In this tutorial, we’ll dive deeper into algorithm complexity, focusing on common operations such as addition, multiplication, logarithmic algorithms, and the role of string manipulation in evaluating time complexity. 1. Complexity of Addition and Multiplication Let’s start by analyzing sequential and nested loops. Example: Sequential Loops Suppose we have the following scenario: These loops run…

When evaluating the complexity of an algorithm, you’ll frequently encounter a few common patterns. Understanding how to approximate, calculate, and represent them using Big-O notation is a crucial step in analyzing algorithm efficiency. Let’s break down the most common complexity patterns and how to handle them. 1. Arithmetic Series: This is a classic arithmetic series.…

1. What is Notation? Notation is a symbolic way of writing mathematical expressions. Instead of writing: “The sum of one and two” We write: This symbolic representation (such as , , , , , etc.) is called mathematical notation. 2. What is Big-O Notation? Big-O notation is a way to describe how fast a function…

Understanding how different functions behave as input values grow is fundamental in computer science, especially in analyzing algorithm efficiency. This tutorial walks you through how to compare functions, understand their rates of growth, and use Big-O notation to describe their behavior concisely. 1. Comparing Simple Functions Let’s begin by considering two simple functions: We want…

1. Why Do We Care About Best and Worst Cases? When analyzing algorithms, we need to know how long an algorithm can take to run.However, depending on the input, the runtime may vary. For example: We study both cases, but in most professional and academic contexts, we focus on the worst case — because that…

Evaluating algorithm complexity is one of the most fundamental skills in computer science and software engineering. It’s how we determine which algorithm is more efficient — both in execution speed and in memory usage. 1. Why Do We Evaluate Complexity? Imagine you’ve solved a problem using two different algorithms. Both give correct results, but you…

Before diving into Big O notation, it’s important to understand why we study it and how it connects to real-world coding problems. 1. Why Study Big O Notation? There are three key reasons why understanding complexity analysis and Big O notation is crucial. Reason 1 — Essential for Coding Interviews In technical interviews, after solving…

1. Problem Statement You are given a list of non-overlapping intervals sorted by their start time. You are also given a new interval that needs to be inserted into the list. Insert the new interval such that the list remains sorted and non-overlapping. If necessary, merge overlapping intervals. Constraints The list is already sorted by…

1. Problem Statement Given a list of intervals, merge all the overlapping intervals and return a list of non-overlapping intervals. An interval is represented as a pair of integers [start, end]. Example 2. Understanding the Problem The core idea is to combine intervals that share common points. If two intervals [a,b] and [c,d] overlap, their…

In this tutorial, we will explore the concept of intervals, which are essential in solving many algorithmic and interview problems, particularly those involving time, tasks, or scheduling. One of the most important subtopics in intervals is overlapping intervals, often asked in coding interviews. 1. What is an Interval? An interval is a range defined by…