Big-O for Time and Space

Big-O Time & Space Basics

Big-Omega Notation

Linearithmic Time O(n log n)

Complexity of a Single Loop

Sequential Code Blocks

Constant Time O(1)

Linear Time O(n)

Logarithmic Time O(log n)

Quadratic Time O(n^2)

Linearithmic Time O(n log n)

Exponential Time O(2^n)

Ordering Complexity Classes

Counting Basic Operations

Dropping Constants

Dropping Lower-Order Terms

Complexity of Nested Loops

Input Size Drives Complexity

How Runtime Scales

What Complexity Analysis Is and Why It Matters

Using Complexity to Compare Algorithms

Best, Average, and Worst Case

Space Complexity Basics

Analyzing Nested Loops for Time Complexity

Analyzing Simple Loops for Time Complexity

Dropping Constants and Lower-Order Terms

Ranking Common Complexity Classes

Single Loop Linear Time

Ordering Growth Rates

Constant Time Array Access

Loop With Doubling Step

Worst Case Of Linear Search

Space Complexity Of Copy

Two Input Variables

Summing Sequential Loops

Dropping Constants In Big-O

Sort Then Loop Complexity

Halving Loop Logarithmic Time

Nested Loops Quadratic Time

Common Big-O Complexity Classes

Big-O as an Upper Bound

Definition and Intuition of Big-O Notation

Dropping Constants in Big-O

Factorial Time O(n!)

Auxiliary Space vs Total Space

Complexity of Nested Loops

Dropping Lower-Order Terms

Quadratic Time O(n^2)

Logarithmic Time O(log n)

Constant Time O(1)

Best, Average, and Worst Case

Counting Operations

Exponential Time O(2^n)

Complexity of Single Loops

Big-O Formal Notation and Meaning

Why We Focus on Worst Case

Big-Theta Notation

Sequential Statements (Addition)

Comparing Growth Rates

Linear Time O(n)

How Runtime Grows as Input Grows

Input Size n: The Basis of Analysis

Counting Operations to Estimate Cost