# Count the number of primes in the prefix sum array of the given array

Given an array arr[] of N integers, the task is to count the number of primes in the prefix sum array of the given array.

Examples:

Input: arr[] = {1, 4, 8, 4}
Output: 3
The prefix sum array is {1, 5, 13, 17}
and the three primes are 5, 13 and 17.

Input: arr[] = {1, 5, 2, 3, 7, 9}
Output: 1

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Create the prefix sum array and then use Sieve of Eratosthenes to count the number of primes in the prefix sum array.

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the count of primes ` `// in the given array ` `int` `primeCount(``int` `arr[], ``int` `n) ` `{ ` `    ``// Find maximum value in the array ` `    ``int` `max_val = *max_element(arr, arr + n); ` ` `  `    ``// USE SIEVE TO FIND ALL PRIME NUMBERS LESS ` `    ``// THAN OR EQUAL TO max_val ` `    ``// Create a boolean array "prime[0..n]". A ` `    ``// value in prime[i] will finally be false ` `    ``// if i is Not a prime, else true. ` `    ``vector<``bool``> prime(max_val + 1, ``true``); ` ` `  `    ``// Remaining part of SIEVE ` `    ``prime[0] = ``false``; ` `    ``prime[1] = ``false``; ` `    ``for` `(``int` `p = 2; p * p <= max_val; 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 <= max_val; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` ` `  `    ``// Find all primes in arr[] ` `    ``int` `count = 0; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``if` `(prime[arr[i]]) ` `            ``count++; ` ` `  `    ``return` `count; ` `} ` ` `  `// Function to generate the prefix array ` `void` `getPrefixArray(``int` `arr[], ``int` `n, ``int` `pre[]) ` `{ ` ` `  `    ``// Fill the prefix array ` `    ``pre[0] = arr[0]; ` `    ``for` `(``int` `i = 1; i < n; i++) { ` `        ``pre[i] = pre[i - 1] + arr[i]; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``int` `arr[] = { 1, 4, 8, 4 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` ` `  `    ``// Prefix array of arr[] ` `    ``int` `pre[n]; ` `    ``getPrefixArray(arr, n, pre); ` ` `  `    ``// Count of primes in the prefix array ` `    ``cout << primeCount(pre, n); ` ` `  `    ``return` `0; ` `} `

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG ` `{  ` `     `  `//returns the max element ` `static` `int` `max_element(``int` `a[]) ` `{ ` `    ``int` `m = a[``0``]; ` `    ``for``(``int` `i = ``0``; i < a.length; i++) ` `        ``m = Math.max(a[i], m); ` `     `  `    ``return` `m; ` `} ` ` `  `// Function to return the count of primes ` `// in the given array ` `static` `int` `primeCount(``int` `arr[], ``int` `n) ` `{ ` `    ``// Find maximum value in the array ` `    ``int` `max_val = max_element(arr); ` ` `  `    ``// USE SIEVE TO FIND ALL PRIME NUMBERS LESS ` `    ``// THAN OR EQUAL TO max_val ` `    ``// Create a boolean array "prime[0..n]". A ` `    ``// value in prime[i] will finally be false ` `    ``// if i is Not a prime, else true. ` `    ``boolean` `prime[] = ``new` `boolean``[max_val + ``1``]; ` `    ``for` `(``int` `p = ``0``; p <= max_val; p++) ` `        ``prime[p] = ``true``;  ` ` `  `    ``// Remaining part of SIEVE ` `    ``prime[``0``] = ``false``; ` `    ``prime[``1``] = ``false``; ` `    ``for` `(``int` `p = ``2``; p * p <= max_val; 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 <= max_val; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` ` `  `    ``// Find all primes in arr[] ` `    ``int` `count = ``0``; ` `    ``for` `(``int` `i = ``0``; i < n; i++) ` `        ``if` `(prime[arr[i]]) ` `            ``count++; ` ` `  `    ``return` `count; ` `} ` ` `  `// Function to generate the prefix array ` `static` `int``[] getPrefixArray(``int` `arr[], ``int` `n, ``int` `pre[]) ` `{ ` ` `  `    ``// Fill the prefix array ` `    ``pre[``0``] = arr[``0``]; ` `    ``for` `(``int` `i = ``1``; i < n; i++) ` `    ``{ ` `        ``pre[i] = pre[i - ``1``] + arr[i]; ` `    ``} ` `    ``return` `pre; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String args[]) ` `{ ` ` `  `    ``int` `arr[] = { ``1``, ``4``, ``8``, ``4` `}; ` `    ``int` `n = arr.length; ` ` `  `    ``// Prefix array of arr[] ` `    ``int` `pre[]=``new` `int``[n]; ` `    ``pre=getPrefixArray(arr, n, pre); ` ` `  `    ``// Count of primes in the prefix array ` `    ``System.out.println(primeCount(pre, n)); ` ` `  `} ` `} ` ` `  `// This code is contributed by Arnab Kundu `

 `# Python3 implementation of the approach  ` ` `  `# Function to return the count  ` `# of primes in the given array  ` `def` `primeCount(arr, n):  ` `  `  `    ``# Find maximum value in the array  ` `    ``max_val ``=` `max``(arr)  ` ` `  `    ``# USE SIEVE TO FIND ALL PRIME NUMBERS LESS  ` `    ``# THAN OR EQUAL TO max_val  ` `    ``# Create a boolean array "prime[0..n]". A  ` `    ``# value in prime[i] will finally be False  ` `    ``# if i is Not a prime, else True.  ` `    ``prime ``=` `[``True``] ``*` `(max_val``+``1``)  ` ` `  `    ``# Remaining part of SIEVE  ` `    ``prime[``0``] ``=` `prime[``1``] ``=` `False` `    ``p ``=` `2` `    ``while` `p ``*` `p <``=` `max_val:   ` ` `  `        ``# 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``, max_val``+``1``, p):  ` `                ``prime[i] ``=` `False` `                 `  `        ``p ``+``=` `1` `          `  `    ``# Find all primes in arr[]  ` `    ``count ``=` `0`  `    ``for` `i ``in` `range``(``0``, n):  ` `        ``if` `prime[arr[i]]:  ` `            ``count ``+``=` `1`  ` `  `    ``return` `count  ` `  `  `# Function to generate the prefix array  ` `def` `getPrefixArray(arr, n, pre):  ` `  `  `    ``# Fill the prefix array  ` `    ``pre[``0``] ``=` `arr[``0``]  ` `    ``for` `i ``in` `range``(``1``, n):   ` `        ``pre[i] ``=` `pre[i ``-` `1``] ``+` `arr[i]  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"``: ` `  `  `    ``arr ``=` `[``1``, ``4``, ``8``, ``4``]   ` `    ``n ``=` `len``(arr)  ` ` `  `    ``# Prefix array of arr[]  ` `    ``pre ``=` `[``None``] ``*` `n  ` `    ``getPrefixArray(arr, n, pre)  ` ` `  `    ``# Count of primes in the prefix array  ` `    ``print``(primeCount(pre, n))  ` ` `  `# This code is contributed by Rituraj Jain `

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{  ` `     `  `// returns the max element ` `static` `int` `max_element(``int``[] a) ` `{ ` `    ``int` `m = a[0]; ` `    ``for``(``int` `i = 0; i < a.Length; i++) ` `        ``m = Math.Max(a[i], m); ` `     `  `    ``return` `m; ` `} ` ` `  `// Function to return the count of primes ` `// in the given array ` `static` `int` `primeCount(``int``[] arr, ``int` `n) ` `{ ` `    ``// Find maximum value in the array ` `    ``int` `max_val = max_element(arr); ` ` `  `    ``// USE SIEVE TO FIND ALL PRIME NUMBERS LESS ` `    ``// THAN OR EQUAL TO max_val ` `    ``// Create a bool array "prime[0..n]". A ` `    ``// value in prime[i] will finally be false ` `    ``// if i is Not a prime, else true. ` `    ``bool``[] prime = ``new` `bool``[max_val + 1]; ` `    ``for` `(``int` `p = 0; p <= max_val; p++) ` `        ``prime[p] = ``true``;  ` ` `  `    ``// Remaining part of SIEVE ` `    ``prime[0] = ``false``; ` `    ``prime[1] = ``false``; ` `    ``for` `(``int` `p = 2; p * p <= max_val; 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 <= max_val; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` ` `  `    ``// Find all primes in arr[] ` `    ``int` `count = 0; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``if` `(prime[arr[i]]) ` `            ``count++; ` ` `  `    ``return` `count; ` `} ` ` `  `// Function to generate the prefix array ` `static` `int``[] getPrefixArray(``int``[] arr, ``int` `n, ``int``[] pre) ` `{ ` ` `  `    ``// Fill the prefix array ` `    ``pre[0] = arr[0]; ` `    ``for` `(``int` `i = 1; i < n; i++) ` `    ``{ ` `        ``pre[i] = pre[i - 1] + arr[i]; ` `    ``} ` `    ``return` `pre; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main() ` `{ ` ` `  `    ``int``[] arr = { 1, 4, 8, 4 }; ` `    ``int` `n = arr.Length; ` ` `  `    ``// Prefix array of arr[] ` `    ``int``[] pre = ``new` `int``[n]; ` `    ``pre = getPrefixArray(arr, n, pre); ` ` `  `    ``// Count of primes in the prefix array ` `    ``Console.Write(primeCount(pre, n)); ` ` `  `} ` `} ` ` `  `// This code is contributed by ChitraNayal `

 ` `

Output:
```3
```

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