ACM is essential (only one after learning!

Time Complexity(Strict definition of time complexity, NP problem, and Time Complexity Analysis Method, Main Theorem)

 
SortAlgorithm(Application of the square sorting algorithm, shell sorting, fast sorting, Merge Sorting, lower time complexity, and three Linear Time Series External sorting)

 
Number Theory (Integer Division, set theory, relation, prime number, carry-in system, moving and division, extended moving and Division, Same-remainder operation, solving linear same-remainder equations, Chinese Remainder Theorem)

Pointer(Chain table, search weighting, adjacent table, hash, binary tree, multi-Tree Representation)

Bitwise operation(And, Or, XOR, SHL, SHR, and some applications)

Graph Theory (Graph Theory Model Creation, Plan, Euler's formula andFive Color Theorem, PleaseStrongly Connected Component, Seek cut points and bridges,Euler Loop, AOV problem, AOE problem,Three algorithms of the Minimum Spanning Tree,Three short-circuit Algorithms, Label method, difference constraint system, verification bipartite graph, Konig theorem,Hungary Algorithm, KM algorithm, stable marriage system,Max stream algorithm, max flow theorem for least cut, Maximum flow algorithm with minimum cost)

Computational ry (number of plane solutions and their applications,Vector, dot product and its application, cross product and Its Application, Semi-plane intersection, finding the convex hull of a point set, the closest point to the problem, the intersection of a convex polygon,Discretization and Scanning)

Data structure (Extended search, Verify the matching of parentheses, expression calculation, recursive compilation,Hash table, Segment hash,Query set,Tarjan Algorithm,Binary heap, Left-side tree, two-way oblique heap, two-way heap,Binary Search Tree, Red/black tree, aVL Balance Tree, treap,Splay, Static Binary Search Tree, 2-D tree,Line Segment tree, Two-dimensional line segment tree, rectangular tree, trie tree, block chain table)

Combined Mathematics (Arrangement and combination, pigeon cage principle, rejection principle, recurrence, Fibonacci series, Catalan series, and Stirling Number, Differential sequence, generation function, replacement, polyA principle)

Probability Theory (simple probability, conditional probability, Bayes Theorem, expected value)

Matrix (Concepts and operations of the matrix, two-part linear recursive equation, Domino board cover number of solutions, Gaussian elimination element)

String processing (KMP, Suffix tree, finite state automation, Huffman encoding, simple cryptography)

Dynamic Planning (monotonous queue, completely convex monotonic, tree-type Dynamic Planning, multi-fork to binary forks, State compression dynamic planning, quadrilateral inequality)

Game Theory (NIM sub-game, game tree, Shannon switch game)

Search (A *, ID, Ida *, Random adjustment, genetic algorithm)

Preliminary calculus (ultimate thinking, derivative, integral, definite integral, three-dimensional analytic ry)