# Finding Median in a Sorted Linked List

Given A sorted linked list of elements. The task is to find the median in the given Sorted Linked List.

We know that median in a sorted array is the middle element.

Procedure to find median of N sorted numbers:

```if N is odd:
median is N/2th element
else
median is N/2th element + (N/2+1)th element
```

Examples:

```Input : 1->2->3->4->5->NULL
Output : 3

Input : 1->2->3->4->5->6->NULL
Output : 3.5
```

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

Simple approach

1. Traverse the linked list and count all elements.
2. if count is odd then again traverse the linked list and find n/2th element.
3. if count is even then again traverse the linked list and find:
(n/2th element+ (n/2+1)th element)/2

Note: The above solution traverse the linked list two times.

Efficient Approach: an efficient approach is to traverse the list using two pointers to find the number of elements. See method 2 of this post.

We can use the above algorithm for finding the median of the linked list. Using this algorithm we won’t need to count the number of element:

1. if the fast_ptr is Not NULL then it means linked list contain odd element we simply print the data of the slow_ptr.
2. else if fast_ptr reach to NULL its means linked list contain even element we create backup of the previous node of slow_ptr and print (previous node of slow_ptr+ slow_ptr->data)/2

Below is the implementation of the above approach:

## C++

 `// C++ program to find median ` `// of a linked list ` `#include ` `using` `namespace` `std; ` ` `  `// Link list node ` `struct` `Node { ` `    ``int` `data; ` `    ``struct` `Node* next; ` `}; ` ` `  `/* Function to get the median of the linked list */` `void` `printMidean(Node* head) ` `{ ` `    ``Node* slow_ptr = head; ` `    ``Node* fast_ptr = head; ` `    ``Node* pre_of_slow = head; ` ` `  `    ``if` `(head != NULL) { ` `        ``while` `(fast_ptr != NULL && fast_ptr->next != NULL) { ` ` `  `            ``fast_ptr = fast_ptr->next->next; ` ` `  `            ``// previous of slow_ptr ` `            ``pre_of_slow = slow_ptr; ` `            ``slow_ptr = slow_ptr->next; ` `        ``} ` ` `  `        ``// if the below condition is true linked list ` `        ``// contain odd Node ` `        ``// simply return middle element ` `        ``if` `(fast_ptr != NULL) ` `            ``cout << ``"Median is : "` `<< slow_ptr->data; ` ` `  `        ``// else linked list contain even element ` `        ``else` `            ``cout << ``"Median is : "` `                 ``<< ``float``(slow_ptr->data + pre_of_slow->data) / 2; ` `    ``} ` `} ` ` `  `/* Given a reference (pointer to  ` `    ``pointer) to the head of a list  ` `    ``and an int, push a new node on  ` `    ``the front of the list. */` `void` `push(``struct` `Node** head_ref, ``int` `new_data) ` `{ ` `    ``// allocate node ` `    ``Node* new_node = ``new` `Node; ` ` `  `    ``// put in the data ` `    ``new_node->data = new_data; ` ` `  `    ``// link the old list ` `    ``// off the new node ` `    ``new_node->next = (*head_ref); ` ` `  `    ``// move the head to point ` `    ``// to the new node ` `    ``(*head_ref) = new_node; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``// Start with the ` `    ``// empty list ` `    ``struct` `Node* head = NULL; ` ` `  `    ``// Use push() to construct ` `    ``// below list ` `    ``// 1->2->3->4->5->6 ` `    ``push(&head, 6); ` `    ``push(&head, 5); ` `    ``push(&head, 4); ` `    ``push(&head, 3); ` `    ``push(&head, 2); ` `    ``push(&head, 1); ` ` `  `    ``// Check the count ` `    ``// function ` `    ``printMidean(head); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find median ` `// of a linked list ` `class` `GFG  ` `{ ` ` `  `    ``// Link list node ` `    ``static` `class` `Node ` `    ``{ ` ` `  `        ``int` `data; ` `        ``Node next; ` `    ``}; ` ` `  `    ``/* Function to get the median of the linked list */` `    ``static` `void` `printMidean(Node head) ` `    ``{ ` `        ``Node slow_ptr = head; ` `        ``Node fast_ptr = head; ` `        ``Node pre_of_slow = head; ` ` `  `        ``if` `(head != ``null``)  ` `        ``{ ` `            ``while` `(fast_ptr != ``null` `&& fast_ptr.next != ``null``)  ` `            ``{ ` ` `  `                ``fast_ptr = fast_ptr.next.next; ` ` `  `                ``// previous of slow_ptr ` `                ``pre_of_slow = slow_ptr; ` `                ``slow_ptr = slow_ptr.next; ` `            ``} ` ` `  `            ``// if the below condition is true linked list ` `            ``// contain odd Node ` `            ``// simply return middle element ` `            ``if` `(fast_ptr != ``null``) ` `            ``{ ` `                ``System.out.print(``"Median is : "` `+ slow_ptr.data); ` `            ``} ` `             `  `            ``// else linked list contain even element ` `            ``else`  `            ``{ ` `                ``System.out.print(``"Median is : "` `                        ``+ (``float``) (slow_ptr.data + pre_of_slow.data) / ``2``); ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``/* Given a reference (pointer to  ` `    ``pointer) to the head of a list  ` `    ``and an int, push a new node on  ` `    ``the front of the list. */` `    ``static` `Node push(Node head_ref, ``int` `new_data) ` `    ``{ ` `        ``// allocate node ` `        ``Node new_node = ``new` `Node(); ` ` `  `        ``// put in the data ` `        ``new_node.data = new_data; ` ` `  `        ``// link the old list ` `        ``// off the new node ` `        ``new_node.next = head_ref; ` ` `  `        ``// move the head to point ` `        ``// to the new node ` `        ``head_ref = new_node; ` `        ``return` `head_ref; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``// Start with the ` `        ``// empty list ` `        ``Node head = ``null``; ` ` `  `        ``// Use push() to construct ` `        ``// below list ` `        ``// 1.2.3.4.5.6 ` `        ``head = push(head, ``6``); ` `        ``head = push(head, ``5``); ` `        ``head = push(head, ``4``); ` `        ``head = push(head, ``3``); ` `        ``head = push(head, ``2``); ` `        ``head = push(head, ``1``); ` ` `  `        ``// Check the count ` `        ``// function ` `        ``printMidean(head); ` `    ``} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

## C#

 `// C# program to find median ` `// of a linked list ` `using` `System; ` ` `  `class` `GFG  ` `{ ` ` `  `    ``// Link list node ` `    ``class` `Node ` `    ``{ ` ` `  `        ``public` `int` `data; ` `        ``public` `Node next; ` `    ``}; ` ` `  `    ``/* Function to get the median  ` `    ``of the linked list */` `    ``static` `void` `printMidean(Node head) ` `    ``{ ` `        ``Node slow_ptr = head; ` `        ``Node fast_ptr = head; ` `        ``Node pre_of_slow = head; ` ` `  `        ``if` `(head != ``null``)  ` `        ``{ ` `            ``while` `(fast_ptr != ``null` `&&  ` `                   ``fast_ptr.next != ``null``)  ` `            ``{ ` `                ``fast_ptr = fast_ptr.next.next; ` ` `  `                ``// previous of slow_ptr ` `                ``pre_of_slow = slow_ptr; ` `                ``slow_ptr = slow_ptr.next; ` `            ``} ` ` `  `            ``// if the below condition is true linked list ` `            ``// contain odd Node ` `            ``// simply return middle element ` `            ``if` `(fast_ptr != ``null``) ` `            ``{ ` `                ``Console.Write(``"Median is : "` `+  ` `                               ``slow_ptr.data); ` `            ``} ` `             `  `            ``// else linked list contain even element ` `            ``else` `            ``{ ` `                ``Console.Write(``"Median is : "` `+  ` `                       ``(``float``)(slow_ptr.data +  ` `                               ``pre_of_slow.data) / 2); ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``/* Given a reference (pointer to  ` `    ``pointer) to the head of a list  ` `    ``and an int, push a new node on  ` `    ``the front of the list. */` `    ``static` `Node push(Node head_ref, ``int` `new_data) ` `    ``{ ` `        ``// allocate node ` `        ``Node new_node = ``new` `Node(); ` ` `  `        ``// put in the data ` `        ``new_node.data = new_data; ` ` `  `        ``// link the old list ` `        ``// off the new node ` `        ``new_node.next = head_ref; ` ` `  `        ``// move the head to point ` `        ``// to the new node ` `        ``head_ref = new_node; ` `        ``return` `head_ref; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main(String[] args)  ` `    ``{ ` `        ``// Start with the ` `        ``// empty list ` `        ``Node head = ``null``; ` ` `  `        ``// Use push() to construct ` `        ``// below list ` `        ``// 1->2->3->4->5->6 ` `        ``head = push(head, 6); ` `        ``head = push(head, 5); ` `        ``head = push(head, 4); ` `        ``head = push(head, 3); ` `        ``head = push(head, 2); ` `        ``head = push(head, 1); ` ` `  `        ``// Check the count ` `        ``// function ` `        ``printMidean(head); ` `    ``} ` `}  ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```Median is : 3.5
```

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