How to efficiently implement k stacks in a single array

Introduction

The ability to effectively manage and use memory is crucial when programming with multiple stacks. We will look at how to implement K stacks in a single array in this article, making sure to use the least amount of memory and perform operations as quickly as possible. To put the idea into practise, we'll also offer a Python implementation.

Description of K Stacks

A stack is a data structure used in programming that adheres to the Last-In-First-Out (LIFO) principle, which states that the last element added is always the first one to be removed. It is frequently employed to carry out different algorithms and effectively resolve issues. However, there are times when we have to manage several stacks at once. It can be inefficient to manage different arrays for each stack in terms of memory usage.

This restriction can be removed by using K stacks implemented in a single array. This strategy enables us to provide the required operations for each individual stack while making efficient use of memory.

Understanding Stacks

Let's quickly review the core ideas behind stacks before delving into the implementation specifics.

Operations on Stacks

Push and pop are the two main operations that a stack typically supports. While the pop operation removes the element at the top of the stack, the push operation adds an element to the stack.

The LIFO Rule

According to the Last-In-First-Out (LIFO) principle, the element that was most recently added is the one that is removed first in a stack. It makes sure that elements are accessed in the opposite order from which they were inserted.

Multiple Stacks in a Single Array Implementation

We can segment the array and assign each segment to a different stack to efficiently implement multiple stacks within a single array. Let's look at the steps in this procedure.

Equally Dividing the Array

Assuming that we want to implement k stacks, divide the array into k equal sections. Each segment will function as a separate stack.

Effective Space Management

Allocate the segments dynamically based on the requirements of each stack to maximise memory usage. We can dynamically adjust each stack's size so that it can expand or contract as needed rather than giving each stack a fixed size.

Pointers Stack

Keep track of a collection of stack pointers, where each pointer represents a stack and tracks the top element. These pointers effectively carry out operations specific to each stack and aid in determining its current state.

Operation by Push

In the push operation, an element is added to the stack. Let's talk about the procedures needed to carry out this operation successfully.

Finding the Active Stack

Decide which stack you want to push the element onto. The stack number or any other pertinent factors can be used to determine this.

Stack Pointer Updating

Before inserting the new element, move the active stack's stack pointer to the proper location. The stack pointer will always point to the top element thanks to this modification.

Placement of the Element

At the location the updated stack pointer indicates, add the element to the array. Update the stack pointer to reflect the new top element as soon as the element has been successfully inserted.

Operation Pop

The topmost element in the stack is removed during the pop operation. Let's talk about the procedures needed to carry out this operation successfully.

Finding the Active Stack

Decide which stack you want to pop the element from. The stack number or any other pertinent factors can be used to determine this.

Checking for Underflow

Make sure that the stack is not empty before popping an element. When the stack is empty, an underflow condition is present, and we should respond appropriately.

The Stack Pointer being updated

Before removing the top element, move the active stack's stack pointer to the proper location. This modification makes sure that after the pop operation, the stack pointer always points to the new top element.

Eliminating the Element

At the location the updated stack pointer indicates, remove the topmost element from the array. Update the stack pointer to reflect the new top element as soon as the element has been successfully removed.

Implementation strategy for K Stacks

Several sections of the array, each devoted to a different stack, must be created in order to implement K stacks in a single array. For each stack, we allot fixed-sized segments, making sure they don't overlap.

The important concept is to keep top and next arrays separate. Each stack's top element is tracked by the top array, which also stores the next available index in the array. The top array's elements are all initially set to -1, signifying that the stacks are empty. The next index for each element is set for the next array.

Implementation in Python

The effective K stacks are implemented in Python using a single array as follows:

Output:

Popped value from stack 0: 5
Popped value from stack 1: 10
Popped value from stack 2: 15

The Benefits of Using K Stacks in a Single Array

K stack implementation in a single array has the following benefits:

Simplified management: Working with a single array makes it simpler to manage multiple stacks as a whole, which facilitates handling and manipulating data.

Implementation simplicity: As shown in the provided Python code snippet, the approach is comparatively easy to implement.

Performance gains: Quick push and pop operations are made possible by the effective implementation, allowing for effective data manipulation within each stack.