When solving sequence-based problems—like finding the next greater element, stock span, or calculating sliding window maximum—efficiency is paramount. Many of these problems involve comparing elements across a sequence, and a brute-force approach often leads to nested loops with a costly O(n^2) time complexity. Enter the monotonic stack: a powerful data…
Frequency Counters 101: The Algorithm Pattern You Need to Know
The Frequency Counter pattern is a fundamental algorithm design approach used to solve problems by counting occurrences of elements in an efficient way. It replaces the need for nested loops (brute-force methods) with hash maps or dictionaries to reduce time complexity. Here’s a structured framework to learn and master this…
Greedy Patterns in Algorithms: Simplify, Solve, Succeed
Greedy algorithms are a powerful approach for solving optimization problems, where the goal is to find the best solution under certain constraints. The concept is simple: make decisions step-by-step, always choosing the option that looks best at the moment, and hope it leads to the best overall solution. How Greedy…
Why K-Way Merge is the Algorithm Pattern You Need to Know
If you’ve ever faced a problem involving multiple sorted arrays or lists that need to be combined into one sorted result, you’ve encountered a k-way merge scenario. It’s an essential algorithmic technique, powering systems like search engines, data processing pipelines, and distributed databases. In this post, we’ll break down the…
Kth Largest Element in a Stream – 703. LeetCode
Imagine you are continuously receiving numbers in a stream, and you want to keep track of the Kth largest element at any given time. This means if you are given a number k, you need to find the k-th largest element among all the numbers you have received so far….
Minimum Window Substring – 76. LeetCode
The Minimum Window Substring is a popular problem in computer science, especially in coding interviews. It combines string manipulation with efficient algorithms, making it both challenging and rewarding to solve. In this post, we’ll break down the problem and its key aspects to set a strong foundation before diving into…
Squares Of Sorted Array – 977. LeetCode
Imagine you have an array of numbers sorted in increasing order, but some numbers are negative. If you square each number, the result is not longer sorted because squaring a negative number makes it positive. Your task is to return a new array where the squares of the numbers are…
Invariants 101: The Golden Rule for Reliable Algorithms
Invariants are a powerful tool in programming. They’re conditions that always remain true at specific points in an algorithm, no matter what. Establishing invariants early in the problem-solving process helps you write correct, efficient, and easy-to-understand code. In this blog, we’ll cover how to quickly establish invariants, explain their benefits,…
Recurrence Relations Made Easy: A Beginner’s Guide to Algorithmic Thinking
Have you ever wondered how recursive algorithms solve complex problems by breaking them into smaller pieces? The answer lies in recurrence relations—the mathematical backbone of recursion and dynamic programming. Whether it’s calculating Fibonacci numbers, optimizing a game strategy, or solving a divide-and-conquer problem like Merge Sort, recurrence relations provide a…
Binary Search Tree Iterator – 173. LeetCode
The Binary Search Tree (BST) Iterator problem asks you to implement an iterator for a BST. This iterator must support operations to efficiently traverse the BST in inorder (left → root → right) order. The iterator needs to provide the next smallest element in the BST using the next() method…
