# Difference between the largest and the smallest primes in an array

Given an array of integers where all the elements are less than 10^6.
The task is to find the difference between the largest and the smallest prime numbers in the array.

Examples:

```Input : Array = 1, 2, 3, 5
Output : Difference is 3
Explanation :
The largest prime number in the array is 5 and the smallest is 2
So, the difference is 3

Input : Array = 3, 5, 11, 17
Output : Difference is 14
```

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

A Simple approach:
In the basic approach, we will check every element of the array whether it is prime or not.
Then, select the largest and the smallest prime numbers and print the difference.

Efficient approach:
The efficient approach is much similar to the basic approach.
We will try to reduce the time for checking the number against prime by creating a Sieve of Eratosthenes to check whether the number is prime or not in O(1) time.
And then, we will select the largest and the smallest prime numbers and print the difference.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` `#define MAX 1000000 ` `bool` `prime[MAX + 1]; ` ` `  `void` `SieveOfEratosthenes() ` `{ ` `    ``// Create a boolean array "prime[0..n]" and initialize ` `    ``// all the entries as true. A value in prime[i] will ` `    ``// finally be false if 'i' is Not a prime, else true. ` ` `  `    ``memset``(prime, ``true``, ``sizeof``(prime)); ` ` `  `    ``// 1 is not prime ` `    ``prime = ``false``; ` ` `  `    ``for` `(``int` `p = 2; p * p <= MAX; 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; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` `} ` ` `  `int` `findDiff(``int` `arr[], ``int` `n) ` `{ ` `    ``// initial min max value ` `    ``int` `min = MAX + 2, max = -1; ` `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// check if the number is prime or not ` `        ``if` `(prime[arr[i]] == ``true``) { ` ` `  `            ``// set the max and min values ` `            ``if` `(arr[i] > max) ` `                ``max = arr[i]; ` `            ``if` `(arr[i] < min) ` `                ``min = arr[i]; ` `        ``} ` `    ``} ` ` `  `    ``return` `(max == -1)? -1 : (max - min); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``// create the sieve ` `    ``SieveOfEratosthenes(); ` `    ``int` `n = 4; ` `    ``int` `arr[n] = { 1, 2, 3, 5 }; ` ` `  `    ``int` `res = findDiff(arr, n); ` ` `  `    ``if` `(res == -1) ` `        ``cout << ``"No prime numbers"` `<< endl; ` `    ``else` `        ``cout << ``"Difference is "` `<< res << endl; ` `    ``return` `0; ` `} `

## Java

 `// java implementation of the approach ` ` `  `import` `java.io.*; ` `class` `GFG { ` `static` `int` `MAX = ``1000000``; ` `  `  `static` `boolean` `prime[] = ``new` `boolean``[MAX + ``1``]; ` ` `  `static` `void` `SieveOfEratosthenes() ` `{ ` `    ``// Create a boolean array "prime[0..n]" and initialize ` `    ``// all the entries 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` `i=``0``;i max) ` `                ``max = arr[i]; ` `            ``if` `(arr[i] < min) ` `                ``min = arr[i]; ` `        ``} ` `    ``} ` ` `  `    ``return` `(max == -``1``)? -``1` `: (max - min); ` `} ` ` `  `// Driver code ` ` `  `    ``public` `static` `void` `main (String[] args) { ` `        ``// create the sieve ` `    ``SieveOfEratosthenes(); ` `    ``int` `n = ``4``; ` `    ``int` `arr[] = { ``1``, ``2``, ``3``, ``5` `}; ` ` `  `    ``int` `res = findDiff(arr, n); ` ` `  `    ``if` `(res == -``1``) ` `        ``System.out.print( ``"No prime numbers"``) ; ` `    ``else` `        ``System.out.println( ``"Difference is "` `+ res); ` `    ``} ` `} ` ` `  `// This code is contributed by inder_verma.. `

## Python 3

 `# Python 3 implementation of the approach ` `MAX` `=` `1000000` ` `  `# Create a boolean array "prime[0..n]" and initialize ` `# all the entries as true. A value in prime[i] will ` `# finally be false if 'i' is Not a prime, else true  ` `prime ``=` `[``True``]``*``(``MAX``+``1``) ` ` `  `def` `SieveOfEratosthenes(): ` ` `  `    ``# 1 is not prime ` `    ``prime[``1``] ``=` `False` `     `  `    ``p ``=` `2` `    ``c``=``0` `    ``while` `(p ``*` `p <``=` `MAX``) : ` `        ``c``+``=` `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``, ``MAX``+``1` `, p): ` `                ``prime[i] ``=` `False` `                 `  `        ``p ``+``=` `1` ` `  ` `  `def` `findDiff(arr, n): ` `     `  `    ``# initial min max value ` `    ``min` `=` `MAX` `+` `2` `    ``max` `=` `-``1` ` `  `    ``for` `i ``in` `range``(n) : ` `         `  `        ``# check if the number is prime or not ` `        ``if` `(prime[arr[i]] ``=``=` `True``) : ` ` `  `            ``# set the max and min values ` `            ``#print("arra ",arr[i]) ` `            ``#print("MAX ",max) ` `            ``#print(" MIN ",min) ` `            ``if` `(arr[i] > ``max``): ` `                ``max` `=` `arr[i] ` `            ``if` `(arr[i] < ``min``): ` `                ``min` `=` `arr[i] ` `             `  `    ``#print(" max ",max) ` `    ``return` `-``1` `if` `(``max` `=``=` `-``1``) ``else` `(``max` `-` `min``) ` ` `  `# Driver code ` `if` `__name__ ``=``=` `"__main__"``: ` `     `  `    ``# create the sieve ` `    ``SieveOfEratosthenes() ` `    ``n ``=` `4` `    ``arr ``=` `[ ``1``, ``2``, ``3``, ``5` `] ` ` `  `    ``res ``=` `findDiff(arr, n) ` ` `  `    ``if` `(res ``=``=` `-``1``): ` `        ``print``(``"No prime numbers"``) ` `    ``else``: ` `        ``print``(``"Difference is "` `,res ) ` ` `  `# this code is contributed by ` `# ChitraNayal `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `static` `int` `MAX = 1000000; ` ` `  `static` `bool` `[]prime = ``new` `bool``[MAX + 1]; ` ` `  `static` `void` `SieveOfEratosthenes() ` `{ ` `    ``// Create a boolean array "prime[0..n]"  ` `    ``// and initialize all the entries 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` `i = 0; i < MAX + 1; i++) ` `    ``prime[i] = ``true``; ` ` `  `    ``// 1 is not prime ` `    ``prime = ``false``; ` ` `  `    ``for` `(``int` `p = 2; p * p <= MAX; 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; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` `} ` ` `  `static` `int` `findDiff(``int` `[]arr, ``int` `n) ` `{ ` `    ``// initial min max value ` `    ``int` `min = MAX + 2, max = -1; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{ ` ` `  `        ``// check if the number is prime or not ` `        ``if` `(prime[arr[i]] == ``true``) ` `        ``{ ` ` `  `            ``// set the max and min values ` `            ``if` `(arr[i] > max) ` `                ``max = arr[i]; ` `            ``if` `(arr[i] < min) ` `                ``min = arr[i]; ` `        ``} ` `    ``} ` ` `  `    ``return` `(max == -1) ? -1 : (max - min); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main ()  ` `{ ` `    ``// create the sieve ` `    ``SieveOfEratosthenes(); ` `    ``int` `n = 4; ` `    ``int` `[]arr = { 1, 2, 3, 5 }; ` `     `  `    ``int` `res = findDiff(arr, n); ` `     `  `    ``if` `(res == -1) ` `        ``Console.WriteLine( ``"No prime numbers"``) ; ` `    ``else` `        ``Console.WriteLine( ``"Difference is "` `+ res); ` `} ` `} ` ` `  `// This code is contributed by inder_verma `

Output:

```Difference is 3
``` My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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Improved By : inderDuMCA, chitranayal