Big o notation python linear binary search code

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*understanding big o notation*

big o notation is a way to classify the efficiency of an algorithm. it describes how the running time or memory usage of an algorithm grows as the input size grows. it's a mathematical notation that focuses on the dominant term in the growth function, ignoring constant factors and lower-order terms.

*why is big o important?*

*algorithm selection:* it helps you choose the most efficient algorithm for a specific problem, especially when dealing with large datasets.
*performance prediction:* it provides a way to estimate how an algorithm's performance will change as the input size increases.
*code optimization:* identifying bottlenecks in your code based on their big o complexity allows you to focus optimization efforts where they'll have the greatest impact.
*communication:* it provides a standard, concise way to communicate the performance characteristics of algorithms.

*key concepts*

1. *input size (n):* represents the size of the input to the algorithm. for example, the number of elements in a list, the number of nodes in a graph, etc.

2. *operations count:* we count the number of basic operations the algorithm performs as a function of `n`. examples of basic operations include comparisons, assignments, arithmetic operations, etc.

3. *dominant term:* as `n` grows very large, some terms in the operations count function become far more important than others. the dominant term is the one that determines the overall growth rate.

4. *ignoring constants and lower-order terms:* big o focuses on the order of growth. constant factors (e.g., multiplying the operations count by 2) and lower-order terms (e.g., `n` compared to `n^2`) become insignificant as `n` approaches infinity.

*common big o notations*

here are some of the most common big o notations, ordered from most efficient to least ef ...

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