Key Points to Identify Monotonic Stack Problems

To identify problems where a monotonic stack may be useful, look for the following characteristics:

• Nearest Greater or Smaller Element: Monotonic stacks are commonly used to find the nearest greater or smaller element to the left or right of each element in an array or sequence. If a problem requires you to find such elements efficiently, it’s a strong indicator that a monotonic stack might be useful.
• Monotonic Property: The term “monotonic” refers to the fact that the stack maintains a specific ordering property. There are two types of monotonic stacks:
  • Increasing Monotonic Stack: This stack is used when you need to find the nearest smaller element to the right for each element. It keeps elements in non-decreasing order, meaning the top of the stack contains the largest element seen so far.
  • Decreasing Monotonic Stack: This stack is used when you need to find the nearest greater element to the right for each element. It keeps elements in non-increasing order, meaning the top of the stack contains the smallest element seen so far.
• Problems Involving Element Removal: Monotonic stacks are often used in problems where you need to remove elements from the stack once their purpose is fulfilled. Elements are pushed onto the stack while certain conditions are met, and they are popped when no longer relevant.
• Immediate Neighbours: The problems that require finding immediate neighbours, such as the nearest greater or smaller elements to the left or right, are good candidates for a monotonic stack.
• Monotonicity Changes: Some problems involve changing monotonicity requirements during traversal, which can be handled using a combination of increasing and decreasing monotonic stacks.
• Typical Use Cases: Monotonic stacks are often used in scenarios like finding the next greater element, next smaller element, calculating the maximum area under histograms, evaluating expressions with infix to postfix conversion, and solving problems related to stock span, building and trapping rainwater, etc.
• Problems with Linear Time Constraints: If the problem statement mentions that you need to solve it in linear time, or it hints at optimizing the time complexity, a monotonic stack might be beneficial.

We all know what is Stack and how it works so today we will learn about a special type of data structure called monotonic stack. Problems using monotonic stack are difficult to identify if you do not know its concept. So in this post, we are going to discuss some key points that will help us to identify these problems.

But Before that let’s discuss the monotonic stack and its features.