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# 10.6 Summary

### 1. Key Review

- Binary search relies on ordered data and searches by repeatedly halving the search interval. It requires the input data to be sorted and applies only to arrays or array-based data structures.
- Brute-force search locates data by traversing the data structure. Linear search applies to arrays and linked lists, while breadth-first search and depth-first search apply to graphs and trees. These algorithms are broadly applicable and require no data preprocessing, but their relatively high time complexity is \(O(n)\).
- Hash-based search, tree search, and binary search are efficient search methods that can quickly locate target elements in specific data structures. Such algorithms are highly efficient with time complexity reaching \(O(\log n)\) or even \(O(1)\), but typically require additional data structures.
- In practice, we need to analyze factors such as data scale, search performance requirements, and data query and update frequency to choose the appropriate search method.
- Linear search is suitable for small datasets or data that is updated frequently; binary search is suitable for large sorted datasets; hash-based search is suitable when high query efficiency is required and range queries are unnecessary; tree search is suitable for large dynamic datasets that must maintain order and support range queries.
- Replacing linear search with hash-based search is a commonly used strategy to optimize runtime, reducing time complexity from \(O(n)\) to \(O(1)\).

##### Feel free to drop your insights, questions or suggestions