i <= num/2; i++)
      if (num % i == 0)
         return 0;
   return 1; //if both failed then num is prime
}
int primeSubarray(int arr[], int n){
   int count=0;
   int maxSeq=0;
   for (int i = 0; i < n; i++) {
      // if non-prime
      if (isprime(arr[i]) == 0)
         count = 0;
         //if prime
      else {
         count++;
         //printf("\n%d",arr[i]); print prime number subsequence
         maxSeq=count>maxSeq?count:maxSeq;
      }
   }
   return maxSeq;
}
int main(){
   int arr[] = { 8,4,2,1,3,5,7,9 };
   int n =8;
   printf("Maximum no. of contiguous Prime Numbers in an array: %d",
   primeSubarray(arr, n));
   return 0;
}

Output

If we run the above code it will generate the following output −

Maximum no. of contiguous Prime Numbers in an array : 3