Advanced Data Structures Library Skill

Purpose

Provide implementations and guidance for advanced data structures commonly needed in competitive programming and complex algorithmic problems.

Capabilities

• Treaps, Splay trees, Link-cut trees
• Persistent data structures
• Wavelet trees
• Heavy-light decomposition
• Centroid decomposition
• Rope data structure
• Order statistics tree

Target Processes

• data-structure-implementation
• advanced-graph-algorithms
• cp-library-creation

Data Structure Catalog

Balanced BSTs

• Treap (randomized BST)
• Splay Tree (self-adjusting)
• AVL Tree
• Red-Black Tree

Tree Decomposition

• Heavy-Light Decomposition
• Centroid Decomposition
• Euler Tour Technique

Advanced Structures

• Link-Cut Trees (dynamic trees)
• Wavelet Tree (range queries)
• Persistent Segment Tree
• Rope (string with fast operations)

Input Schema

{
  "type": "object",
  "properties": {
    "dataStructure": { "type": "string" },
    "operations": { "type": "array" },
    "language": {
      "type": "string",
      "enum": ["cpp", "python", "java"]
    },
    "includeTests": { "type": "boolean", "default": false }
  },
  "required": ["dataStructure"]
}

Output Schema

{
  "type": "object",
  "properties": {
    "success": { "type": "boolean" },
    "code": { "type": "string" },
    "complexity": { "type": "object" },
    "usage": { "type": "string" },
    "applications": { "type": "array" }
  },
  "required": ["success"]
}