Data Structures for trees

• List baised binary trees
  • Let the root be stored at position 1.
  • leftChild(node n) is at positioni 2n
  • RightChild(n) is at position 2n+1
  • Parent(n) = int(n/2)
  • How would you do sibling?
  • Worst Case O(2^(n+1)/2) elements in the array
  • Best case O(n) elements in the array.
  • Access is O(1) for almost everything ( except iterators over elements)
• Pointer baised binary trees
  each node contains a pointer to a parent, a left child and a right child

  • struct nodeT{
        ElementT element
        nodeT * parent;
        nodeT * lchild;
        nodeT * rchild;
    };
    
    class TreeT{
        private:
           int size;
           nodeT * root;
    }
           

  • for the root node, the parent pointer is NULL
  • For leaf nodes, lchild and rchild are NULL
  • Binary Tree update functions
    • expandExternal(v) - adds two children to an external node
    • removeAboveExternal(v) - removes node w as well as w.parent, replaces w.parent with w.sibling
  • Pointer baised general trees
    • use a vector or list to hold the child pointers
  • Representing general trees with binary trees
    • Make the first child of a node the right tree
    • Make it's siblings the left child of the first child