Design a stack with operations on middle element

15 Jul, 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. 
Method 1: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. 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.  
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/* C++ Program to implement a stackthat supports findMiddle() anddeleteMiddle in O(1) time */#include <bits/stdc++.h>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
/* Program to implement a stack that supports findMiddle()   and deleteMiddle in O(1) time */#include <stdio.h>#include <stdlib.h>  /* 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 stackint 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 myStackint 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 Program to implement a stack that supportsfindMiddle() 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 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 codeif __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# Program to implement a stackthat 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);ber144 index143 alt1">          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
Popped : 99
Popped : 88
Middle Element : 44
New Middle Element : 55
Method 2: Using a standard stack and a deque 
We will use a standard stack to store half of the elements and the other half of the elements which were added recently will be present in the deque. Insert operation on myStack will add an element into the back of the deque. The number of elements in the deque stays 1 more or equal to that in the stack, however, whenever the number of elements present in the deque exceeds the number of elements in the stack by more than 1 we pop an element from the front of the deque and push it into the stack. The pop operation on myStack will remove an element from the back of the deque. If after the pop operation, the size of the deque is less than the size of the stack, we pop an element from the top of the stack and insert it back into the front of the deque so that size of the deque is not less than the stack. We will see that the middle element is always the front element of the deque. So deleting of the middle element can be done in O(1) if we just pop the element from the front of the deque. 
Consider Operations on My_stack:
Operation                             stack                                   deque
add(2)                                    { }                                        {2}
add(5)                                    {2}                                       {5}
add(3)                                    {2}                                       {5,3}
add(7)                                    {2,5}                                    {3,7}
add(4)                                    {2,5}                                    {3,7,4}
deleteMiddle()                       {2,5}                                     {7,4}
deleteMiddle()                       {2}                                        {5,4}
pop()                                     {2}                                        {5}
pop()                                     { }                                         {2}
deleteMiddle()                       { }                                         { }
C++
#include <bits/stdc++.h>using namespace std;  class myStack {    stack<int> st;    deque<int> dq;  public:    void add(int data)    {        dq.push_back(data);        if (dq.size() > st.size() + 1) {            int temp = dq.front();            dq.pop_front();            st.push(temp);        }    }      void pop()    {        int data = dq.back();        dq.pop_back();        if (st.size() > dq.size()) {            int temp = st.top();            st.pop();            dq.push_front(temp);        }    }      int getMiddleElement() {       return dq.front();     }      void deleteMiddleElement()    {        dq.pop_front();        if (st.size() > dq.size()) { // new middle element            int temp = st.top();     // should come at front of deque            st.pop();            dq.push_front(temp);        }    }};  int main(){    myStack st;    st.add(2);    st.add(5);    cout << "Middle Element: " << st.getMiddleElement() << endl;    st.add(3);    st.add(7);    st.add(4);    cout << "Middle Element: " << st.getMiddleElement() << endl;    st.deleteMiddleElement();    cout << "Middle Element: " << st.getMiddleElement() << endl;    st.deleteMiddleElement();    cout << "Middle Element: " << st.getMiddleElement() << endl;    st.pop();    st.pop();    st.deleteMiddleElement();}  //By- Vijay Chadokar
Middle Element: 5
Middle Element: 3
Middle Element: 7
Middle Element: 5
This article is contributed by Chandra Prakash. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above 
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