# Competitive programming topics

###### tags: `Competitive programming`

# Problem theme list and tags
- Basic
+ Calculation
+ Conditionals
+ Loops
+ for
+ while
+ else, break, continue
+ Strings
+ Arrays/Lists
+ 2D arrays
+ Functions
+ Recursive functions
- Number theory & maths
+ Number systems
+ Binary, Octal, Decimal, Hexadecimal
+ Bitwise operations
+ Prime & composite numbers
+ Primality tests
+ Prime generation techniques
+ GCD, LCM
+ Integer Factorization
+ Count, sum, product of divisors
- Modulus arithmetic
+ Modular Inverse
+ Modulus arithmetic, basic postulates (Including modular linear equations, Continued fraction and Pell's equation)
+ Fermat's theorem
+ Euler’s Totient theorem (totient function, order, primitive roots )
+ Chinese remainder theorem
+ Wilson theorem: nCr % p in O(p) preprocess and O(log n ) query
+ Lucas Theorem
- Math
+ Set theory
+ Inclusion-exclusion
+ Fibonacci
+ Catalan
+ Big number operations
+ Logarithmic Exponentiation
+ Josephus problem
+ Sequences
+ Polynomials
+ Matrix
+ Probability
+ Counting
+ Combination
+ Permutation
+ Permutation cycles
+ Bài toán chia kẹo của Euler
+ Burnside's lemma
+ Cayley's formula
- Computational geometry
+ Area of triangles
+ Area of polygons
+ Convex and concave polygons
+ Point inside, outside polygons
+ Center of mass
+ Overlapping rectangles
+ Line intersection
+ Circle intersection
+ Angles
+ Distances
+ Transformations:
+ Translation (Slide)
+ Reflection (Flip)
+ Rotation (Turn)
+ Enlargement (Dilation)
+ Dot product
+ Cross product
+ Convex hull
+ Sweep Line
- String
+ String manipulation
+ Search in strings
+ String prefix
+ Trie structure
+ Z-algorithm
- Prefix sum
- Data structures
+ Array/List/Vector
+ Stack/Queue
+ Linked list
+ Double linked list
+ 2D arrays, Multi-dimensional arrays
+ Map/dict
+ Set
+ Heap & priority queue
+ Hash Tables
- Searching
+ Backtracking
+ Binary Search
+ Ternary Search
+ Meet in the middle
- Greedy
- Sorting
+ Simple sorting
+ Quick sort
+ Merge sort
+ O(n) sort (distribution counting)
- Recursive
+ Recursive
+ Recursive with caching
+ Divide and Conquer
- Dynamic programming
+ 1-D DP
+ 1-D DP with tracing
+ 2-D DP
+ 2-D DP with tracing
+ 3-D DP
+ Interval DP
+ Tree DP
+ Subset DP
- Backtracking
+ Brute force
+ Backtracking with greedy paradigm
+ Backtracking with pruning
- Ad-hoc
- Suffix Array
- Graph Search
+ BFS
+ DFS
- Graph connectivity, strongly connected components
- Eulerian Graph
- Hamiltonian Graph
- Binary tree traversal
- Reverse Polish notation: RPN
- Binary search tree: BST
- Shortest Path in a weighted Graph
- Minimum Spanning Tree
- Maximal Flow
- Maximal matching in a bipartite graph
- Game theory
- Amortized analysis
+ Two pointers
+ Sliding window
- Range queries
+ Range minimum Query(RMQ)
+ Fenwick tree (binary indexed tree)
+ Segment tree / Interval tree
- AVL Trees