# Design a stack with operations on middle element

How to implement a stack which will support 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 implementation of stack?

Please note that, we need to find and delete middle element. Deleting an element from middle is not O(1) for array. Also, we may need to move the middle pointer up when we push an element and move down when we pop(). In singly linked list, moving middle pointer in both directions is not possible.

The idea is to use Doubly Linked List (DLL). We can delete middle element in O(1) time by maintaining mid pointer. We can move 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; ` ` `  `/* A Doubly Linked List Node */` `class` `DLLNode  ` `{  ` `    ``public``: ` `    ``DLLNode *prev;  ` `    ``int` `data;  ` `    ``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 */` `class` `myStack  ` `{  ` `    ``public``: ` `    ``DLLNode *head;  ` `    ``DLLNode *mid;  ` `    ``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_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 even ` `        ``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)  ` `    ``{  ` `        ``cout<<``"Stack is empty\n"``;  ` `        ``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 odd 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(myStack *ms)  ` `{  ` `    ``if` `(ms->count == 0)  ` `    ``{  ` `        ``cout << ``"Stack is empty now\n"``;  ` `        ``return` `-1;  ` `    ``}  ` ` `  `    ``return` `ms->mid->data;  ` `}  ` ` `  `// Driver code  ` `int` `main()  ` `{  ` `    ``/* Let us create a stack using push() operation*/` `    ``myStack *ms = createMyStack();  ` `    ``push(ms, 11);  ` `    ``push(ms, 22);  ` `    ``push(ms, 33);  ` `    ``push(ms, 44);  ` `    ``push(ms, 55);  ` `    ``push(ms, 66);  ` `    ``push(ms, 77);  ` ` `  `    ``cout << ``"Item popped is "` `<< pop(ms) << endl;  ` `    ``cout << ``"Item popped is "` `<< pop(ms) << endl;  ` `    ``cout << ``"Middle Element is "` `<< findMiddle(ms) << endl;  ` `    ``return` `0;  ` `}  ` ` `  `// This code is contributed by rathbhupendra `

## 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; ` `} ` ` `  `// 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); ` ` `  `    ``printf``(``"Item popped is %d\n"``, pop(ms)); ` `    ``printf``(``"Item popped is %d\n"``, pop(ms)); ` `    ``printf``(``"Middle Element is %d\n"``, findMiddle(ms)); ` `    ``return` `0; ` `} `

## Java

 `/* Java Program to implement a stack that supports findMiddle() and deleteMiddle ` `in O(1) time */` ` `  `public` `class` `GFG  ` `{ ` `    ``/* A Doubly Linked List Node */` `    ``class` `DLLNode ` `    ``{ ` `        ``DLLNode prev; ` `        ``int` `data; ` `        ``DLLNode next; ` `        ``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 */` `    ``class` `myStack ` `    ``{ ` `        ``DLLNode head; ` `        ``DLLNode mid; ` `        ``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; ` `             `  `            ``if``((ms.count % ``2``) != ``0``) ``// 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(myStack ms) ` `    ``{ ` `        ``/* Stack underflow */` `        ``if``(ms.count == ``0``) ` `        ``{ ` `            ``System.out.println(``"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``) ` `        ``{ ` `            ``System.out.println(``"Stack is empty now"``); ` `            ``return` `-``1``; ` `        ``} ` `        ``return` `ms.mid.data; ` `    ``} ` `     `  `    ``// Driver program to test functions of myStack ` `    ``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``); ` `         `  `        ``System.out.println(``"Item popped is "` `+ ob.pop(ms)); ` `        ``System.out.println(``"Item popped is "` `+ ob.pop(ms)); ` `        ``System.out.println(``"Middle Element is "` `+ ob.findMiddle(ms)); ` `    ``} ` `} ` ` `  `// This code is contributed by Sumit Ghosh  `

## 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; ` `    ``} ` `     `  `    ``// 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); ` `         `  `        ``Console.WriteLine(``"Item popped is "` `+  ` `                            ``ob.pop(ms)); ` `        ``Console.WriteLine(``"Item popped is "` `+  ` `                            ``ob.pop(ms)); ` `        ``Console.WriteLine(``"Middle Element is "` `+ ` `                            ``ob.findMiddle(ms)); ` `    ``} ` `} ` ` `  `// This code is contributed  ` `// by Arnab Kundu `

Output:

```Item popped is 77
Item popped is 66
Middle Element is 33```

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