Asymptotic Notations: Big O, Big Omega and Big Theta Explained (With Notes)
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- Опубліковано 31 лип 2020
- This video explains Big O, Big Omega and Big Theta notations used to analyze algorithms and data structures.
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*Let's simplify things.* 😊
Asymptotic notation is like a tool that helps us compare how fast different computer programs can solve problems as the problems get bigger and bigger.
Imagine you have two superheroes, SuperFastMan and SuperSlowMan, and they both want to solve a puzzle. The puzzle has different levels, and as they go to higher levels, the puzzle becomes bigger and more challenging.
1. Big O notation (O):
Let's say SuperFastMan can solve a puzzle in no more than 5 minutes, no matter how big it is. We write this as O(5 minutes). It means his speed to solve the puzzle is like a "speed limit" or an "upper bound."
Example: O(5 minutes) means that the time it takes to solve the puzzle is never worse (never longer) than 5 minutes, no matter how big the puzzle is.
2. Omega notation (Ω):
Now, let's consider SuperSlowMan, who takes at least 10 minutes to solve a puzzle, no matter how small it is. We write this as Ω(10 minutes). It means his speed to solve the puzzle is like a "slowest speed" or a "lower bound."
Example: Ω(10 minutes) means that the time it takes to solve the puzzle is never better (never shorter) than 10 minutes, no matter how small the puzzle is.
3. Theta notation (Θ):
Finally, let's talk about a third superhero, SuperAverageMan, who always takes around 7 minutes to solve the puzzle. We write this as Θ(7 minutes). It means his speed to solve the puzzle is like a "best guess" or an "average speed."
Example: Θ(7 minutes) means that the time it takes to solve the puzzle is neither worse nor better, but it's around 7 minutes, no matter how big or small the puzzle is.
These notations help computer programmers decide which superhero (algorithm) is the best for a specific puzzle (problem) based on their speed (efficiency) for large puzzles (big data).
So, when programmers talk about Big O, Omega, and Theta notation, they are just comparing superheroes' abilities to solve puzzles of different sizes!
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🎯 Key Takeaways for quick navigation:
00:57 📚 Asymptotic notation is used to compare algorithms' efficiency.
02:20 📈 Big O notation (O) represents an upper time complexity bound.
08:27 📉 Big Omega notation (Ω) represents a lower time complexity bound.
13:33 📊 Big Theta notation (Θ) provides both upper and lower time complexity bounds.
16:00 🧮 Big Theta (Θ) implies Big O and Big Omega for the same function.
21:27 📈 Big-(Θ) notation defines a function f(n) as Θ(g(n)) if constants C1, C2, and n0 exist such that 0 ≤ C1g(n) ≤ f(n) and 0 ≤ f(n) ≤ C2g(n) for all n ≥ n0.
22:25 🧠 Report algorithm's runtime in big-(Θ), big-O, or big-(Ω) notation; big-(Θ) is preferred as it represents both upper and lower bounds.
24:19 📚 Comprehensive notes with clear graphs on big O, big Theta (Θ), and big Omega (Ω) help understanding and revision.
26:38 📝 Simplified mathematical definitions and graphical representations make understanding big O, big Theta (Θ), and big Omega (Ω) easier.
28:30 🎯 Always answer time complexity questions using big Theta (Θ) for a wider perspective; understand big O, big Theta (Θ), and big Omega (Ω) to stand out in interviews.
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