算法工程师应当了解哪些算法？标准很乱啊

Here is a more strictly categorized list of algorithms, with brief explanations for each category:

1. Sorting Algorithms

• Quick Sort: Efficient sorting by partitioning arrays around a pivot.
• Merge Sort: Divide-and-conquer sorting that merges sorted subarrays.
• Heap Sort: Uses a binary heap to repeatedly extract the maximum element.

2. Search Algorithms

• Binary Search: Efficiently finds an item in a sorted list by dividing the search space.
• Depth-First Search (DFS): Explores as far as possible along each branch before backtracking.
• Breadth-First Search (BFS): Explores all neighbors at the present depth before moving on to the next depth level.

3. Dynamic Programming Algorithms

• Knapsack Problem: Optimizes item selection to maximize value without exceeding weight.
• Longest Common Subsequence (LCS): Finds the longest subsequence common to two sequences.
• Fibonacci Sequence: Calculates Fibonacci numbers efficiently using dynamic programming.

4. Graph Algorithms

• Dijkstra’s Algorithm: Finds shortest paths in weighted graphs.
• Bellman-Ford Algorithm: Computes shortest paths accommodating negative weights.
• Kruskal’s Algorithm: Finds a minimum spanning tree by adding the smallest edges.

5. Greedy Algorithms

• Huffman Coding: Compresses data by creating a prefix-free binary tree.
• Prim’s Algorithm: Builds a minimum spanning tree by adding the nearest vertex.
• Activity Selection: Selects the maximum number of non-overlapping activities.

6. Divide and Conquer Algorithms

• Merge Sort: Recursively divides and merges arrays.
• Quick Sort: Recursively partitions arrays around a pivot.
• Strassen’s Algorithm: Efficiently multiplies large matrices.

7. Backtracking Algorithms

• N-Queens Problem: Places N queens on an NxN board without conflicts.
• Sudoku Solver: Fills Sudoku grids by ensuring no conflicts arise.
• Hamiltonian Path: Finds a path visiting each vertex exactly once.

8. Machine Learning Algorithms

• Linear Regression: Models the relationship between variables.
• Decision Trees: Tree-like models for classification and regression.
• K-Means Clustering: Partitions data into k clusters by minimizing variance.

9. String Algorithms

• KMP Algorithm: Efficient string searching by using pattern information.
• Rabin-Karp Algorithm: Searches for patterns using hashing.
• Longest Palindromic Substring: Finds the longest palindromic substring.

10. Computational Geometry Algorithms

• Convex Hull: Finds the smallest convex polygon containing all points.
• Line Intersection: Detects intersections between line segments.
• Voronoi Diagram: Partitions space based on distance to a set of points.

11. Mathematical Algorithms

• Euclidean Algorithm: Finds the greatest common divisor (GCD) of two numbers.
• Sieve of Eratosthenes: Finds all prime numbers up to a specified integer.
• Fast Fourier Transform (FFT): Computes the discrete Fourier transform and its inverse.

12. Cryptographic Algorithms

• RSA Algorithm: Public key encryption and decryption.
• AES Algorithm: Symmetric encryption for secure data transmission.
• SHA-256 Algorithm: Hashing algorithm for data integrity and security.

13. Optimization Algorithms

• Gradient Descent: Optimizes functions by iteratively moving towards the steepest descent.
• Simulated Annealing: Probabilistically optimizes to avoid local minima.
• Genetic Algorithm: Uses natural selection principles to find optimal solutions.

14. Numerical Algorithms

• Newton-Raphson Method: Finds successively better approximations to the roots of a real-valued function.
• Gauss-Seidel Method: Iteratively solves linear systems of equations.
• Runge-Kutta Methods: Solves ordinary differential equations (ODEs).

15. Data Structure Algorithms

• Union-Find: Efficiently manages a partition of a set into disjoint subsets.
• AVL Tree: Self-balancing binary search tree.
• Hashing: Maps data to fixed-size values for efficient lookup.

This structured categorization covers a broad spectrum of algorithms, ensuring familiarity with diverse problem-solving techniques in algorithm engineering.