A5Data structures & algorithms

Data structures and algorithms are what make any of the math actually run within finite time and memory. A correct model that is too slow to train or serve is useless, so this discipline gives you the toolkit for choosing representations and procedures that scale, and the analysis to know in advance which ones will.

You will begin with asymptotic complexity and amortized analysis, then build the core structures (dynamic arrays and hash maps, linked lists, stacks and queues, balanced search trees, and heaps) and the sorting algorithms that hit the n log n bound. From there come the algorithm-design paradigms: divide and conquer with the master theorem, dynamic programming, and greedy methods with the exchange argument. The discipline then covers graphs (representations, BFS and DFS, Dijkstra's shortest paths, and minimum spanning trees) and finishes with probabilistic structures, Bloom filters and HyperLogLog, that trade exactness for huge space savings.

These skills are the difference between a pipeline that finishes and one that stalls. Graph algorithms feed directly into the graph neural networks of pillar D, and the probabilistic sketches and nearest-neighbor thinking here reappear across retrieval, feature stores, and large-scale systems.