# Minimum and Maximum Prime Numbers of a Singly Linked List

Given a singly linked list containing N nodes, the task is to find the minimum and maximum prime number.

Examples:

```Input : List = 15 -> 16 -> 6 -> 7 -> 17
Output : Minimum : 7
Maximum : 17

Input : List = 15 -> 3 -> 4 -> 2 -> 9
Output : Minimum : 2
Maximum : 3
```

Approach:

1. The idea is to traverse the linked list to the end and initialize the max and min variable to INT_MIN and INT_MAX respectively.
2. Check if the current node is prime or not. If Yes:
• If current node’s value is greater than max then assign current node’s value to max.
• If current node’s value is less than min then assign current node’s value to min.
3. Repeat above step until end of list is reached.

Below is the implementation of above idea:

## C++

 `// C++ implementation to find minimum ` `// and maximum prime number of ` `// the singly linked list ` `#include ` ` `  `using` `namespace` `std; ` ` `  `// Node of the singly linked list ` `struct` `Node { ` `    ``int` `data; ` `    ``Node* next; ` `}; ` ` `  `// Function to insert a node at the beginning ` `// of the singly Linked List ` `void` `push(Node** head_ref, ``int` `new_data) ` `{ ` `    ``Node* new_node = ``new` `Node; ` `    ``new_node->data = new_data; ` `    ``new_node->next = (*head_ref); ` `    ``(*head_ref) = new_node; ` `} ` ` `  `// Function to check if a number is prime ` `bool` `isPrime(``int` `n) ` `{ ` `    ``// Corner cases ` `    ``if` `(n <= 1) ` `        ``return` `false``; ` `    ``if` `(n <= 3) ` `        ``return` `true``; ` ` `  `    ``// This is checked so that we can skip ` `    ``// middle five numbers in below loop ` `    ``if` `(n % 2 == 0 || n % 3 == 0) ` `        ``return` `false``; ` ` `  `    ``for` `(``int` `i = 5; i * i <= n; i = i + 6) ` `        ``if` `(n % i == 0 || n % (i + 2) == 0) ` `            ``return` `false``; ` ` `  `    ``return` `true``; ` `} ` ` `  `// Function to find maximum and minimum ` `// prime nodes in a linked list ` `void` `minmaxPrimeNodes(Node** head_ref) ` `{ ` `    ``int` `minimum = INT_MAX; ` `    ``int` `maximum = INT_MIN; ` `    ``Node* ptr = *head_ref; ` ` `  `    ``while` `(ptr != NULL) { ` `        ``// If current node is prime ` `        ``if` `(isPrime(ptr->data)) { ` `            ``// Update minimum ` `            ``minimum = min(minimum, ptr->data); ` ` `  `            ``// Update maximum ` `            ``maximum = max(maximum, ptr->data); ` `        ``} ` `        ``ptr = ptr->next; ` `    ``} ` ` `  `    ``cout << ``"Minimum : "` `<< minimum << endl; ` `    ``cout << ``"Maximum : "` `<< maximum << endl; ` `} ` ` `  `// Driver program ` `int` `main() ` `{ ` `    ``// start with the empty list ` `    ``Node* head = NULL; ` ` `  `    ``// create the linked list ` `    ``// 15 -> 16 -> 7 -> 6 -> 17 ` `    ``push(&head, 17); ` `    ``push(&head, 7); ` `    ``push(&head, 6); ` `    ``push(&head, 16); ` `    ``push(&head, 15); ` ` `  `    ``minmaxPrimeNodes(&head); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation to find minimum  ` `// and maximum prime number of  ` `// the singly linked list  ` `class` `GFG ` `{ ` `     `  `// Node of the singly linked list  ` `static` `class` `Node  ` `{  ` `    ``int` `data;  ` `    ``Node next;  ` `};  ` ` `  `// Function to insert a node at the beginning  ` `// of the singly Linked List  ` `static` `Node push(Node head_ref, ``int` `new_data)  ` `{  ` `    ``Node new_node = ``new` `Node();  ` `    ``new_node.data = new_data;  ` `    ``new_node.next = (head_ref);  ` `    ``(head_ref) = new_node;  ` `    ``return` `head_ref; ` `}  ` ` `  `// Function to check if a number is prime  ` `static` `boolean` `isPrime(``int` `n)  ` `{  ` `    ``// Corner cases  ` `    ``if` `(n <= ``1``)  ` `        ``return` `false``;  ` `    ``if` `(n <= ``3``)  ` `        ``return` `true``;  ` ` `  `    ``// This is checked so that we can skip  ` `    ``// middle five numbers in below loop  ` `    ``if` `(n % ``2` `== ``0` `|| n % ``3` `== ``0``)  ` `        ``return` `false``;  ` ` `  `    ``for` `(``int` `i = ``5``; i * i <= n; i = i + ``6``)  ` `        ``if` `(n % i == ``0` `|| n % (i + ``2``) == ``0``)  ` `            ``return` `false``;  ` ` `  `    ``return` `true``;  ` `}  ` ` `  `// Function to find maximum and minimum  ` `// prime nodes in a linked list  ` `static` `void` `minmaxPrimeNodes(Node head_ref)  ` `{  ` `    ``int` `minimum = Integer.MAX_VALUE;  ` `    ``int` `maximum = Integer.MIN_VALUE;  ` `    ``Node ptr = head_ref;  ` ` `  `    ``while` `(ptr != ``null``)  ` `    ``{  ` `        ``// If current node is prime  ` `        ``if` `(isPrime(ptr.data)) ` `        ``{  ` `            ``// Update minimum  ` `            ``minimum = Math.min(minimum, ptr.data);  ` ` `  `            ``// Update maximum  ` `            ``maximum = Math.max(maximum, ptr.data);  ` `        ``}  ` `        ``ptr = ptr.next;  ` `    ``}  ` ` `  `    ``System.out.println(``"Minimum : "` `+ minimum );  ` `    ``System.out.println(``"Maximum : "` `+ maximum );  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `main(String args[]) ` `{  ` `    ``// start with the empty list  ` `    ``Node head = ``null``;  ` ` `  `    ``// create the linked list  ` `    ``// 15 . 16 . 7 . 6 . 17  ` `    ``head = push(head, ``17``);  ` `    ``head = push(head, ``7``);  ` `    ``head = push(head, ``6``);  ` `    ``head = push(head, ``16``);  ` `    ``head = push(head, ``15``);  ` ` `  `    ``minmaxPrimeNodes(head);  ` ` `  `} ` `} ` ` `  `// This code is contributed by Arnab Kundu `

## Python3

 `# Python3 implementation to find minimum  ` `# and maximum prime number of  ` `# the singly linked list  ` `     `  `# Structure of a Node  ` `class` `Node:  ` `    ``def` `__init__(``self``, data):  ` `        ``self``.data ``=` `data  ` `        ``self``.``next` `=` `None` ` `  `# Function to insert a node at the beginning  ` `# of the singly Linked List  ` `def` `push(head_ref, new_data) : ` ` `  `    ``new_node ``=` `Node(``0``)  ` `    ``new_node.data ``=` `new_data  ` `    ``new_node.``next` `=` `(head_ref)  ` `    ``(head_ref) ``=` `new_node  ` `    ``return` `head_ref ` ` `  `# Function to check if a number is prime  ` `def` `isPrime(n):  ` ` `  `    ``# Corner cases  ` `    ``if` `(n <``=` `1``) : ` `        ``return` `False` `    ``if` `(n <``=` `3``) : ` `        ``return` `True` `         `  `    ``# This is checked so that we can skip  ` `    ``# middle five numbers in below loop  ` `    ``if` `(n ``%` `2` `=``=` `0` `or` `n ``%` `3` `=``=` `0``) : ` `        ``return` `False` `    ``i ``=` `5` `    ``while``(i ``*` `i <``=` `n) : ` `        ``if` `(n ``%` `i ``=``=` `0` `or` `n ``%` `(i ``+` `2``) ``=``=` `0``):  ` `            ``return` `False` `        ``i ``=` `i ``+` `6` `     `  `    ``return` `True` ` `  `# Function to find maximum and minimum  ` `# prime nodes in a linked list  ` `def` `minmaxPrimeNodes(head_ref) : ` ` `  `    ``minimum ``=` `999999999` `    ``maximum ``=` `-``999999999` `    ``ptr ``=` `head_ref  ` ` `  `    ``while` `(ptr !``=` `None``):  ` `         `  `        ``# If current node is prime  ` `        ``if` `(isPrime(ptr.data)): ` `         `  `            ``# Update minimum  ` `            ``minimum ``=` `min``(minimum, ptr.data)  ` ` `  `            ``# Update maximum  ` `            ``maximum ``=` `max``(maximum, ptr.data)  ` `         `  `        ``ptr ``=` `ptr.``next` ` `  `    ``print` `(``"Minimum : "``, minimum) ` `    ``print` `(``"Maximum : "``, maximum) ` ` `  `# Driver code  ` ` `  `# start with the empty list  ` `head ``=` `None` ` `  `# create the linked list  ` `# 15 . 16 . 7 . 6 . 17  ` `head ``=` `push(head, ``17``)  ` `head ``=` `push(head, ``7``)  ` `head ``=` `push(head, ``6``)  ` `head ``=` `push(head, ``16``)  ` `head ``=` `push(head, ``15``)  ` ` `  `minmaxPrimeNodes(head)  ` ` `  `# This code is contributed by Arnab Kundu `

## C#

 `// C# implementation to find minimum  ` `// and maximum prime number of  ` `// the singly linked list  ` `using` `System; ` `     `  `class` `GFG ` `{ ` `     `  `// Node of the singly linked list  ` `public` `class` `Node  ` `{  ` `    ``public` `int` `data;  ` `    ``public` `Node next;  ` `};  ` ` `  `// Function to insert a node at the beginning  ` `// of the singly Linked List  ` `static` `Node push(Node head_ref, ``int` `new_data)  ` `{  ` `    ``Node new_node = ``new` `Node();  ` `    ``new_node.data = new_data;  ` `    ``new_node.next = (head_ref);  ` `    ``(head_ref) = new_node;  ` `    ``return` `head_ref; ` `}  ` ` `  `// Function to check if a number is prime  ` `static` `bool` `isPrime(``int` `n)  ` `{  ` `    ``// Corner cases  ` `    ``if` `(n <= 1)  ` `        ``return` `false``;  ` `    ``if` `(n <= 3)  ` `        ``return` `true``;  ` ` `  `    ``// This is checked so that we can skip  ` `    ``// middle five numbers in below loop  ` `    ``if` `(n % 2 == 0 || n % 3 == 0)  ` `        ``return` `false``;  ` ` `  `    ``for` `(``int` `i = 5; i * i <= n; i = i + 6)  ` `        ``if` `(n % i == 0 || n % (i + 2) == 0)  ` `            ``return` `false``;  ` ` `  `    ``return` `true``;  ` `}  ` ` `  `// Function to find maximum and minimum  ` `// prime nodes in a linked list  ` `static` `void` `minmaxPrimeNodes(Node head_ref)  ` `{  ` `    ``int` `minimum = ``int``.MaxValue;  ` `    ``int` `maximum = ``int``.MinValue;  ` `    ``Node ptr = head_ref;  ` ` `  `    ``while` `(ptr != ``null``)  ` `    ``{  ` `        ``// If current node is prime  ` `        ``if` `(isPrime(ptr.data)) ` `        ``{  ` `            ``// Update minimum  ` `            ``minimum = Math.Min(minimum, ptr.data);  ` ` `  `            ``// Update maximum  ` `            ``maximum = Math.Max(maximum, ptr.data);  ` `        ``}  ` `        ``ptr = ptr.next;  ` `    ``}  ` ` `  `    ``Console.WriteLine(``"Minimum : "` `+ minimum);  ` `    ``Console.WriteLine(``"Maximum : "` `+ maximum);  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `Main() ` `{  ` `    ``// start with the empty list  ` `    ``Node head = ``null``;  ` ` `  `    ``// create the linked list  ` `    ``// 15 . 16 . 7 . 6 . 17  ` `    ``head = push(head, 17);  ` `    ``head = push(head, 7);  ` `    ``head = push(head, 6);  ` `    ``head = push(head, 16);  ` `    ``head = push(head, 15);  ` ` `  `    ``minmaxPrimeNodes(head);  ` `} ` `} ` ` `  `// This code is contributed by Princi Singh `

Output:

```Minimum : 7
Maximum : 17
```

Time Complexity: O(N), where N is the number of nodes in the linked list.

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