Backtracking is a powerful and versatile algorithmic technique used to solve problems that require exploring all possible solutions while eliminating unpromising paths along the way. It works by incrementally building candidates for a solution and abandoning those that fail to satisfy the problem’s constraints. Think of it as navigating a…

In the world of algorithms, the Top-K pattern stands out as one of the most versatile and practical techniques. Whether you’re ranking search results, analyzing data trends, or solving complex coding problems, the Top-K algorithm pattern is your go-to strategy. This blog will walk you through a structured framework to…

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…

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 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…

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…

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,…

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…