Review session2

Data Structures Review Session 2 Ramakrishna, PhD student. Grading Assistant for this course

Binary Search Trees ,[object Object],[object Object],[object Object],parent left child right child root 17 11 19

Problems ,[object Object],[object Object],[object Object],[object Object]

Binary Search Tree properties ,[object Object],[object Object],[object Object],[object Object],[object Object]

Balance of Binary Trees ,[object Object],[object Object],[object Object]

Sorting Using BST ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example Sorting Using BST ,[object Object],[object Object],2 1 3 4 8 6 5 7 2.4 2.5

Example Sorting Using BST (cont.) ,[object Object],[object Object],2 1 3 4 8 6 5 7 2.4 2.5 2 1

Example Sorting Using BST (cont.) ,[object Object],[object Object],2 1 3 4 8 6 5 7 2.4 2.5 2 1 2.4 2.5 3

Example Sorting Using BST (cont.) ,[object Object],[object Object],2 1 3 4 8 6 5 7 2.4 2.5 2 1 2.4 2.5 3 4 5 6 7 8 Sorted Array

Worst cases ,[object Object],[object Object],[object Object],2 3 10 8 2 3 4 8

Finding Min & Max ,[object Object],[object Object],[object Object],[object Object],Q: How long do they take? ,[object Object],[object Object],[object Object]

Algorithm LCA (Node v, Node w): ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Note that LCA algorithm is applicable for any tree

[object Object],[object Object]

Algorithm buildExpressionTree (E): ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Algorithm PostFix (E): ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Representing Graphs ,[object Object],[object Object],[object Object]

Graphs: Adjacency Matrix ,[object Object],1 2 4 3 a d b c How much storage does the adjacency matrix require? A: O(V 2 ) 0 1 0 0 4 0 0 0 0 3 0 1 0 0 2 0 1 1 0 1 4 3 2 1 A

Graphs: Adjacency List ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],1 2 4 3 ,[object Object]

Graph Problems ,[object Object]

Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Solution ,[object Object],[object Object],[object Object],[object Object],[object Object]

Predecessor and Successor in a BST ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Pseudo-code for Successor ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Code for predecessor is symmetric. Running time: O ( h ) 56 26 200 18 28 190 213 12 24 27

Properties of Binary Trees ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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