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

Formal Definition of Big-Theta

Learning the mathematical definition: f(n) = Θ(g(n)) if there exist constants c₁, c₂, n₀ such that c₁g(n) ≤ f(n) ≤ c₂g(n).

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