20-binary-search-tree - CSE 143 Lecture 20 Binary Search...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
CSE 143 Lecture 20 Binary Search Trees read 17.3 slides created by Marty Stepp http://www.cs.washington.edu/143/
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 Binary search trees binary search tree ("BST"): a binary tree that is either: – empty ( null ), or – a root node R such that: • every element of R's left subtree contains data "less than" R's data, • every element of R's right subtree contains data "greater than" R's, • R's left and right subtrees are also binary search trees. • BSTs store their elements in sorted order, which is helpful for searching/sorting tasks. 91 60 87 29 55 42 -3 overall root
Background image of page 2
3 Exercise • Which of the trees shown are legal binary search trees? x k q g m e b 18 10 11 5 8 4 2 7 20 18 42 -7 -1 -5 21.3 8.1 9.6 1.9 7.2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Searching a BST • Describe an algorithm for searching the tree below for the value 31. • Then search for the value 6. • What is the maximum number of nodes you would need to examine to perform any search? 12 18 7 4 15 overall root -2 16 13 35 31 22 58 19 87 40
Background image of page 4
5 Exercise • Convert the IntTree class into a SearchTree class. – The elements of the tree will constitute a legal binary search tree. • Add a method contains to the SearchTree class that searches the tree for a given integer, returning true if found. – If a SearchTree variable tree referred to the tree below, the following calls would have these results: •tree.contains(29) true •tree.contains(55) true •tree.contains(63) false •tree.contains(35) false 91 60 87 29 55 42 -3 overall root
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6 Exercise solution // Returns whether this tree contains the given integer. public boolean contains(int value) { return contains(overallRoot, value); } private boolean contains(IntTreeNode node, int value) { if (node == null) { return false; } else if (node.data == value) { return true; } else if (node.data > value) { return contains(node.left, value); } else { // root.data < value return contains(node.right, value); } }
Background image of page 6
7 Adding to a BST • Suppose we want to add the value 14 to the BST below. – Where should the new node be added?
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 23

20-binary-search-tree - CSE 143 Lecture 20 Binary Search...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online