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9 Trees

# 9 Trees - Tree Overview 2 Each cell may have zero or more...

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9/16/2010 1 TREES Lecture 9 CS2110 – Fall 2009 Tree Overview 2 Tree : recursive data structure (similar to list) Each cell may have zero or more successors (children) Each cell has exactly one predecessor (parent) except 5 4 7 8 9 2 5 4 7 8 2 the root , which has none All cells are reachable from root Binary tree : tree in which each cell can have at most two children: a left child and a right child General tree Binary tree 5 4 7 8 Not a tree 5 6 8 List-like tree Tree Terminology 3 M is the root of this tree G is the root of the left subtree of M B, H, J, N, and S are leaves N is the left child of P; S is the right child P is the parent of N M G W M and G are ancestors of D P, N, and S are descendants of W Node J is at depth 2 (i.e., depth = length of path from root = number of edges) Node W is at height 2 (i.e., height = length of longest path to a leaf) A collection of several trees is called a ...? P J D N H B S Class for Binary Tree Cells 4 class TreeCell<T> { private T datum ; private TreeCell<T> left , right ; public TreeCell(T x) { datum = x; } public TreeCell(T x, TreeCell<T> lft, TreeCell<T> rgt) { datum = x; left = lft; right = rgt; } more methods: getDatum, setDatum, getLeft, setLeft, getRight, setRight } ... new TreeCell <String> ("hello") ... Class for General Trees 5 class GTreeCell { private Object datum ; private GTreeCell left ; private GTreeCell sibling ; appropriate getter and 5 4 7 8 9 2 7 8 3 1 General tree setter methods } 5 4 7 8 9 2 7 8 3 1 Tree represented using GTreeCell Parent node points directly only to its leftmost child Leftmost child has pointer to next sibling, which points to next sibling, etc. Applications of Trees 6 Most languages (natural and computer) have a recursive, hierarchical structure This structure is implicit in ordinary textual representation Recursive structure can be made explicit by representing sentences in the language as trees: Abstract Syntax Trees (ASTs) ASTs are easier to optimize, generate code from, etc.

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