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Algorithm Complexity Analysis PART I - Big O
- Big O notation is a key concept in Algorithm Complexity Analysis, focusing on time and space complexity in relation to input size.
- Asymptotic notation is crucial for consistent evaluation of algorithm efficiency with large inputs, using Big O, Omega, and Theta notations.
- Time complexity measures algorithm efficiency concerning the input size, categorized into O(1), O(n), and O(n^2) based on operation scaling.
- Space complexity evaluates memory usage efficiency relative to input size, distinguishing between Auxiliary Space and Space Complexity.
- Recursive algorithms like Fibonacci demonstrate time complexity of O(2^n) and space complexity of O(n) due to call stack growth.
- Key principles of Big O include considering worst-case scenarios, dropping constants, handling different inputs, and focusing on dominant terms.
- Trade-offs between space and time complexity are common, with Big O aiding in comparing algorithm efficiency based on Asymptotic Analysis.
- Pros of Big O include facilitating algorithm comparison, aiding in trade-off understanding, and providing a theoretical, generalizable framework.
- Cons of Big O include potential misuse, focusing on worst cases only, ignoring constants, and the need for considering other complexity analysis notations.
- References are provided for further exploration of Algorithm Complexity Analysis, Big O rules, and theoretical foundations.
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