Ten Core Algorithms: Sorting, Search, Graphs, Optimization, and Classification
Summary
This introductory overview explains ten general-purpose algorithms and problem-solving methods: quicksort, heapsort, merge sort, binary search, BFPRT selection, depth-first and breadth-first search, Dijkstra’s shortest paths, dynamic programming, and naive Bayes classification. It outlines the main steps or principles behind each, from partitioning and merging data to traversing graphs, reusing solutions to overlapping subproblems, and applying a conditional-independence assumption for classification.
The article gives selected complexity claims, including average-case performance for quicksort, logarithmic search for binary search, and worst-case linear selection for BFPRT. It also notes that Dijkstra’s method requires nonnegative edge weights and that dynamic programming suits problems with optimal substructure and repeated subproblems. This is a broad primer rather than a detailed implementation guide: it offers no code, benchmarks, or trading applications, and some descriptions are simplified. Readers applying the methods to quantitative research would need to adapt them to their data structures and specific computational constraints.
Key ideas
- Quicksort, heapsort, and merge sort organize data using partitioning, heaps, or merging, with different performance characteristics.
- Binary search repeatedly halves a sorted search range, while BFPRT selects an order statistic with a worst-case linear-time guarantee.
- Depth-first and breadth-first search traverse graphs using different exploration orders, and Dijkstra finds shortest paths when edge weights are nonnegative.
- Dynamic programming stores solutions to repeated subproblems when the problem has optimal substructure.
- Naive Bayes classification uses Bayes-based probability calculations with a simplifying assumption that features are independent.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.