Applications of Monotonic Stack

What is Monotonic Stack?

A Monotonic Stack is a common data structure in computer science that maintains its elements in a specific order. Unlike traditional stacks, Monotonic Stacks ensure that elements inside the stack are arranged in an increasing or decreasing order based on their arrival time. In order to achieve the monotonic stacks, we have to enforce the push and pop operation depending on whether we want a monotonic increasing stack or monotonic decreasing stack....

Types of Monotonic Stack:

Monotonic Stacks can be broadly classified into two types:...

Monotonic Increasing Stack:

A Monotonically Increasing Stack is a stack where elements are placed in increasing order from the bottom to the top. Each new element added to the stack is greater than or equal to the one below it. If a new element is smaller, we remove elements from the top of the stack until we find one that is smaller or equal to the new element, or until the stack is empty. This ensures that the stack always stays in increasing order....

Monotonic Decreasing Stack:

A Monotonically Decreasing Stack is a stack where elements are placed in decreasing order from the bottom to the top. Each new element added to the stack must be smaller than or equal to the one below it. If a new element is greater than top of stack then we remove elements from the top of the stack until we find one that is greater or equal to the new element, or until the stack is empty. This ensures that the stack always stays in decreasing order....

Practice Problem on Monotonic Stack:

Problem Next Greater Element (NGE) for every element in given Array Next Smaller Element Find next Smaller of next Greater in an array Next Greater Frequency Element Largest Rectangular Area in a Histogram using Stack Check for Balanced Brackets in an expression (well-formedness) Maximum size rectangle binary sub-matrix with all 1s Expression Evaluation The Stock Span Problem Expression contains redundant bracket or not Find the nearest smaller numbers on left side in an array Find maximum of minimum for every window size in a given array Minimum number of bracket reversals needed to make an expression balanced Tracking current Maximum Element in a Stack Lexicographically largest subsequence containing all distinct characters only once Sum of maximum elements of all possible sub-arrays of an array...

Applications of Monotonic Stack :

Here are some applications of monotonic stacks:...

Advantages of Monotonic Stack:

Efficient for finding the next greater or smaller element in an array.Useful for solving a variety of problems, such as finding the nearest smaller element or calculating the maximum area of histograms.In many cases, the time complexity of algorithms using monotonic stacks is linear, making them efficient for processing large datasets....

Disadvantages of Monotonic Stack:

Requires extra space to store the stack.May not be intuitive for beginners to understand and implement....

Frequently Asked Questions (FAQs) on Monotonic Stack:

1. What is a monotonic stack?...