Plan and main algorithms

Thank, DeepSeek

Sure! Competitive programming is a separate field where it's not only important to know how to write code but also to understand key algorithms and data structures that are frequently used in competitions. Here's a list of essential algorithms and topics you need to learn to perform well in serious programming contests:

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1. Basic Algorithms and Data Structures

• Sorting:
  • Quick Sort
  • Merge Sort
  • Counting Sort
  • Radix Sort
• Binary Search:
  • Searching in a sorted array
  • Binary search on the answer
• Two Pointers:
  • Solving problems related to subarrays, pairs, etc.
• Prefix Sums:
  • Fast computation of sums on subarrays.
• Stack, Queue, Deque:
  • Implementation and applications in problems.
• Hashing:
  • Hash tables, polynomial hashes for strings.

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2. Graphs

• Graph Representation:
  • Adjacency lists, adjacency matrix.
• Graph Traversal:
  • Depth-First Search (DFS)
  • Breadth-First Search (BFS)
• Connected Components:
  • Finding connected components in undirected graphs.
• Topological Sorting:
  • For Directed Acyclic Graphs (DAG).
• Shortest Paths:
  • Dijkstra's Algorithm
  • Bellman-Ford Algorithm
  • Floyd-Warshall Algorithm
• Minimum Spanning Tree (MST):
  • Kruskal's Algorithm
  • Prim's Algorithm
• Cycle Detection:
  • In directed and undirected graphs.
• Bridges and Articulation Points:
  • Tarjan's Algorithm.

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3. Dynamic Programming (DP)

• Basics of DP:
  • Knapsack Problem
  • Longest Increasing Subsequence (LIS)
• DP on Subarrays:
  • Problems related to substrings, subarrays.
• DP on Trees:
  • Problems involving counting paths, subtrees.
• DP with Bitmasks:
  • Problems involving subset enumeration.
• DP Optimizations:
  • Divide and Conquer, Convex Hull Trick.

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4. Trees

• Binary Trees:
  • Search, insert, delete operations.
• Segment Tree:
  • Range minimum/maximum queries, range sum queries.
• Fenwick Tree (Binary Indexed Tree):
  • Fast updates and prefix queries.
• Search Trees (BST, AVL, Splay):
  • Tree balancing.
• Lowest Common Ancestor (LCA):
  • Binary Lifting Algorithm.

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5. Strings

• Prefix Function and Z-Function:
  • Substring search.
• Knuth-Morris-Pratt Algorithm (KMP):
  • Substring search.
• Aho-Corasick Algorithm:
  • Multiple substring search.
• Suffix Array:
  • Construction and applications.
• String Hashing:
  • Polynomial hashes for substring comparison.

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6. Mathematics

• Number Theory:
  • Greatest Common Divisor (GCD), Euclidean Algorithm.
  • Sieve of Eratosthenes for prime numbers.
  • Integer factorization.
• Combinatorics:
  • Binomial coefficients, combinations.
• Fast Exponentiation:
  • Fast modular exponentiation.
• Chinese Remainder Theorem:
  • Solving systems of congruences.
• Linear Algebra:
  • Matrix multiplication, fast matrix exponentiation.

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7. Geometry

• Points, Vectors, Lines:
  • Dot product, cross product.
• Segment Intersection:
  • Algorithm for checking intersection.
• Convex Hull:
  • Andrew's monotone chain algorithm.
• Triangulation:
  • Decomposing polygons into triangles.

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8. Advanced Topics

• Network Flow:
  • Ford-Fulkerson Algorithm.
  • Edmonds-Karp Algorithm.
• Matchings:
  • Hungarian Algorithm.
• Segment Tree with Lazy Propagation:
  • Lazy updates in segment trees.
• Persistent Data Structures:
  • Persistent Segment Tree.
• Square Root Decomposition:
  • SQRT decomposition, Mo's Algorithm.

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9. Useful Skills

• Bit Manipulation:
  • Bitmasks, bitwise operations.
• Greedy Algorithms:
  • Solving problems using greedy strategies.
• Divide and Conquer:
  • Solving problems by breaking them into subproblems.
• Two Pointers Technique:
  • Solving problems involving subarrays, pairs, etc.

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10. Practice

• Platforms for Practice:
  • Codeforces (regular contests, problems of varying difficulty).
  • AtCoder (Japanese contests, problems on DP and graphs).
  • LeetCode (algorithm and data structure problems).
  • Timus Online Judge (Russian-language problems).
  • CSES Problem Set (great collection for beginners and advanced programmers).

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How to Learn:

1. Start with basic algorithms (sorting, binary search, prefix sums).
2. Solve problems on graphs and dynamic programming — these are the most common topics in competitions.
3. Learn advanced data structures (segment trees, Fenwick trees, suffix arrays).
4. Regularly participate in contests (Codeforces, AtCoder).

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Example Learning Plan:

1. Week 1-2: Basic algorithms (sorting, binary search, two pointers).
2. Week 3-4: Graphs (DFS, BFS, shortest paths).
3. Week 5-6: Dynamic programming (knapsack, LIS, problems on subarrays).
4. Week 7-8: Trees (segment trees, Fenwick trees, LCA).
5. Week 9-10: Strings (KMP, Z-function, hashing).

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If you'd like, I can explain any specific algorithm or topic in more detail! 😊