1 / 10

DS.I.1

DS.I.1. CSE 373: Data Structures and Algorithms. Autumn Quarter 2000. Instructor: Prof. Linda Shapiro Email: shapiro@cs.washington.edu Tas: Valentin Razmov Ann Li Karen Liu. Purpose: to study the fundamental data

cael
Download Presentation

DS.I.1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. DS.I.1 CSE 373: Data Structures and Algorithms Autumn Quarter 2000 Instructor: Prof. Linda Shapiro Email: shapiro@cs.washington.edu Tas: Valentin Razmov Ann Li Karen Liu Purpose: to study the fundamental data structures and algorithms used in computer science. • Data Structures • Algorithm Analysis • Applications

  2. DS.I.2 Text: Data Structures and Algorithm Analysis in C Topics to be Covered • Introduction (Ch 1) • Algorithm Analysis (Ch 2) • Review of Lists, Stacks, Queues (Ch 3) • Trees and Search Trees (Ch 4) • Hashing (Ch 5) • Priority Queues: Heaps (Ch 6) • Disjoint Sets: Union-Find (Ch 8) • Graph Algorithms (Ch 9) Applications Computer Graphics Computer Vision Artificial Intelligence Databases

  3. DS.I.3 INTRODUCTION Chapter 1 Overview • Motivation for Good Algorithm Design • Math Review (for use in reading proofs) • Proofs by Induction, Counterexample, Contradiction • Recursion What is an algorithm ? What would be a good algorithm for achieving tulips in my garden next spring?

  4. DS.I.4 An algorithm to achieve X is a procedure that: 1. Halts 2. Correctly achieves X Procedure for computing N / 5 for integer N count = 0; do { count = count + 1; N = N - 5; } until (N <= 0) Does it always halt? Does it correctly compute N / 5?

  5. DS.I.5 What is a data structure ? Informal Definition: a method of organizing data Examples? Formal Definition: an abstract data type (ADT) In C: • structs • functions that operate on them In C++: • classes • methods

  6. DS.I.6 Example: VectorArray Conceptual: Size (of array) NumElements Data 0 1 Size-1 What abstract operations are needed?

  7. DS.I.7 Iteration, Recursion, Induction 1. Write an iterative function to find the sum of the first num elements of a VectorArray stored in array v. int sumit ( int v[ ], int num) { int sum; sum = 0; for ( ) sum = ; return sum; }

  8. DS.I.8 2. Write a recursive function to find the sum of the first num elements of a VectorArray stored in array v. int sumit ( int v[ ], int num) { } Strengths of recursive approach: - simplifies code - can be proven correct Weaknesses: - slower than iteration - uses more memory for the stack

  9. DS.I.9 Principle of Mathematical Induction Let P(c) be true for small constant c >= 0. Suppose whenever P(k) is true, so is P(k+1). Then P(n) is true for all n >= 0. Ex. 1.10a Prove by induction that N  (2i - 1) = N . i=1 2 Basis: N=1 Inductive Hypothesis: Induction Step:

  10. DS.I.10 int sumit (int v[ ], int num) { if (num == 0) return 0; else return v[num-1] + sumit(v,num-1); } Prove by induction that sumit(v,n) correctly returns the sum of the first n elements of array v, n0. Basis: If n=0, Inductive Hypothesis: Assume sumit(v,k) ... Inductive Step: sumit(v,k+1)

More Related