How to Delete the Middle Element of a Stack?

Introduction

Deleting, inserting, searching, and popping are some basic operations done in the stack data structure. There are a whole lot of problems available with these operations. For example, Inserting element at the bottom of a stack. 

Problem Statement

Given a stack, delete the middle element of it without using any additional data structure. You can use basic stack operations like push(), pop() and empty().

For example : 

INPUT : STACK [ ] = [ 1 , 2 , 3 , 4 , 5 ] , N = 5OUTPUT:  [ 1 , 2 , 4,  5 ] The above example contains an odd number of elements, hence the middle element is clearly the N / 2th element, which is removed from the stack in the output. INPUT : STACK [ ] = [ 5, 6, 7, 8 ] , N = 4OUTPUT:  [ 5, 7, 8 ]The above example contains an even number of elements, so out of the two middle elements, we consider the one which occurs first. Hence, the middle element would be (N / 2 – 1) element, which is 6 and is removed from the stack in the output.

Note: We’ll be deleting and returning the same stack. No new stack will be created.

Solution Approach

The idea is to tackle it using Recursion. We will keep removing the elements one by one from the top of the stack recursively and then at the end push all of them except the middle one. 

The steps are as follows :

Declare and initialize a variable named current to 0. This “current” will keep record of the position we are at now. Pop the top element of the stack.Call the deleteMiddle function after incrementing current by one( which signifies that we are moving on to the next position).Keep repeating steps 2 and 3 until the stack is not empty or current is not equal to n.Once the stack is empty or current==n, means that we’ve popped every element of the stack. Now, keep pushing back the elements one by one except for the case where curr==n/2. Thus we have the stack now with all the elements except for the middle one.

Before directly jumping to the solution, we suggest you try and solve this delete middle element of a stack on Codestudio.

Implementation

Let’s see the implementation of the above approach.

#include <bits/stdc++.h>
using namespace std;

 // Function that deletes the middle of the stack of size n. Current is current 
 // position we’re on 
void deleteMiddle(stack<int> &s, int n,int current)
{
   // If stack becomes empty or all items already are traversed
   if (s.empty() || current == n)
     return;
 
   // Remove current item
   int x = s.top();
   s.pop();
 
   // Call for removing the other items
   deleteMiddle(s, n, current+1);
 
   // Push all the elements back other than the middle one
   if (current != n/2)
     s.push(x);
}


int main()
{
    stack<int> s;
 
    //push elements into the stack
    s.push(5);
    s.push(6);
    s.push(7);
    s.push(8);
    s.push(9);
    s.push(10);
    s.push(11);
    int current = 0;
    deleteMiddle(s, s.size(),current);
 
    // Printing stack after deletion of the middle element.
    while (!s.empty())
    {
        int p = s.top();
        s.pop();
        cout << p << " ";
    }
    return 0;
   
}

Output

11 10 9 7 6 5

8 was the middle element so it has been removed.

Time Complexity

O(n), where n is the size of the stack. 

Reason : Since we’re iterating over the stack recursively by making only one recursive call, which takes O(n) time and popping and pushing operations take only O(1) time, the overall time complexity will be O(n). 

Space Complexity

O(n), where n is the size of the stack. 

Reason: We haven’t used any other data structure or any other stack. Therefore, the only space taken is the space to store the elements in the stack, i.e; the size of the stack.

If you’ve made it this far, congratulations, Champ. The problem of “Delete middle element of stack ” is now resolved. If you haven’t already submitted it to CodeStudio. Without further ado, have it accepted as early as possible.

Frequently Asked Questions

Key Takeaways

As mentioned earlier, questions related to basic stack operations, inserting and deleting are prevalent.

These questions are asked during various coding contests as well as placements tests.

We discussed one such problem: delete middle element of a stack, along with its approach and implementation in C++, in this article.

Another similar problem is Insert An Element At Its Bottom In A Given Stack . Don’t forget to try it out as it’ll help you understand the operations well.

To practice more such problems, Codestudio is a one-stop destination. This platform will help you acquire effective coding techniques and give you an overview of student interview experience in various product-based companies.

Happy Coding!

By: Shreya Deep