BiteSizedChunks.comLearn one small thing at a time.

Course contentsShow

Computer Science

270What is Runtime Analysis?
271Counting Primitive Operations
272Best-Case, Worst-Case, and Average-Case
273Input Size as a Variable
274Analyzing Simple Loops
275Analyzing Nested Loops
276Analyzing Sequential Statements
277Analyzing Conditional Statements
278Growth Rates and Dominant Terms
279Constant Factors and Why They're Dropped
280What is Big-O Notation?
281Ignoring Constants in Big-O
282Identifying Dominant Terms
283O(1): Constant Time
284O(log n): Logarithmic Time
285O(n): Linear Time
286O(n log n): Linearithmic Time
287O(n²): Quadratic Time
288O(n³) and Higher Polynomial Time
289O(2ⁿ): Exponential Time
290O(n!): Factorial Time
291Comparing Growth Rates
292Introduction to Big-Theta Notation
293Formal Definition of Big-Theta
294Proving Big-Theta Bounds
295Big-Theta Examples and Common Functions
296Introduction to Big-Omega Notation
297Formal Definition of Big-Omega
298Proving Big-Omega Bounds
299Relationship Between Big-O, Big-Omega, and Big-Theta
300Best-Case, Worst-Case, and Average-Case Analysis
301Practical Applications of Tight Bounds
302What is Space Complexity?
303Auxiliary Space vs Total Space
304Space Complexity Notation
305Constant Space: O(1)
306Linear Space: O(n)
307Space-Time Tradeoffs
308Recursion and Call Stack Space
309In-Place Algorithms
310Space Complexity of Common Data Structures
311Analyzing Multi-Dimensional Space

Computer Science

270What is Runtime Analysis?
271Counting Primitive Operations
272Best-Case, Worst-Case, and Average-Case
273Input Size as a Variable
274Analyzing Simple Loops
275Analyzing Nested Loops
276Analyzing Sequential Statements
277Analyzing Conditional Statements
278Growth Rates and Dominant Terms
279Constant Factors and Why They're Dropped
280What is Big-O Notation?
281Ignoring Constants in Big-O
282Identifying Dominant Terms
283O(1): Constant Time
284O(log n): Logarithmic Time
285O(n): Linear Time
286O(n log n): Linearithmic Time
287O(n²): Quadratic Time
288O(n³) and Higher Polynomial Time
289O(2ⁿ): Exponential Time
290O(n!): Factorial Time
291Comparing Growth Rates
292Introduction to Big-Theta Notation
293Formal Definition of Big-Theta
294Proving Big-Theta Bounds
295Big-Theta Examples and Common Functions
296Introduction to Big-Omega Notation
297Formal Definition of Big-Omega
298Proving Big-Omega Bounds
299Relationship Between Big-O, Big-Omega, and Big-Theta
300Best-Case, Worst-Case, and Average-Case Analysis
301Practical Applications of Tight Bounds
302What is Space Complexity?
303Auxiliary Space vs Total Space
304Space Complexity Notation
305Constant Space: O(1)
306Linear Space: O(n)
307Space-Time Tradeoffs
308Recursion and Call Stack Space
309In-Place Algorithms
310Space Complexity of Common Data Structures
311Analyzing Multi-Dimensional Space

← Computer Science

Lesson 296 of 2,872·7. Introduction to Complexity AnalysisPro lesson

Introduction to Big-Omega Notation

Understanding Big-Omega as a lower bound that describes the best-case or minimum growth rate of an algorithm.

This lesson is for subscribers

You've completed the free preview. Subscribe to unlock every lesson in every course.

See pricing Back to course