# Minimum and Maximum prime numbers in an array

Given an array arr[] of N positive integers. The task is to find the minimum and maximum prime elements in the given array.

Examples:

```Input: arr[] = 1, 3, 4, 5, 7
Output: Minimum : 3
Maximum : 7

Input: arr[] = 1, 2, 3, 4, 5, 6, 7, 11
Output: Minimum : 2
Maximum : 11
```

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

Naive Approach:
Take a variable min and max. Initialize min with INT_MAX and max with INT_MIN.Traverse the array and keep checking for every element if it is prime or not and update the minimum and maximum prime element at the same time.
Efficient Approach:
Generate all primes upto maximum element of the array using sieve of Eratosthenes and store them in a hash. Now traverse the array and find the minimum and maximum element which are prime using the hash table.

Below is the implementation of above approach:

 `// CPP program to find minimum and maximum ` `// prime number in given array. ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find count of prime ` `void` `prime(``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 = ``false``; ` `    ``prime = ``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``; ` `        ``} ` `    ``} ` ` `  `    ``// Minimum and Maximum prime number ` `    ``int` `minimum = INT_MAX; ` `    ``int` `maximum = INT_MIN; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``if` `(prime[arr[i]]) { ` `            ``minimum = min(minimum, arr[i]); ` `            ``maximum = max(maximum, arr[i]); ` `        ``} ` ` `  `    ``cout << ``"Minimum : "` `<< minimum << endl; ` `    ``cout << ``"Maximum : "` `<< maximum << endl; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``int` `arr[] = { 1, 2, 3, 4, 5, 6, 7 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` ` `  `    ``prime(arr, n); ` ` `  `    ``return` `0; ` `} `

 `// Java program to find minimum and maximum  ` `// prime number in given array. ` `import` `java.util.*; ` ` `  `class` `GFG {  ` ` `  `// Function to find count of prime  ` `static` `void` `prime(``int` `arr[], ``int` `n)  ` `{  ` `    ``// Find maximum value in the array  ` `    ``int` `max_val = Arrays.stream(arr).max().getAsInt(); ` ` `  `         `  `    ``// 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 prime = ``new` `Vector();  ` `        ``for``(``int` `i= ``0``;i

 `# Python3 program to find minimum and  ` `# maximum prime number in given array. ` `import` `math as mt ` ` `  `# Function to find count of prime ` `def` `Prime(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` `for` `i ``in` `range``(max_val ``+` `1``)] ` ` `  `    ``# Remaining part of SIEVE ` `    ``prime[``0``] ``=` `False` `    ``prime[``1``] ``=` `False` `    ``for` `p ``in` `range``(``2``, mt.ceil(mt.sqrt(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``(``2` `*` `p, max_val ``+` `1``, p): ` `                    ``prime[i] ``=` `False` `         `  `    ``# Minimum and Maximum prime number ` `    ``minimum ``=` `10``*``*``9` `    ``maximum ``=` `-``10``*``*``9` `    ``for` `i ``in` `range``(n): ` `        ``if` `(prime[arr[i]] ``=``=` `True``): ` `            ``minimum ``=` `min``(minimum, arr[i]) ` `            ``maximum ``=` `max``(maximum, arr[i]) ` `         `  `    ``print``(``"Minimum : "``, minimum ) ` `    ``print``(``"Maximum : "``, maximum ) ` ` `  `# Driver code ` `arr ``=` `[``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``] ` `n ``=` `len``(arr) ` ` `  `Prime(arr, n) ` ` `  `# This code is contributed by ` `# Mohit kumar 29 `

 `// A C# program to find minimum and maximum  ` `// prime number in given array. ` `using` `System; ` `using` `System.Linq; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG  ` `{  ` ` `  `// Function to find count of prime  ` `static` `void` `prime(``int` `[]arr, ``int` `n)  ` `{  ` `    ``// Find maximum value in the array  ` `    ``int` `max_val = arr.Max(); ` ` `  `         `  `    ``// 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.  ` `    ``List<``bool``>prime = ``new` `List<``bool``>();  ` `        ``for``(``int` `i = 0; i < max_val + 1;i++) ` `            ``prime.Add(``true``); ` `         `  `    ``// Remaining part of SIEVE  ` `    ``prime.Insert(0, ``false``); ` `    ``prime.Insert(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.Insert(i, ``false``);  ` `        ``}  ` `    ``}  ` ` `  `    ``// Minimum and Maximum prime number  ` `    ``int` `minimum = ``int``.MaxValue;  ` `    ``int` `maximum = ``int``.MinValue;  ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `        ``if` `(prime[arr[i]])  ` `        ``{  ` `            ``minimum = Math.Min(minimum, arr[i]);  ` `            ``maximum = Math.Max(maximum, arr[i]);  ` `        ``}  ` ` `  `    ``Console.WriteLine(``"Minimum : "` `+ minimum) ; ` `    ``Console.WriteLine(``"Maximum : "` `+ maximum );  ` `}  ` ` `  `    ``// Driver code  ` `    ``public` `static` `void` `Main()  ` `    ``{ ` `        ``int` `[]arr = { 1, 2, 3, 4, 5, 6, 7 };  ` `        ``int` `n = arr.Length;  ` ` `  `        ``prime(arr, n);  ` `    ``} ` `} ` ` `  `/* This code contributed by PrinciRaj1992 */`

Output:
```Minimum : 2
Maximum : 7
```

Time complexity : O(n*log(log(n)))

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