1. Introduction to Algorithms
The Role of Algorithms
Introduction to Algorithms
Jeff Chastine

2. Algorithms Studying algorithms is about studying efficiency
How fast does it run?
Can I make it run faster?
Jeff Chastine

3. Algorithms
An algorithm is any well-defined computational procedure that takes some input and produces output
A sequence of steps
An algorithm is correct if for all input, it halts with the correct output
We say that a correct algorithm solves the computational problem
An incorrect algorithm may not halt!
Jeff Chastine

4. Example: Sorting Problem
Input: A sequence of n numbers <a1, a2, …, an>
Output: A permutation <a'1, a'2, …, a'n> of the original such that a'1 ≤ a'2 ≤ … ≤ a'n
Sorting is fundamental to computer science, so we’ll be studying several different solutions to it
Jeff Chastine

5. The Challenge = 20,000 secs ≈ 5.56 hours 2 (106)2 instrs
Suppose we have 1 million numbers to sort
Your computer executes 100 million ips
Mine executes 1 million ips
You have optimized compiler (take hit of 2)
I have crummy compiler (take hit of 50)
You use insertion sort (n2), I use merge sort (n log n)
2 (106)2 instrs
= 20,000 secs ≈ 5.56 hours
108 instruction/sec
50(106lg 106) instrs
= 1,000 secs ≈ minutes
106 instruction/sec
Jeff Chastine

6. I WIN!
Jeff Chastine

7. Problems to Think About…
Searching large amounts of information
Most efficient path from A to B (how many routes are there?)
Find a convex hull that contains all points
Travel to a series of points and return home
Best way to schedule classes
Impossible to solve problems?
Jeff Chastine

8. What you’ll be studying
The Design and Analysis of Algorithms
Growth of Functions
Recurrences
Heapsort, Quicksort, Counting Sort…
Medians and Order Statistics
Elementary Data Structures
Hashing
Jeff Chastine

9. What you’ll be studying
Binary Search Trees
Dynamic Programming
Greedy Algorithms
Amortized Analysis
Elementary Graph Algorithms
Jeff Chastine

10. What you’ll be studying
Minimum Spanning Trees
Single-Source Shortest Paths
All-Pairs Shortest Paths
NP-Completeness
Approximation Algorithms
Jeff Chastine

11. A Most Excellent Quote
“Having a solid base of algorithmic knowledge and technique is one characteristic that separates the truly skilled programmers from the novices.”
Jeff Chastine

12. The Proof (and why you should pay attention)
Jeff Chastine