Delete Middle Element of Stack.

Created On: 03 February 2024

Given a stack of integers. The task is to delete the middle element from the stack without using extra space. The middle element is defined as the element at position (size of stack / 2 +1). Write a function/method that takes the stack as input and modifies it to delete the middle element.

Example:

Input:  [1, 2, 3, 4, 5]

Output: [1, 2, 4, 5]

Explanation: The middle element is 3, and after deletion, the stack becomes [1, 2, 4, 5].


Input:  [10, 20, 30, 40, 50, 60]

Output: [10, 20, 30, 50, 60]

Explanation: The middle element is 40, and after deletion, the stack becomes [10, 20, 30, 50, 60].


It is very easy to delete the middle element of the given stack by using any extra data structure. Still, the main challenge of this problem is to solve this without using any additional space. Actually, that is also quite simple if our powerful programming tool known as recursion. Before moving to the recursive solution to delete the middle element of the stack. Let's check a simple brute-force solution for this.

Brute Force Approach to Delete Middle Element of Stack.

In this approach, we will use another auxiliary stack or a list to store the given stack element until we reach the middle element and then we will remove (pop) the middle element from the stack and then push back all the elements of the auxiliary stack back to the main stack.

Algorithm Steps:
  • Create a stack auxStack to temporarily store elements.
  • Calculate the position of the middle element (middle = size / 2 +1).
  • Iterate over the first half of the original stack (up to the element just before the middle) and Push each element to the auxStack and pop it from the original stack.
  • Skip the middle element of the stack and pop it from the original stack.
  • Pop elements from the auxStack and push them back to the original stack.

Below is the code implementation of the above approach:
// C++ code implementation to delete middle element of stack
// Brute force approach using extra space
#include <iostream>
#include <stack>
using namespace std;

// Function to delete the middle element of a stack without recursion
void deleteMiddle(stack<int>& s) {
    int size = s.size();
    int middle = size / 2 + 1;

    stack<int> auxStack;

    // Push the first half of elements to the auxiliary stack
    for (int i = 0; i < middle - 1; i++) {
        auxStack.push(s.top());
        s.pop();
    }

    // Skip the middle element
    s.pop();

    // Push the elements back to the original stack
    while (!auxStack.empty()) {
        s.push(auxStack.top());
        auxStack.pop();
    }
}

// Function to print the stack
void printStack(stack<int> s) {
    while (!s.empty()) {
        cout << s.top() << " ";
        s.pop();
    }
    cout << endl;
}

int main() {
    // Example usage
    stack<int> myStack;

    // Push elements onto the stack
    myStack.push(1);
    myStack.push(2);
    myStack.push(3);
    myStack.push(4);
    myStack.push(5);

    cout << "Original Stack: ";
    printStack(myStack);

    // Delete the middle element without recursion
    deleteMiddle(myStack);

    cout << "Stack after deleting middle element: ";
    printStack(myStack);

    return 0;
}

// Java code implementation to delete middle element of stack
import java.util.Stack;

public class Main {
    public static void main(String[] args) {
        Stack<Integer> myStack = new Stack<>();

        // Push elements onto the stack
        myStack.push(1);
        myStack.push(2);
        myStack.push(3);
        myStack.push(4);
        myStack.push(5);

        System.out.println("Original Stack: " + myStack);

        // Delete the middle element without recursion
        deleteMiddle(myStack);

        System.out.println("Stack after deleting middle element: " + myStack);
    }

    // Function to delete the middle element of a stack without recursion
    public static void deleteMiddle(Stack<Integer> s) {
        int size = s.size();
        int middle = size / 2 + 1;

        Stack<Integer> auxStack = new Stack<>();

        // Push the first half of elements to the auxiliary stack
        for (int i = 0; i < middle - 1; i++) {
            auxStack.push(s.pop());
        }

        // Skip the middle element
        s.pop();

        // Push the elements back to the original stack
        while (!auxStack.isEmpty()) {
            s.push(auxStack.pop());
        }
    }
}

# Python code to delete middle element of stack
def delete_middle(s):
size = len(s)
middle = size // 2 + 1

aux_stack = []

# Push the first half of elements to the auxiliary stack
for i in range(middle - 1):
    aux_stack.append(s.pop())

# Skip the middle element
s.pop()

# Push the elements back to the original stack
while aux_stack:
    s.append(aux_stack.pop())

# Example usage
my_stack = [1, 2, 3, 4, 5]

print("Original Stack:", my_stack)

# Delete the middle element without recursion
delete_middle(my_stack)

print("Stack after deleting middle element:", my_stack)

// C# code implementation to delete middle element of stack
using System;
using System.Collections.Generic;

class MainClass {
    public static void Main(string[] args) {
        Stack<int> myStack = new Stack<int>();

        // Push elements onto the stack
        myStack.Push(1);
        myStack.Push(2);
        myStack.Push(3);
        myStack.Push(4);
        myStack.Push(5);

        Console.WriteLine("Original Stack: " + string.Join(" ", myStack));

        // Delete the middle element without recursion
        DeleteMiddle(myStack);

        Console.WriteLine("Stack after deleting middle element: " + string.Join(" ", myStack));
    }

    // Function to delete the middle element of a stack without recursion
    public static void DeleteMiddle(Stack<int> s) {
        int size = s.Count;
        int middle = size / 2 + 1;

        Stack<int> auxStack = new Stack<int>();

        // Push the first half of elements to the auxiliary stack
        for (int i = 0; i < middle - 1; i++) {
            auxStack.Push(s.Pop());
        }

        // Skip the middle element
        s.Pop();

        // Push the elements back to the original stack
        while (auxStack.Count > 0) {
            s.Push(auxStack.Pop());
        }
    }
}
Output: 
Original Stack: 5 4 3 2 1
Stack after deleting middle element: 5 4 2 1
  • Time Complexity: O(n) where n is the number of elements present in the given stack.
  • Space Complexity: O(n) as we are using an extra stack to delete the middle element of the stack.

Delete Middle Element of the Stack Using Recursion.

We can delete the middle element of the stack using recursion without using any extra space. In this approach, we will recursively pop the stack element, and while unwinding we will push back all the elements except the middle element.

Algorithm Steps:
  • The base case of our recursive call is when our stack gets empty.
  • Pop an element from the stack and recursively call the function.
  • While unwinding from the recursive calls, increment a counter to keep track of the number of elements.
  • If the counter indicates the middle element, skip pushing it back onto the stack.
  • While unwinding, push the elements back onto the stack.

Below is the code implementation of the above recursive approach:
// C++ code for recurisvely delete middle element of stack
#include <iostream>
#include <stack>

using namespace std;

// Function to delete the middle element of a stack using recursion
void deleteMiddle(stack<int>& s, int current, int middle) {
    // Base case: stack is empty
    if (s.empty()) {
        return;
    }

    // Recursive call: pop an element and make a recursive call
    int temp = s.top();
    s.pop();
    deleteMiddle(s, current + 1, middle);

    // Count elements and skip pushing the middle element
    if (current != middle) {
        s.push(temp);
    }
}

// Function to print the stack
void printStack(stack<int> s) {
    while (!s.empty()) {
        cout << s.top() << " ";
        s.pop();
    }
    cout << endl;
}

int main() {
    stack<int> myStack;

    // Push elements onto the stack
    myStack.push(1);
    myStack.push(2);
    myStack.push(3);
    myStack.push(4);
    myStack.push(5);

    cout << "Original Stack: ";
    printStack(myStack);

    int middle = myStack.size() / 2;
    
    // Delete the middle element using recursion
    deleteMiddle(myStack, 0, middle);

    cout << "Stack after deleting middle element: ";
    printStack(myStack);

    return 0;
}

import java.util.Stack;

public class Main {
  public static void main(String[] args) {
      Stack<Integer> myStack = new Stack<>();

      // Push elements onto the stack
      myStack.push(1);
      myStack.push(2);
      myStack.push(3);
      myStack.push(4);
      myStack.push(5);

      System.out.println("Original Stack: " + myStack);

      int middle = myStack.size() / 2;

      // Delete the middle element using recursion
      deleteMiddle(myStack, 0, middle);

      System.out.println("Stack after deleting middle element: " + myStack);
  }

  // Function to delete the middle element of a stack using recursion
  public static void deleteMiddle(Stack<Integer> s, int current, int middle) {
      if (s.isEmpty()) {
          return;
      }

      int temp = s.pop();
      deleteMiddle(s, current + 1, middle);

      if (current != middle) {
          s.push(temp);
      }
  }
}

# Python program to delete middle element of stack using Recursive

def delete_middle(s, current, middle):
# Base case: stack is empty
if not s:
    return

# Recursive call: pop an element and make a recursive call
temp = s.pop()
delete_middle(s, current + 1, middle)

# Count elements and skip pushing the middle element
if current != middle:
    s.append(temp)

# Example usage
my_stack = [1, 2, 3, 4, 5]

print("Original Stack:", my_stack)
middle = len(my_stack) // 2

# Delete the middle element using recursion
delete_middle(my_stack, 0, middle)

print("Stack after deleting middle element:", my_stack)

//C# code to delete middle element of stack using Recursion
using System;
using System.Collections.Generic;

class MainClass {
    public static void Main(string[] args) {
        Stack<int> myStack = new Stack<int>();

        // Push elements onto the stack
        myStack.Push(1);
        myStack.Push(2);
        myStack.Push(3);
        myStack.Push(4);
        myStack.Push(5);

        Console.WriteLine("Original Stack: " + string.Join(" ", myStack));

        int middle = myStack.Count / 2;

        // Delete the middle element using recursion
        DeleteMiddle(myStack, 0, middle);

        Console.WriteLine("Stack after deleting middle element: " + string.Join(" ", myStack));
    }

    // Function to delete the middle element of a stack using recursion
    public static void DeleteMiddle(Stack<int> s, int current, int middle) {
        if (s.Count == 0) {
            return;
        }

        int temp = s.Pop();
        DeleteMiddle(s, current + 1, middle);

        if (current != middle) {
            s.Push(temp);
        }
    }
}
Output: 
Original Stack: 5 4 3 2 1 
Stack after deleting middle element: 5 4 2 1
  • Time Complexity: O(n) where n is the number of elements in the stack.
  • Space Complexity: O(n) using auxiliary space for Recursion.

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