COMP 250 INTRODUCTION TO COMPUTER SCIENCE Week 13-1 : Maps Giulia Alberini, Fall 2020 Slides adapted from Michael Langer’s WHAT ARE WE GOING TO DO IN THIS VIDEO? Maps MAP (MATHEMATICS) “domain” A map is a set of pairs { (𝑥, 𝑓(𝑥)) }. “codomain” Each 𝑥 in domain maps to exactly one 𝑓(𝑥) in […]
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BST & AVL Juan Zhai juan.zhai@rutgers.edu Inorder traversal (left, root, right) 1. Traversetheleftsubtree 2. Visittheroot 3. Traversetherightsubtree 1, 3, 4, 6, 7, 8, 10, 13, 14 Inorder traversal prints all the keys in ascending order. Juan Zhai, juan.zhai@Rutgers.edu 2 Inorder traversal (left, root, right) public void inorder(Node root) { //check if bst is empty if(root
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COMP 250 INTRODUCTION TO COMPUTER SCIENCE Week 4-4 : OOD7 Polymorphism Giulia Alberini, Fall 2020 WHAT ARE WE GOING TO DO IN THIS VIDEO? OOD7 instanceof Intro to Polymorphism Abstract Classes and Methods A LITTLE ABOUT instanceof The instanceof operator is used to test whether an object is an instance of the
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COMP 250 INTRODUCTION TO COMPUTER SCIENCE Week 11-3 : Binary Trees Giulia Alberini, Fall 2020 Slides adapted from Michael Langer’s WHAT ARE WE GOING TO DO IN THIS VIDEO? Binary Trees Expression Trees BINARY TREES BINARY TREES Each node has at most 2 children! BINARY TREES Q: What is the maximum number of nodes 𝑛
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CS 112: Data Structures Sesh Venugopal Hash Table – Part 1 Until now, we have seen that the best worst-case time for searching in a set of n keys is O(log n), attributed to binary search of a sorted array and search in an AVL tree. But why stop there? Wouldn’t it be great if
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CS 112: Data Structures Sesh Venugopal Topological Sorting of Graphs Using DFS or BFS Precedence Graph A precedence graph is a Directed Acyclic Graph (DAG), i.e. a directed graph that does not have any cycles BBB AAA CCC acyclic has cycle has cycle An edge xày means that x precedes y. Precedence graphs are used
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CS 112: Data Structures Sesh Venugopal Quicksort Algorithm Divide and Conquer Mergesort and Quicksort both use what’s called a “divide and conquer” technique In Mergesort, the “divide” step is trivial – just divide the array in two halves. All the work is done in “combine”, where sorted subarrays are merged Sesh Venugopal CS 112: Quicksort
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CS 112: Data Structures Sesh Venugopal Dijkstra’s Shortest Path Algorithm for Graphs Shortest Path Numerous graph applications need to know what is the shortest path from point A to point B. If the graph does not have edge weights, this is not a hard problem to solve (think of using DFS or BFS) But when
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CS 112: Data Structures Sesh Venugopal Hash Table – Part 2 We started out with a quest to find a structure that would search in O(1) time in the worst case, but found that the worst case search time is actually O(n) We are going to keep at it, and find a way to get
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CS 112 : Data Structures Sesh Venugopal Huffman Coding: Tree Building, Encoding Text, Decoding Back to Text Building the Huffman Tree Sesh Venugopal CS 112: Huffman Coding 3 Input Symbols with Probabilities pfrsate 0.05 0.05 0.1 0.15 0.2 0.2 0.25 Input Symbols, with probabilities of occurrence in text (Pre-sorted IN INCREASING ORDER OF PROBABILITIES) Symbols
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