# Design a stack with operations on middle element

• Difficulty Level : Medium
• Last Updated : 24 May, 2022

How to implement a stack which will support the following operations in O(1) time complexity
1) push() which adds an element to the top of stack.
2) pop() which removes an element from top of stack.
3) findMiddle() which will return middle element of the stack.
4) deleteMiddle() which will delete the middle element.
Push and pop are standard stack operations.
The important question is, whether to use a linked list or array for the implementation of the stack?
Please note that we need to find and delete the middle element. Deleting an element from the middle is not O(1) for the array. Also, we may need to move the middle pointer up when we push an element and move down when we pop(). In a singly linked list, moving the middle pointer in both directions is not possible.
The idea is to use a Doubly Linked List (DLL). We can delete the middle element in O(1) time by maintaining mid pointer. We can move the mid pointer in both directions using previous and next pointers.
Following is implementation of push(), pop() and findMiddle() operations. Implementation of deleteMiddle() is left as an exercise. If there are even elements in stack, findMiddle() returns the second middle element. For example, if stack contains {1, 2, 3, 4}, then findMiddle() would return 3.

## C++

 `/* C++ Program to implement a stack``that supports findMiddle() and``deleteMiddle in O(1) time */``#include ``using` `namespace` `std;` `class` `myStack {``    ``struct` `Node {``        ``int` `num;``        ``Node* next;``        ``Node* prev;` `        ``Node(``int` `num) { ``this``->num = num; }``    ``};` `    ``// Members of stack``    ``Node* head = NULL;``    ``Node* mid = NULL;``    ``int` `size = 0;` `public``:``    ``void` `push(``int` `data)``    ``{``        ``Node* temp = ``new` `Node(data);``        ``if` `(size == 0) {``            ``head = temp;``            ``mid = temp;``            ``size++;``            ``return``;``        ``}` `        ``head->next = temp;``        ``temp->prev = head;` `        ``// update the pointers``        ``head = head->next;``        ``if` `(size % 2 == 1) {``            ``mid = mid->next;``        ``}``        ``size++;``    ``}` `    ``int` `pop()``    ``{``      ``int` `data=-1;``        ``if` `(size != 0) {``          ``data=head->num;``            ``if` `(size == 1) {``                ``head = NULL;``                ``mid = NULL;``            ``}``            ``else` `{``                ``head = head->prev;``                ``head->next = NULL;``                ``if` `(size % 2 == 0) {``                    ``mid = mid->prev;``                ``}``            ``}``            ``size--;``        ``}``      ``return` `data;``    ``}` `    ``int` `findMiddle()``    ``{``        ``if` `(size == 0) {``            ``return` `-1;``        ``}``        ``return` `mid->num;``    ``}` `    ``void` `deleteMiddle()``    ``{``        ``if` `(size != 0) {``            ``if` `(size == 1) {``                ``head = NULL;``                ``mid = NULL;``            ``}``            ``else` `if` `(size == 2) {``                ``head = head->prev;``                ``mid = mid->prev;``                ``head->next = NULL;``            ``}``            ``else` `{``                ``mid->next->prev = mid->prev;``                ``mid->prev->next = mid->next;``                ``if` `(size % 2 == 0) {``                    ``mid = mid->prev;``                ``}``                ``else` `{``                    ``mid = mid->next;``                ``}``            ``}``            ``size--;``        ``}``    ``}``};` `int` `main()``{``    ``myStack st;``    ``st.push(11);``    ``st.push(22);``    ``st.push(33);``    ``st.push(44);``    ``st.push(55);``    ``st.push(66);``    ``st.push(77);``    ``st.push(88);``    ``st.push(99);``    ``cout <<``"Popped : "``<< st.pop() << endl;``    ``cout <<``"Popped : "``<< st.pop() << endl;``    ``cout <<``"Middle Element : "``<< st.findMiddle() << endl;``    ``st.deleteMiddle();``    ``cout <<``"New Middle Element : "``<< st.findMiddle() << endl;``    ``return` `0;``}``// This code is contributed by Nikhil Goswami``// Updated by Amsavarthan LV`

## C

 `/* Program to implement a stack that supports findMiddle()``   ``and deleteMiddle in O(1) time */``#include ``#include ` `/* A Doubly Linked List Node */``struct` `DLLNode {``    ``struct` `DLLNode* prev;``    ``int` `data;``    ``struct` `DLLNode* next;``};` `/* Representation of the stack data structure that supports``   ``findMiddle() in O(1) time.  The Stack is implemented``   ``using Doubly Linked List. It maintains pointer to head``   ``node, pointer to middle node and count of nodes */``struct` `myStack {``    ``struct` `DLLNode* head;``    ``struct` `DLLNode* mid;``    ``int` `count;``};` `/* Function to create the stack data structure */``struct` `myStack* createMyStack()``{``    ``struct` `myStack* ms``        ``= (``struct` `myStack*)``malloc``(``sizeof``(``struct` `myStack));``    ``ms->count = 0;``    ``return` `ms;``};` `/* Function to push an element to the stack */``void` `push(``struct` `myStack* ms, ``int` `new_data)``{``    ``/* allocate DLLNode and put in data */``    ``struct` `DLLNode* new_DLLNode``        ``= (``struct` `DLLNode*)``malloc``(``sizeof``(``struct` `DLLNode));``    ``new_DLLNode->data = new_data;` `    ``/* Since we are adding at the beginning,``      ``prev is always NULL */``    ``new_DLLNode->prev = NULL;` `    ``/* link the old list off the new DLLNode */``    ``new_DLLNode->next = ms->head;` `    ``/* Increment count of items in stack */``    ``ms->count += 1;` `    ``/* Change mid pointer in two cases``       ``1) Linked List is empty``       ``2) Number of nodes in linked list is odd */``    ``if` `(ms->count == 1) {``        ``ms->mid = new_DLLNode;``    ``}``    ``else` `{``        ``ms->head->prev = new_DLLNode;` `        ``if` `(ms->count & 1) ``// Update mid if ms->count is odd``            ``ms->mid = ms->mid->prev;``    ``}` `    ``/* move head to point to the new DLLNode */``    ``ms->head = new_DLLNode;``}` `/* Function to pop an element from stack */``int` `pop(``struct` `myStack* ms)``{``    ``/* Stack underflow */``    ``if` `(ms->count == 0) {``        ``printf``(``"Stack is empty\n"``);``        ``return` `-1;``    ``}` `    ``struct` `DLLNode* head = ms->head;``    ``int` `item = head->data;``    ``ms->head = head->next;` `    ``// If linked list doesn't become empty, update prev``    ``// of new head as NULL``    ``if` `(ms->head != NULL)``        ``ms->head->prev = NULL;` `    ``ms->count -= 1;` `    ``// update the mid pointer when we have even number of``    ``// elements in the stack, i,e move down the mid pointer.``    ``if` `(!((ms->count) & 1))``        ``ms->mid = ms->mid->next;` `    ``free``(head);` `    ``return` `item;``}` `// Function for finding middle of the stack``int` `findMiddle(``struct` `myStack* ms)``{``    ``if` `(ms->count == 0) {``        ``printf``(``"Stack is empty now\n"``);``        ``return` `-1;``    ``}` `    ``return` `ms->mid->data;``}` `void` `deleteMiddle(``struct` `myStack* ms)``{``    ``if` `(ms->count == 0) {``        ``printf``(``"Stack is empty now\n"``);``        ``return``;``    ``}``  ` `    ``ms->count -= 1;``    ``ms->mid->next->prev = ms->mid->prev;``    ``ms->mid->prev->next = ms->mid->next;` `    ``if` `(ms->count % 2 != 0) {``      ``ms->mid=ms->mid->next;``    ``}``else` `{``      ``ms->mid=ms->mid->prev;``    ``}``}` `// Driver program to test functions of myStack``int` `main()``{``    ``/* Let us create a stack using push() operation*/``    ``struct` `myStack* ms = createMyStack();``    ``push(ms, 11);``    ``push(ms, 22);``    ``push(ms, 33);``    ``push(ms, 44);``    ``push(ms, 55);``    ``push(ms, 66);``    ``push(ms, 77);``    ``push(ms, 88);``    ``push(ms, 99);` `    ``printf``(``"Popped : %d\n"``, pop(ms));``    ``printf``(``"Popped : %d\n"``, pop(ms));``    ``printf``(``"Middle Element : %d\n"``, findMiddle(ms));``      ``deleteMiddle(ms);``      ``printf``(``"New Middle Element : %d\n"``, findMiddle(ms));``    ``return` `0;``}``//Updated by Amsavarthan Lv`

## Java

 `/* Java Program to implement a stack that supports``findMiddle() and deleteMiddle in O(1) time */``/* A Doubly Linked List Node */``class` `DLLNode {``    ``DLLNode prev;``    ``int` `data;``    ``DLLNode next;``    ``DLLNode(``int` `data) { ``this``.data = data; }``}` `/* Representation of the stack data structure that``   ``supports findMiddle() in O(1) time.  The Stack is``   ``implemented using Doubly Linked List. It maintains``   ``pointer to head node, pointer to middle node and``   ``count of nodes */``public` `class` `myStack {``    ``DLLNode head;``    ``DLLNode mid;``    ``DLLNode prev;``    ``DLLNode next;``    ``int` `size;``    ``/* Function to push an element to the stack */``    ``void` `push(``int` `new_data)``    ``{` `        ``/* allocate DLLNode and put in data */``        ``DLLNode new_node = ``new` `DLLNode(new_data);``        ``// if stack is empty``        ``if` `(size == ``0``) {``            ``head = new_node;``            ``mid = new_node;``            ``size++;``            ``return``;``        ``}``        ``head.next = new_node;``        ``new_node.prev = head;` `        ``head = head.next;``        ``if` `(size % ``2` `!= ``0``) {``            ``mid = mid.next;``        ``}``        ``size++;``    ``}` `    ``/* Function to pop an element from stack */``    ``int` `pop()``    ``{``        ``int` `data = -``1``;``        ``/* Stack underflow */``        ``if` `(size == ``0``) {``            ``System.out.println(``"Stack is empty"``);``            ``// return -1;``        ``}` `        ``if` `(size != ``0``) {``            ``if` `(size == ``1``) {``                ``head = ``null``;``                ``mid = ``null``;``            ``}``            ``else` `{``                ``data = head.data;``                ``head = head.prev;``                ``head.next = ``null``;``                ``if` `(size % ``2` `== ``0``) {``                    ``mid = mid.prev;``                ``}``            ``}``            ``size--;``        ``}``        ``return` `data;``    ``}` `    ``// Function for finding middle of the stack``    ``int` `findMiddle()``    ``{``        ``if` `(size == ``0``) {``            ``System.out.println(``"Stack is empty now"``);``            ``return` `-``1``;``        ``}``        ``return` `mid.data;``    ``}``    ``void` `deleteMiddleElement()``    ``{``        ``// This function will not only delete the middle``        ``// element``        ``// but also update the mid in case of even and``        ``// odd number of Elements``        ``// when the size is even then findmiddle() will show the``        ``// second middle element as mentioned in the problem``        ``// statement``        ``if` `(size != ``0``) {``            ``if` `(size == ``1``) {``                ``head = ``null``;``                ``mid = ``null``;``            ``}``            ``else` `if` `(size == ``2``) {``                ``head = head.prev;``                ``mid = mid.prev;``                ``head.next = ``null``;``            ``}``            ``else` `{``                ``mid.next.prev = mid.prev;``                ``mid.prev.next = mid.next;``                ``if` `(size % ``2` `== ``0``) {``                    ``mid = mid.prev;``                ``}``                ``else` `{``                    ``mid = mid.next;``                ``}``            ``}``            ``size--;``        ``}``    ``}` `    ``// Driver program to test functions of myStack``    ``public` `static` `void` `main(String args[])``    ``{``        ``myStack ms = ``new` `myStack();``        ``ms.push(``11``);``        ``ms.push(``22``);``        ``ms.push(``33``);``        ``ms.push(``44``);``        ``ms.push(``55``);``        ``ms.push(``66``);``        ``ms.push(``77``);``        ``ms.push(``88``);``        ``ms.push(``99``);` `        ``System.out.println(``"Popped : "` `+ ms.pop());``        ``System.out.println(``"Popped : "` `+ ms.pop());``        ``System.out.println(``"Middle Element : "``                           ``+ ms.findMiddle());``        ``ms.deleteMiddleElement();``        ``System.out.println(``"New Middle Element : "``                           ``+ ms.findMiddle());``    ``}``}``// This code is contributed by Abhishek Jha``// Updated by Amsavarthan Lv`

## Python3

 `''' Python3 Program to implement a stack``that supports findMiddle()``and deleteMiddle in O(1) time '''` `''' A Doubly Linked List Node '''`  `class` `DLLNode:` `    ``def` `__init__(``self``, d):``        ``self``.prev ``=` `None``        ``self``.data ``=` `d``        ``self``.``next` `=` `None`  `''' Representation of the stack``data structure that supports``findMiddle() in O(1) time. The``Stack is implemented using``Doubly Linked List. It maintains``pointer to head node, pointer``to middle node and count of``nodes '''`  `class` `myStack:` `    ``def` `__init__(``self``):``        ``self``.head ``=` `None``        ``self``.mid ``=` `None``        ``self``.count ``=` `0`  `''' Function to create the stack data structure '''`  `def` `createMyStack():``    ``ms ``=` `myStack()``    ``ms.count ``=` `0``    ``return` `ms`  `''' Function to push an element to the stack '''`  `def` `push(ms, new_data):``    ``''' allocate DLLNode and put in data '''``    ``new_DLLNode ``=` `DLLNode(new_data)` `    ``''' Since we are adding at the beginning,``    ``prev is always NULL '''``    ``new_DLLNode.prev ``=` `None` `    ``''' link the old list off the new DLLNode '''``    ``new_DLLNode.``next` `=` `ms.head` `    ``''' Increment count of items in stack '''``    ``ms.count ``+``=` `1` `    ``''' Change mid pointer in two cases``    ``1) Linked List is empty``    ``2) Number of nodes in linked list is odd '''``    ``if``(ms.count ``=``=` `1``):``        ``ms.mid ``=` `new_DLLNode` `    ``else``:``        ``ms.head.prev ``=` `new_DLLNode` `        ``# Update mid if ms->count is odd``        ``if``((ms.count ``%` `2``) !``=` `0``):``            ``ms.mid ``=` `ms.mid.prev` `    ``''' move head to point to the new DLLNode '''``    ``ms.head ``=` `new_DLLNode`  `''' Function to pop an element from stack '''`  `def` `pop(ms):``    ``''' Stack underflow '''``    ``if``(ms.count ``=``=` `0``):` `        ``print``(``"Stack is empty"``)``        ``return` `-``1` `    ``head ``=` `ms.head``    ``item ``=` `head.data``    ``ms.head ``=` `head.``next` `    ``# If linked list doesn't become empty,``    ``# update prev of new head as NULL``    ``if``(ms.head !``=` `None``):``        ``ms.head.prev ``=` `None``    ``ms.count ``-``=` `1` `    ``# update the mid pointer when``    ``# we have even number of elements``    ``# in the stack, i,e move down``    ``# the mid pointer.``    ``if``(ms.count ``%` `2` `=``=` `0``):``        ``ms.mid ``=` `ms.mid.``next``    ``return` `item` `# Function for finding middle of the stack`  `def` `findMiddle(ms):``    ``if``(ms.count ``=``=` `0``):``        ``print``(``"Stack is empty now"``)``        ``return` `-``1``    ``return` `ms.mid.data` `def` `deleteMiddle(ms):``  ``if``(ms.count ``=``=` `0``):``    ``print``(``"Stack is empty now"``)``    ``return``  ``ms.count``-``=``1``  ``ms.mid.``next``.prev``=``ms.mid.prev``  ``ms.mid.prev.``next``=``ms.mid.``next``  ` `  ``if` `ms.count ``%``2``=``=``1``:``    ``ms.mid``=``ms.mid.``next``  ``else``:``    ``ms.mid``=``ms.mid.prev` `# Driver code``if` `__name__ ``=``=` `'__main__'``:` `    ``ms ``=` `createMyStack()``    ``push(ms, ``11``)``    ``push(ms, ``22``)``    ``push(ms, ``33``)``    ``push(ms, ``44``)``    ``push(ms, ``55``)``    ``push(ms, ``66``)``    ``push(ms, ``77``)``    ``push(ms, ``88``)``    ``push(ms, ``99``)` `    ``print``(``"Popped : "` `+``          ``str``(pop(ms)))``    ``print``(``"Popped : "` `+``          ``str``(pop(ms)))``    ``print``(``"Middle Element : "` `+``          ``str``(findMiddle(ms)))``    ``deleteMiddle(ms)``    ``print``(``"New Middle Element : "` `+``          ``str``(findMiddle(ms)))` `    ``# This code is contributed by rutvik_56.``    ``# Updated by Amsavarthan Lv`

## C#

 `/* C# Program to implement a stack``that supports findMiddle()``and deleteMiddle in O(1) time */``using` `System;` `class` `GFG {``    ``/* A Doubly Linked List Node */``    ``public` `class` `DLLNode {``        ``public` `DLLNode prev;``        ``public` `int` `data;``        ``public` `DLLNode next;``        ``public` `DLLNode(``int` `d) { data = d; }``    ``}` `    ``/* Representation of the stack``    ``data structure that supports``    ``findMiddle() in O(1) time. The``    ``Stack is implemented using``    ``Doubly Linked List. It maintains``    ``pointer to head node, pointer``    ``to middle node and count of``    ``nodes */``    ``public` `class` `myStack {``        ``public` `DLLNode head;``        ``public` `DLLNode mid;``        ``public` `int` `count;``    ``}` `    ``/* Function to create the stack data structure */``    ``myStack createMyStack()``    ``{``        ``myStack ms = ``new` `myStack();``        ``ms.count = 0;``        ``return` `ms;``    ``}` `    ``/* Function to push an element to the stack */``    ``void` `push(myStack ms, ``int` `new_data)``    ``{` `        ``/* allocate DLLNode and put in data */``        ``DLLNode new_DLLNode = ``new` `DLLNode(new_data);` `        ``/* Since we are adding at the beginning,``        ``prev is always NULL */``        ``new_DLLNode.prev = ``null``;` `        ``/* link the old list off the new DLLNode */``        ``new_DLLNode.next = ms.head;` `        ``/* Increment count of items in stack */``        ``ms.count += 1;` `        ``/* Change mid pointer in two cases``        ``1) Linked List is empty``        ``2) Number of nodes in linked list is odd */``        ``if` `(ms.count == 1) {``            ``ms.mid = new_DLLNode;``        ``}``        ``else` `{``            ``ms.head.prev = new_DLLNode;` `            ``// Update mid if ms->count is odd``            ``if` `((ms.count % 2) != 0)``                ``ms.mid = ms.mid.prev;``        ``}` `        ``/* move head to point to the new DLLNode */``        ``ms.head = new_DLLNode;``    ``}` `    ``/* Function to pop an element from stack */``    ``int` `pop(myStack ms)``    ``{``        ``/* Stack underflow */``        ``if` `(ms.count == 0) {``            ``Console.WriteLine(``"Stack is empty"``);``            ``return` `-1;``        ``}` `        ``DLLNode head = ms.head;``        ``int` `item = head.data;``        ``ms.head = head.next;` `        ``// If linked list doesn't become empty,``        ``// update prev of new head as NULL``        ``if` `(ms.head != ``null``)``            ``ms.head.prev = ``null``;` `        ``ms.count -= 1;` `        ``// update the mid pointer when``        ``// we have even number of elements``        ``// in the stack, i,e move down``        ``// the mid pointer.``        ``if` `(ms.count % 2 == 0)``            ``ms.mid = ms.mid.next;` `        ``return` `item;``    ``}` `    ``// Function for finding middle of the stack``    ``int` `findMiddle(myStack ms)``    ``{``        ``if` `(ms.count == 0) {``            ``Console.WriteLine(``"Stack is empty now"``);``            ``return` `-1;``        ``}``        ``return` `ms.mid.data;``    ``}``  ` `  ``void` `deleteMiddle(myStack ms){``    ``if` `(ms.count == 0) {``            ``Console.WriteLine(``"Stack is empty now"``);``           ``return``;``        ``}``    ` `    ``ms.count-=1;``    ``ms.mid.next.prev=ms.mid.prev;``    ``ms.mid.prev.next=ms.mid.next;``    ` `    ``if``(ms.count %2!=0){``      ``ms.mid=ms.mid.next;``    ``}``else``{``     ``ms.mid=ms.mid.prev;``    ``}``      ` `  ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``GFG ob = ``new` `GFG();``        ``myStack ms = ob.createMyStack();``        ``ob.push(ms, 11);``        ``ob.push(ms, 22);``        ``ob.push(ms, 33);``        ``ob.push(ms, 44);``        ``ob.push(ms, 55);``        ``ob.push(ms, 66);``        ``ob.push(ms, 77);``      ``ob.push(ms, 88);``      ``ob.push(ms, 99);` `        ``Console.WriteLine(``"Popped : "` `+ ob.pop(ms));``        ``Console.WriteLine(``"Popped : "` `+ ob.pop(ms));``        ``Console.WriteLine(``"Middle Element : "``                          ``+ ob.findMiddle(ms));``      ``ob.deleteMiddle(ms);``      ``Console.WriteLine(``"New Middle Element : "``                          ``+ ob.findMiddle(ms));``    ``}``}` `// This code is contributed``// by Arnab Kundu` `// Updated by Amsavarthan Lv`
Output
```Popped : 99
Popped : 88
Middle Element : 44
New Middle Element : 55
```