Data Structure Tree

1. Tree

1.1 Basic idea

Tree is an abstract model of hierarchical structure

• A tree is composed of nodes in a parent-child relationship

  • Often change time from space
  • Depends on the sorting of elements, which means the sorting of memory blocks

• Tree term

  • Root: no parent node
  • Internal node: A node with at least one child node
  • External node: no child nodes
  • Ancestor of node: parents, grandparents, etc.
  • Descendant of a node: child, grandson, great-grandson, etc.
  • Depth of a node: The number of ancestor heights of the tree: the maximum depth of any node
  • Height: the maximum depth of any node
  • Sibling: brothers and sisters
  • Subtree: The tree is composed of nodes and descendants
  • Edge of tree: a pair of nodes (u, v), u is the parent node of v
  • Path: A sequence of node ST, from any two consecutive nodes on the edge

• Tree ADT

  • Binary tree data can be realized by storing one node plus two sub-pointers
  • Trees with more than two children can be implemented using a list of nodes in a linked list

• Traverse pre

• Post-order traversal: the node is visited after its descendants

• Sequential traversal: visit the node inorder before the left subtree and the right subtree

1.2 Binary tree

1.3 Binary search tree