Optimization Common:

Eulerian DP greedy/bf Binary Search Branch & Bound RMQST Line sweep Sweep line

DP (Dynamic Programming):

General State representation(s) Diff sub-states calc? move to max? Cycles? Prob? Disjoint / BFS Extremum: inc-dec Types Interval / Range Counting Tree / Partitioning Extending table Knapsack Random order Search space? Standard-n pars Recurrence pars

Data Structures:

Set/Heap /Disjoint Sets BIT Segmentation Tree Treap, KDT LCA/RMQ Hashing Interval Compression Quad Tree

Mathematics:

GCD/LCM/Phi/Mob NIM/Grundy/Chinese Sieve/Factorization System of Linear Eqs Determinant Simpson's Rule Pick's Theo Numerical Integration Matrix Power Closed Form Pigeon Hole Triangle inequality Voronoi diagram

Graph Algorithms:

MST, Kruskal Dijkstra / Topological Johnson Hull / Floyd Max Flow/Min Cut Graph Matching Min Indep Set Min path-vertex cover Bellman / D-Costs Flow Postman

Adhoc Algorithms:

Greedy Line Sweep Sliding Window Canonical Form Grid Compression Constructive algos Test cases driven Randomization Stress Test & Observe

Search Algorithms:

BFS / DFS / Bi-BFS Backtracking Binary Search Golden Ratio Meet in middle Divide & Conquer Branch & Bound Min Enclosing Circle

String Algorithms:

Trie Permutation Cycles LIS / LCS Polynomial Hashing KMP / Aho Corasick suffix tree/array

Counting Problems:

DP Combinations / Perms Inclusion-Exclusion Graph Power

Decision Algorithms:

2SAT Difference constraints N Queens Bipartite?