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Efficiency of algorithms is evaluated based on their performance as input size varies. The worst-case scenario is typically used to measure efficiency, while average-case analysis, though useful, is more complex to determine. The concept of big O notation provides a shorthand to express this efficiency by indicating how the time complexity grows with input size. Understanding the limits of computation based on algorithm efficiency is crucial for problem-solving in programming and data analysis.
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Chapter 15.pdfClass Notes
Memorization
What we have learnt
- The efficiency of algorithm...
- Big O notation is a concise...
- The capacity of algorithms ...
Final Test
Revision Tests
What we have learnt
- The efficiency of algorithms is often measured in terms of worst-case scenarios.
- Big O notation is a concise way to express the time complexity of algorithms.
- The capacity of algorithms to handle large inputs varies significantly based on their time complexity.
Key Concepts
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Term: Efficiency of Algorithms
Definition: A measure of how effectively an algorithm performs in terms of its time or space usage as the size of the input changes.
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Term: Worst Case Efficiency
Definition: The maximum time taken by an algorithm for the most difficult input of a specific size.
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Term: Big O Notation
Definition: A mathematical notation used to classify algorithms according to how their run time or space requirements grow as the input size grows.
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Term: Average Case Efficiency
Definition: An analysis based on a probabilistic approach to measure the efficiency of an algorithm for typical cases.