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.

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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.

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

The Time Complexity is 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).

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 Coding Ninjas Studio. Without further ado, have it accepted as early as possible.

When the stack is empty and we are trying to remove an element from the stack then the condition is called as?

In a stack, if a user tries to remove an element from the empty stack then it is called as underflow.

What is the term used to delete an element from the stack?

“Pop” is the term used to delete an element from the stack.

Where can I submit my “Delete middle element of a stack” code?

You can submit your code on Coding Ninjas Studio and get it accepted right away.

Are there more Data Structures and Algorithms problems in Coding Ninjas Studio?

Yes, Coding Ninjas Studio is a platform that provides both practice coding questions and commonly asked interview questions. The more we’ll practice, the better our chances are of getting into a dream company of ours.

Conclusion

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

We discussed one suchproblem: deleting the middle element of a stack, along with its approach and implementation in C++, in this article.