Maximum no. of contiguous Prime Numbers in an array
Given an array arr[] of N elements. The task is to find the maximum number of the contiguous prime numbers in the given array.
Examples:
Input: arr[] = {3, 5, 2, 66, 7, 11, 8}
Output: 3
Maximum contiguous prime number sequence is {2, 3, 5}
Input: arr[] = {1, 0, 2, 11, 32, 8, 9}
Output: 2
Maximum contiguous prime number sequence is {2, 11}
Approach:
- Create a sieve to check whether an element is prime or not in O(1).
- Traverse the array with two variables named current_max and max_so_far.
- If a prime number is found then increment current_max and compare it with max_so_far.
- If current_max is greater than max_so_far, then assign max_so_far with current_max
- Every time a non-prime element is found reset current_max to 0.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;void SieveOfEratosthenes(bool prime[], int p_size){ // false here indicates // that it is not prime prime[0] = false; prime[1] = false; for (int p = 2; p * p <= p_size; p++) { // If prime[p] is not changed, // then it is a prime if (prime[p]) { // Update all multiples of p, // set them to non-prime for (int i = p * p; i <= p_size; i += p) prime[i] = false; } }}// Function that finds// maximum contiguous subarray of prime numbersint maxPrimeSubarray(int arr[], int n){ int max_ele = *max_element(arr, arr+n); bool prime[max_ele + 1]; memset(prime, true, sizeof(prime)); SieveOfEratosthenes(prime, max_ele); int current_max = 0, max_so_far = 0; for (int i = 0; i < n; i++) { // check if element is non-prime if (prime[arr[i]] == false) current_max = 0; // If element is prime, than update // current_max and max_so_far accordingly. else { current_max++; max_so_far = max(current_max, max_so_far); } } return max_so_far;}// Driver codeint main(){ int arr[] = { 1, 0, 2, 4, 3, 29, 11, 7, 8, 9 }; int n = sizeof(arr) / sizeof(arr[0]); cout << maxPrimeSubarray(arr, n); return 0;} |
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Java
// Java implementation of the approachimport java.util.*;class GFG {static void SieveOfEratosthenes(boolean prime[], int p_size){ // false here indicates // that it is not prime prime[0] = false; prime[1] = false; for (int p = 2; p * p <= p_size; p++) { // If prime[p] is not changed, // then it is a prime if (prime[p]) { // Update all multiples of p, // set them to non-prime for (int i = p * p; i <= p_size; i += p) prime[i] = false; } }}// Function that finds// maximum contiguous subarray of prime numbersstatic int maxPrimeSubarray(int arr[], int n){ int max_ele = Arrays.stream(arr).max().getAsInt(); boolean prime[] = new boolean[max_ele + 1]; Arrays.fill(prime, true); SieveOfEratosthenes(prime, max_ele); int current_max = 0, max_so_far = 0; for (int i = 0; i < n; i++) { // check if element is non-prime if (prime[arr[i]] == false) current_max = 0; // If element is prime, than update // current_max and max_so_far accordingly. else { current_max++; max_so_far = Math.max(current_max, max_so_far); } } return max_so_far;}// Driver codepublic static void main(String[] args) { int arr[] = { 1, 0, 2, 4, 3, 29, 11, 7, 8, 9 }; int n = arr.length; System.out.print(maxPrimeSubarray(arr, n));}}/* This code contributed by PrinciRaj1992 */ |
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Python 3
# Python3 implementation of # the approach def SieveOfEratosthenes( prime, p_size): # false here indicates # that it is not prime prime[0] = False prime[1] = False for p in range(2,p_size+1): if(p*p>p_size): break # If prime[p] is not changed, # then it is a prime if (prime[p]): # Update all multiples of p, # set them to non-prime i=p*p while(i<=p_size): prime[i] = False i = i + p # Function that finds # maximum contiguous subarray of prime numbers def maxPrimeSubarray( arr, n): max_ele = max(arr) prime=[True]*(max_ele + 1) SieveOfEratosthenes(prime, max_ele) current_max = 0 max_so_far = 0 for i in range(n): # check if element is non-prime if (prime[arr[i]] == False): current_max = 0 # If element is prime, than update # current_max and max_so_far accordingly. else: current_max=current_max + 1 max_so_far = max(current_max, max_so_far) return max_so_far # Driver code if __name__=='__main__': arr = [ 1, 0, 2, 4, 3, 29, 11, 7, 8, 9 ] n = len(arr) print(maxPrimeSubarray(arr, n))# this code is contributed by # ash264 |
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C#
// C# implementation of the approachusing System; using System.Linq;class GFG {static void SieveOfEratosthenes(bool []prime, int p_size){ // false here indicates // that it is not prime prime[0] = false; prime[1] = false; for (int p = 2; p * p <= p_size; p++) { // If prime[p] is not changed, // then it is a prime if (prime[p]) { // Update all multiples of p, // set them to non-prime for (int i = p * p; i <= p_size; i += p) prime[i] = false; } }}// Function that finds maximum // contiguous subarray of prime numbersstatic int maxPrimeSubarray(int []arr, int n){ int max_ele = arr.Max(); bool []prime = new bool[max_ele + 1]; for(int i = 0; i < max_ele + 1; i++) prime[i]=true; SieveOfEratosthenes(prime, max_ele); int current_max = 0, max_so_far = 0; for (int i = 0; i < n; i++) { // check if element is non-prime if (prime[arr[i]] == false) current_max = 0; // If element is prime, than update // current_max and max_so_far accordingly. else { current_max++; max_so_far = Math.Max(current_max, max_so_far); } } return max_so_far;}// Driver codepublic static void Main(String[] args) { int []arr = { 1, 0, 2, 4, 3, 29, 11, 7, 8, 9 }; int n = arr.Length; Console.Write(maxPrimeSubarray(arr, n));}}// This code contributed by Rajput-Ji |
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Output
4
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