Algorithms that programmers need to master include but are not limited to:
1. Sorting algorithms: including bubble sort, selection sort, insertion sort, quick sort, merge sort, etc.
2. Search algorithms: including linear search, binary search, hash search, tree search, etc.
3. Graph algorithms: including shortest path algorithm, minimum spanning tree algorithm, topological sorting, etc.
4. Dynamic programming algorithm: including knapsack problem, longest common subsequence, longest rising subsequence, etc.
5. String matching algorithms: including naive matching, KMP algorithm, Boyer-Moore algorithm, etc.
6. Mathematical algorithms: including Euclidean algorithm, prime number related algorithms, prime factorization, and fast idempotence.
7. Computational geometry algorithms: including calculation problems related to points, lines, and surfaces.
These algorithms are the basic knowledge that programmers need to master when writing efficient programs and solving complex problems. At the same time, mastering algorithms can improve programmers' programming thinking skills and problem-solving abilities.