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Randomized Algorithms: Reservoir Sampling and Quickselect
Master randomized DSA algorithms: reservoir sampling for streams, quickselect for O(n) kth element, and random shuffling.
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Game Theory: Nim, Grundy Numbers, and Sprague-Grundy
Master combinatorial game theory: Nim XOR strategy, Grundy (nimber) values, and Sprague-Grundy theorem for composite games.
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Computational Geometry: Points, Lines, and Convex Hull
Tackle geometry problems in coding interviews: cross product, point-in-polygon, line intersection, and Graham scan convex hull.
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Probability and Expected Value in Competitive Programming
Apply probability theory and expected value DP to competitive programming: dice problems, random walks, and geometric distribution.
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Integer Overflow, Precision, and Safe Arithmetic
Prevent integer overflow in competitive programming: safe multiplication, __int128, binary search on answers, and floating-point gotchas.
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