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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COMP 250 INTRODUCTION TO COMPUTER SCIENCE Week 12-2 : Heaps Giulia Alberini, Fall 2020 Slides adapted from Michael Langer’s WHAT ARE WE GOING TO DO IN THIS VIDEO? Heaps HEAPS PRIORITY QUEUE Assume a set of comparable elements or “keys”. Like a queue, but now we have a more general definition of which element
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COMP 250 INTRODUCTION TO COMPUTER SCIENCE Week 9-1 : Induction Giulia Alberini, Fall 2020 WHAT ARE WE GOING TO DO IN THIS VIDEO? Inductive/Recursive definitions Inductive/Recursive proofs Mathematical Induction INDUCTION PROOFS For all 𝑛 ≥ 1, 1+2+3+ ….+ 𝑛−1 +𝑛= 𝑛 𝑛+1 2 How can we prove such a statement ? By “proof”, we mean
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COMP 250 INTRODUCTION TO COMPUTER SCIENCE Week 9-3 : Recursion 2 (Binary Search) Giulia Alberini, Fall 2020 WHAT ARE WE GOING TO DO IN THIS VIDEO? More recursive algorithms Decimal to Binary conversion Power function Binary Search RECALL: DECIMAL TO BINARY (ITERATIVE) ALGORITHM Constructing Base 2 Expansions procedure BinaryExpansion(𝑛) 𝑘≔0 While 𝑛 > 0
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CS 112: Data Structures Sesh Venugopal Heap – Implementation Implementation: Structure for storage of heap items As far as the conceptual structure goes, the heap is a binary tree. Therefore, one would expect that a heap could be implemented using a linked binary tree structure, as we did with BSTs However, the fact that the
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CS 112 – Data Structures Sesh Venugopal Sequential Search Average Case return false; } Sesh Venugopal Sequential Search on a list: Array or Linked List // on an array of integers for (int i=0; i < arr.length; i++) { if (target == arr[i]) { return true; // on a linked list, Node has int data
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COMP 250 INTRODUCTION TO COMPUTER SCIENCE Week 12-1 : Binary Search Trees Giulia Alberini, Fall 2020 Slides adapted from Michael Langer’s WHAT ARE WE GOING TO DO IN THIS VIDEO? Binary Search Trees BINARY SEARCH TREES BSTNode The keys are “comparable” e.g. numbers, strings. class BSTNode{ K key; BSTNode leftchild; BSTNode rightchild; : }
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CS 112: Data Structures Sesh Venugopal Quicksort Algorithm – Fine Tuning Fine Tuning Running Time Since quicksort can sort an array in place (without using extra array space, unlike mergesort, which needs extra storage), and the average running time is O(nlogn),it is widely used in practice A core set of fine-tuning techniques have been developed
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COMP 250 INTRODUCTION TO COMPUTER SCIENCE Week 7-1 : Stacks Giulia Alberini, Fall 2020 Slides adapted from Michael Langer’s WHAT ARE WE GOING TO DO IN THIS VIDEO? Stacks ABSTRACT DATA TYPE (ADT) An ADT is a model for a data type. It defines a data type by its behavior from the user’s perspective
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COMP 250 INTRODUCTION TO COMPUTER SCIENCE Week 10-2 : Recurrences Giulia Alberini, Fall 2020 WHAT ARE WE GOING TO DO IN THIS VIDEO? Recurrences ALGORITHM ANALYSIS We would like to find a function 𝑇(𝑛) that describes the running time of an algorithm given an input size 𝑛. It is relatively easy to determine
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