删除一个元素后的最长素数子数组

给定一个整数数组 A。我们最多可以从数组中删除一个索引。我们的目标是最大化包含所有素数的子数组的长度。打印通过从数组中删除一个元素可以实现的最大长度子数组。

例子：

Input : arr[] = { 2, 8, 5, 7, 9, 5, 7 }
Output : 4
Explanation :If we remove the number 9 which is at index 5 then the remaining array contains a subarray whose length is 4 which is maximum.

Input : arr[] = { 2, 3, 5, 7 }
Output : 3
If we remove the number 3 which is at index 1 then the remaining array contains a subarray whose length is 3 which is maximum.

这个想法是在每个索引之前和每个索引之后计算连续的素数。现在再次遍历数组并找到一个索引，其中前后素数之和最大。

C++

// CPP program to find length of the longest
// subarray with all primes except possibly
// one.
#include 
using namespace std;
#define N 100000
 
bool prime[N];
 
void SieveOfEratosthenes()
{
    // Create a boolean array "prime[0..n]" and
    // initialize all entries it as true. A value
    // in prime[i] will finally be false if i is
    // Not a prime, else true.
    memset(prime, true, sizeof(prime));
 
    for (int p = 2; p * p <= N; p++) {
 
        // If prime[p] is not changed,
        // then it is a prime
        if (prime[p] == true) {
            
            // Update all multiples of p
            for (int i = p * 2; i <= N; i += p)
                prime[i] = false;
        }
    }
}
 
 
int longestPrimeSubarray(int arr[], int n)
{
    int left[n], right[n];
    int primecount = 0, res = 0;
 
    // left array used to count number of
    // continuous prime numbers starting
    // from left of current element
    for (int i = 0; i < n; i++) {
        left[i] = primecount;
        if (prime[arr[i]]) {
            primecount++;
        }
        else
            primecount = 0;
    }
 
    // right array used to count number of
    // continuous prime numbers starting from
    // right of current element
    primecount = 0;
    for (int i = n - 1; i >= 0; i--) {
        right[i] = primecount;
        if (prime[arr[i]]) {
            primecount++;
        }
        else
            primecount = 0;
    }
 
    for (int i = 0; i < n; i++)
        res = max(res, left[i] + right[i]);
     
    return res;
}
 
// Driver code
int main()
{
    int arr[] = { 2, 8, 5, 7, 9, 5, 7 };
 
    // used of SieveOfEratosthenes method to
    // detect a number prime or not
    SieveOfEratosthenes();
    int n = sizeof(arr) / sizeof(arr[0]);
 
    cout << "largest length of PrimeSubarray "
         << longestPrimeSubarray(arr, n) << endl;
 
    return 0;
}

Java

// Java program to find length of the longest
// subarray with all primes except possibly
// one.
import java.util.*;
 
class GFG
{
     
static int N = 100000;
 
static boolean prime[] = new boolean[N];
 
static void SieveOfEratosthenes()
{
    // Create a boolean array "prime[0..n]" and
    // initialize all entries it as true. A value
    // in prime[i] will finally be false if i is
    // Not a prime, else true.
    Arrays.fill(prime,true);
 
    for (int p = 2; p * p <= N; p++)
    {
 
        // If prime[p] is not changed,
        // then it is a prime
        if (prime[p] == true)
        {
             
            // Update all multiples of p
            for (int i = p * 2; i < N; i += p)
                prime[i] = false;
        }
    }
}
 
 
static int longestPrimeSubarray(int arr[], int n)
{
    int []left = new int[n];int[] right = new int[n];
    int primecount = 0, res = 0;
 
    // left array used to count number of
    // continuous prime numbers starting
    // from left of current element
    for (int i = 0; i < n; i++)
    {
        left[i] = primecount;
        if (prime[arr[i]])
        {
            primecount++;
        }
        else
            primecount = 0;
    }
 
    // right array used to count number of
    // continuous prime numbers starting from
    // right of current element
    primecount = 0;
    for (int i = n - 1; i >= 0; i--)
    {
        right[i] = primecount;
        if (prime[arr[i]])
        {
            primecount++;
        }
        else
            primecount = 0;
    }
 
    for (int i = 0; i < n; i++)
        res = Math.max(res, left[i] + right[i]);
     
    return res;
}
 
// Driver code
public static void main(String[] args)
{
    int arr[] = { 2, 8, 5, 7, 9, 5, 7 };
 
    // used of SieveOfEratosthenes method to
    // detect a number prime or not
    SieveOfEratosthenes();
    int n = arr.length;
 
    System.out.println("largest length of PrimeSubarray "
        + longestPrimeSubarray(arr, n));
}
}
 
// This code contributed by Rajput-Ji

Python3

# Python 3 program to find length of the
# longest subarray with all primes except
# possibly one.
from math import sqrt
N = 100000
 
prime = [True for i in range(N + 1)]
 
def SieveOfEratosthenes():
     
    # Create a boolean array "prime[0..n]"
    # and initialize all entries it as true.
    # A value in prime[i] will finally be
    # false if i is Not a prime, else true.
    k = int(sqrt(N)) + 1
    for p in range(2, k, 1):
         
        # If prime[p] is not changed,
        # then it is a prime
        if (prime[p] == True):
             
            # Update all multiples of p
            for i in range(p * 2, N + 1, p):
                prime[i] = False
                 
def longestPrimeSubarray(arr, n):
    left = [0 for i in range(n)]
    right = [0 for i in range(n)]
    primecount = 0
    res = 0
 
    # left array used to count number of
    # continuous prime numbers starting
    # from left of current element
    for i in range(n):
        left[i] = primecount
        if (prime[arr[i]]):
            primecount += 1
         
        else:
            primecount = 0
         
    # right array used to count number of
    # continuous prime numbers starting
    # from right of current element
    primecount = 0
    i = n - 1
    while(i >= 0):
        right[i] = primecount
        if (prime[arr[i]]):
            primecount += 1
     
        else:
            primecount = 0
             
        i -= 1
 
    for i in range(n):
        res = max(res, left[i] + right[i])
     
    return res
 
# Driver code
if __name__ == '__main__':
    arr = [2, 8, 5, 7, 9, 5, 7]
 
    # used of SieveOfEratosthenes method
    # to detect a number prime or not
    SieveOfEratosthenes()
    n = len(arr)
    print("largest length of PrimeSubarray",
               longestPrimeSubarray(arr, n))
     
# This code is contributed by
# Surendra_Gangwar

C#

// C# program to find length of the longest
// subarray with all primes except possibly
// one.
using System;
 
class GFG
{
     
    static int N = 100000;
     
    static bool []prime = new bool[N];
     
    static void SieveOfEratosthenes()
    {
        // Create a boolean array "prime[0..n]" and
        // initialize all entries it as true. A value
        // in prime[i] will finally be false if i is
        // Not a prime, else true.
        for(int i =0;i= 0; i--)
        {
            right[i] = primecount;
            if (prime[arr[i]])
            {
                primecount++;
            }
            else
                primecount = 0;
        }
     
        for (int i = 0; i < n; i++)
            res = Math.Max(res, left[i] + right[i]);
         
        return res;
    }
     
    // Driver code
    public static void Main(String[] args)
    {
        int []arr = { 2, 8, 5, 7, 9, 5, 7 };
     
        // used of SieveOfEratosthenes method to
        // detect a number prime or not
        SieveOfEratosthenes();
        int n = arr.Length;
     
        Console.WriteLine("largest length of PrimeSubarray "
            + longestPrimeSubarray(arr, n));
    }
}
 
// This code has been contributed by 29AjayKumar

PHP

= 0; $i--)
    {
        $right[$i] = $primecount;
        if ($prime[$arr[$i]])
        {
            $primecount++;
        }
        else
            $primecount = 0;
    }
 
    for ($i = 0; $i < $n; $i++)
        $res = max($res, $left[$i] +   
                         $right[$i]);
     
    return $res;
}
 
// Driver Code
$arr = array(2, 8, 5, 7, 9, 5, 7);
 
// used of SieveOfEratosthenes method
// to detect a number prime or not
SieveOfEratosthenes();
$n = count($arr);
 
echo "largest length of PrimeSubarray " .
      longestPrimeSubarray($arr, $n);
 
// This code is contributed by mits
?>

Javascript

 
// Javascript program to find length of the longest
// subarray with all primes except possibly
// one.
var N = 100000;
var prime = Array.from({length: N}, (_, i) => true);
 
function SieveOfEratosthenes()
{
     
    // Create a boolean array "prime[0..n]" and
    // initialize all entries it as true. A value
    // in prime[i] will finally be false if i is
    // Not a prime, else true.
    for (var p = 2; p * p <= N; p++)
    {
         
        // If prime[p] is not changed,
        // then it is a prime
        if (prime[p] == true)
        {
             
            // Update all multiples of p
            for(var i = p * 2; i < N; i += p)
                prime[i] = false;
        }
    }
}
 
function longestPrimeSubarray(arr , n)
{
    var left = Array.from({length: n}, (_, i) => 0);
    var right = Array.from({length: n}, (_, i) => 0);
    var primecount = 0, res = 0;
 
    // Left array used to count number of
    // continuous prime numbers starting
    // from left of current element
    for(var i = 0; i < n; i++)
    {
        left[i] = primecount;
        if (prime[arr[i]])
        {
            primecount++;
        }
        else
            primecount = 0;
    }
 
    // Right array used to count number of
    // continuous prime numbers starting from
    // right of current element
    primecount = 0;
    for(var i = n - 1; i >= 0; i--)
    {
        right[i] = primecount;
        if (prime[arr[i]])
        {
            primecount++;
        }
        else
            primecount = 0;
    }
 
    for(var i = 0; i < n; i++)
        res = Math.max(res, left[i] + right[i]);
     
    return res;
}
 
// Driver code
var arr = [ 2, 8, 5, 7, 9, 5, 7 ];
 
// Used of SieveOfEratosthenes method to
// detect a number prime or not
SieveOfEratosthenes();
var n = arr.length;
 
document.write("largest length of PrimeSubarray " +
      longestPrimeSubarray(arr, n));
 
// This code is contributed by shikhasingrajput
 

输出：

largest length of PrimeSubarray 4