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Design a stack with operations on middle element

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  • Difficulty Level : Medium
  • Last Updated : 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. 
 

C++




/* C++ Program to implement a stack
that supports findMiddle() and
deleteMiddle 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


C




/* 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 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

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


Output

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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