Kurikulum Competitive Programming

Berikut adalah daftar lengkap algoritma dan struktur data yang harus dikuasai untuk Olimpiade Komputer, diurutkan berdasarkan tingkat kesulitan dan prioritas:

Level 1: Fundamental (Pemula)

1. Kompleksitas Algoritma

• Big O Notation
• Analisis waktu dan ruang

2. Struktur Data Dasar

• Array dan String
• Stack dan Queue
• Linked List
• Hash Table / Hash Map

3. Algoritma Dasar

• Linear Search dan Binary Search
• Sorting: Bubble, Selection, Insertion, Merge, Quick Sort
• Two Pointers Technique
• Sliding Window

4. Matematika Dasar

• Bilangan Prima (Sieve of Eratosthenes)
• GCD dan LCM (Euclidean Algorithm)
• Modular Arithmetic
• Fast Power (Exponentiation by Squaring)

Level 2: Intermediate (Menengah)

5. Rekursi dan Backtracking

• Pemahaman rekursi mendalam
• Backtracking untuk permutasi, kombinasi
• N-Queens Problem
• Sudoku Solver

6. Dynamic Programming (DP)

• Fibonacci, Coin Change
• Knapsack Problem (0/1 dan Unbounded)
• Longest Common Subsequence (LCS)
• Longest Increasing Subsequence (LIS)
• Edit Distance
• Matrix Chain Multiplication
• DP on Trees
• Digit DP
• Bitmask DP

7. Graph – Dasar

• Representasi Graph (Adjacency List/Matrix)
• DFS (Depth-First Search)
• BFS (Breadth-First Search)
• Cycle Detection
• Topological Sort
• Connected Components

8. Graph – Shortest Path

• Dijkstra’s Algorithm
• Bellman-Ford Algorithm
• Floyd-Warshall Algorithm
• 0-1 BFS

9. Greedy Algorithms

• Activity Selection
• Fractional Knapsack
• Huffman Coding
• Job Sequencing

10. Divide and Conquer

• Merge Sort, Quick Sort
• Binary Search variants
• Closest Pair of Points

Level 3: Advanced (Lanjutan)

11. Tree Algorithms

• Binary Tree Traversal
• Binary Search Tree (BST)
• AVL Tree dan Red-Black Tree
• Segment Tree
• Fenwick Tree (Binary Indexed Tree)
• Lowest Common Ancestor (LCA)
• Heavy-Light Decomposition

12. Graph – Advanced

• Minimum Spanning Tree (Kruskal, Prim)
• Strongly Connected Components (Kosaraju, Tarjan)
• Articulation Points dan Bridges
• Bipartite Matching
• Maximum Flow (Ford-Fulkerson, Edmonds-Karp)
• Min-Cut Max-Flow Theorem

13. String Algorithms

• KMP (Knuth-Morris-Pratt)
• Rabin-Karp Algorithm
• Z-Algorithm
• Trie (Prefix Tree)
• Suffix Array dan Suffix Tree
• Aho-Corasick Algorithm
• Manacher’s Algorithm (Longest Palindrome)

14. Advanced Data Structures

• Disjoint Set Union (DSU / Union-Find)
• Sparse Table
• Square Root Decomposition
• Persistent Data Structures

Level 4: Expert (Mahir)

15. Advanced DP

• DP Optimization (Convex Hull Trick, Divide and Conquer Optimization)
• SOS DP (Sum over Subsets)
• DP on DAG
• Profile DP

16. Computational Geometry

• Convex Hull (Graham Scan, Jarvis March)
• Line Intersection
• Point in Polygon
• Sweep Line Algorithm
• Closest Pair of Points

17. Number Theory

• Prime Factorization
• Euler’s Totient Function
• Chinese Remainder Theorem
• Modular Inverse
• Matrix Exponentiation

18. Game Theory

• Nim Game
• Grundy Numbers (Sprague-Grundy Theorem)
• Minimax Algorithm
• Alpha-Beta Pruning

19. Advanced Graph

• Network Flow variants
• Min Cost Max Flow
• Hungarian Algorithm
• 2-SAT Problem
• Centroid Decomposition

20. Advanced Techniques

• Meet in the Middle
• Binary Lifting
• Mo’s Algorithm
• Parallel Binary Search
• FFT (Fast Fourier Transform) untuk polinomial

Keterampilan Tambahan Penting

Problem Solving Skills:

• Pattern recognition
• Breaking down complex problems
• Optimization thinking

Implementation Skills:

• Clean dan efficient code
• Debugging cepat
• Template management

Contest Strategy:

• Time management
• Problem selection
• Partial points strategy

Rekomendasi Urutan Belajar

Untuk persiapan Olimpiade yang sistematis, saya sarankan:

1. 3-6 bulan pertama: Fokus pada Level 1 dan mulai Level 2
2. 6-12 bulan: Kuasai Level 2, terutama DP dan Graph dasar
3. 12-18 bulan: Level 3, fokus pada Tree dan String algorithms
4. 18+ bulan: Level 4 dan spesialisasi pada area tertentu

Platform Latihan yang Direkomendasikan:

• Codeforces
• AtCoder
• CSES Problem Set
• LeetCode
• HackerRank
• USACO Training