15. Efficiency
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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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
- -- Efficiency of Algorithms
- A measure of how effectively an algorithm performs in terms of its time or space usage as the size of the input changes.
- -- Worst Case Efficiency
- The maximum time taken by an algorithm for the most difficult input of a specific size.
- -- Big O Notation
- A mathematical notation used to classify algorithms according to how their run time or space requirements grow as the input size grows.
- -- Average Case Efficiency
- An analysis based on a probabilistic approach to measure the efficiency of an algorithm for typical cases.
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