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Tree Fundamentals

Essential concepts and operations for working with tree data structures.

Tree terminology & properties​

  • Node: Individual element in tree with data and references to children
  • Root: Top node with no parent
  • Leaf: Node with no children
  • Height: Length of longest path from root to leaf
  • Depth: Length of path from root to specific node
  • Subtree: Tree formed by node and all its descendants

Tree traversal (pre, in, post, level)​

  • Pre-order: Process root, then left subtree, then right subtree
  • In-order: Process left subtree, then root, then right subtree
  • Post-order: Process left subtree, then right subtree, then root
  • Level-order: Process nodes level by level (BFS)

Tree construction & validation​

  • Construction: Building tree from array, string, or other representation
  • Validation: Checking if tree satisfies certain properties
  • Balanced Trees: Ensuring tree height is logarithmic
  • Complete Trees: Trees where all levels are filled except possibly last

Tree height & depth​

  • Height Calculation: Recursive approach to find maximum depth
  • Depth Calculation: Distance from root to specific node
  • Balanced Height: Ensuring height difference between subtrees is minimal
  • Height-based Operations: Using height for tree balancing and optimization

Tree serialization​

  • Serialization: Converting tree to string or array representation
  • Deserialization: Reconstructing tree from serialized format
  • Format Choices: Pre-order, level-order, or custom formats
  • Handling Nulls: Representing missing nodes in serialized form