In fact, they work so well that I think we are on track to see a fundamental shift in how software is built. There is one side of the hype around these technologies that I come across pretty often, which is that these technologies are bad for some $reason ('they are stochastic parrots', 'they create bullshit', 'they can't reason', 'they make up facts', 'they might replace junior developers, but they will not replace senior developers'), which, while technically true, is missing a much bigger point: if you are in the business of writing software, these things work. Int C ( int n, int k ) $, and the binomial coefficient is $0$.Heard about Large Language Models like ChatGPT4, Bing, GPT3? I'm sure you have.

The Stern-Brocot Tree and Farey Sequences Optimal schedule of jobs given their deadlines and durationsġ5 Puzzle Game: Existence Of The Solution MEX task (Minimal Excluded element in an array) Search the subsegment with the maximum/minimum sum RMQ task (Range Minimum Query - the smallest element in an interval) Kuhn's Algorithm - Maximum Bipartite Matching Maximum flow - Push-relabel algorithm improved Maximum flow - Ford-Fulkerson and Edmonds-Karp Lowest Common Ancestor - Tarjan's off-line algorithm Lowest Common Ancestor - Farach-Colton and Bender algorithm Second best Minimum Spanning Tree - Using Kruskal and Lowest Common AncestorĬhecking a graph for acyclicity and finding a cycle in O(M) Minimum Spanning Tree - Kruskal with Disjoint Set Union Number of paths of fixed length / Shortest paths of fixed length Strongly Connected Components and Condensation Graphĭijkstra - finding shortest paths from given vertexīellman-Ford - finding shortest paths with negative weightsįloyd-Warshall - finding all shortest paths

Half-plane intersection - S&I Algorithm in O(N log N)Ĭonnected components, bridges, articulations points Search for a pair of intersecting segmentsĭelaunay triangulation and Voronoi diagram Pick's Theorem - area of lattice polygons Straightforward calculation using analytical formulaīinomial coefficient modulo an arbitrary numberīinomial coefficient for large n and small moduloīurnside's lemma / Pólya enumeration theoremįinding the equation of a line for a segmentĬheck if points belong to the convex polygon in O(log N) Manacher's Algorithm - Finding all sub-palindromes in O(N) Euclidean algorithm for computing the greatest common divisorĭeleting from a data structure in O(T(n) log n)ĭynamic Programming on Broken Profile.

Mathematica dynamic programming