Todays announcements: MT1 Oct 10, 19:00-21:00 CIRS 1250 Todays Plan - - PowerPoint PPT Presentation

Today’s announcements:

◮ MT1 Oct 10, 19:00-21:00 CIRS 1250

Today’s Plan

◮ Binary Search Trees

Warm up: Level (Depth) order

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void levelOrder( ) { If( root == NULL) return; }}

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Binary Search Trees

Dictionary ADT

Operations

◮ insert ◮ remove ◮ find

key value (data) Multics MULTiplexed Information and Computing Service Unix Uniplexed Multics BSD Berkeley Software Distribution GNU GNU’s Not Unix

◮ insert(Linux, Linus Torvald’s Unix) ◮ find(Unix) returns “Uniplexed Multics”

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Dictionary ADT Implementations

Worst Case time insert find remove (after find) Linked list Unsorted array Sorted array

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Binary Search in a Sorted Array

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int bSearch(int A[], int key, int i, int j) { if (j < i) return -1; int m = (i + j) / 2; if (key < A[m]) return bSearch(A, key, i, m-1); else if (key > A[m]) return bSearch(A, key, m+1, j); else return m; }

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Binary Search Tree as Dictionary Data Structure

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Kai Kuro Shiro Mei Koko Fuku Mikan Sakura Rin Hime Kinako Maru

Binary tree property

◮ each node has ≤ 2 children

Search tree property

For all nodes x,

◮ all keys in left subtree of x smaller than x’s key ◮ all keys in right subtree of x larger than x’s key

Result: easy to find any given key

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Dictionary ADT: BST implementation

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Chiro Shiro Kuro Kai Tora Hime Rin Minto Fuku

template<class K, class D> class Dictionary{ public: //ctors etc. ... private: struct Node { K key; D data; Node * left; Node * right; }; Node * root; ... };

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Finding a Node

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Chiro Shiro Kuro Kai Tora Hime Rin Minto Fuku

Node *& pfind(K & key, Node *& r) { if (r == NULL) return r; if (key < r->key) return pfind(key, r->left); if (key > r->key) return pfind(key, r->right); return r; } Runtime?

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Insert

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Chiro Shiro Kuro Kai Tora Hime Rin Minto Fuku

void pinsert(K & key, D & data, Node *& root) { Node *& target = pfind(key, root); if( target != NULL) { cerr<<"Duplicate:"<<key<<"\n"; } target = new Node(key, data); } One reason to have the *& version of pfind.

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