1. Data Structures and Algorithms
What This Course Is About
Data structures – how data is organized
Algorithms – unambiguous sequence of steps to compute something
Data Structures + Algorithms = Programs
Algorithm analysis – determining how long an algorithm will take to solve a problem
Who cares? Aren’t computers fast enough and getting faster?
Oct 1, 2001
CSE 373

2. An Example Given an array of 1,000,000 integers, …
find the maximum integer in the array.
Now suppose we are asked to find the kth largest element. (The Selection Problem) … 1 2
999,999
Oct 1, 2001
CSE 373

3. Candidate Solutions + Candidate solution 1
Sort the entire array (from small to large), using insertion sort. Pick out the (1,000,000 – k)th element.
+ Candidate solution 2
Sort the first k elements.
For each of the remaining (1,000,000 – k) elements,
keep the k smallest in an array.
Pick out the smallest of the k survivors.
Oct 1, 2001
CSE 373

4. Is either solution good?
Is there a better solution?
How would you go about determining the answer to these questions?
Oct 1, 2001
CSE 373

5. Method 1 Code each algorithm and run them to see how long they take.
Problem: How will you know if there is a better program or whether there is no better program?
What will happen when the number of inputs is twice as many? Three? A hundred?
Oct 1, 2001
CSE 373

6. Method 2
Develop a model of the way computers work and compare how the algorithms behave in the model.
Goal: To be able to predict performance at a coarse level. That is, to be able to distinguish between good and bad algorithms.
Another benefit: when assumptions change, we can predict the effects of those changes.
Oct 1, 2001
CSE 373

7. Why algorithm analysis?
As computers get faster and problem sizes get bigger, analysis will become more important.
Why? The difference between good and bad algorithms will get bigger.
Oct 1, 2001
CSE 373

8. Why data structures? When programming, you are an engineer.
Engineers have a bag of tools and tricks – and the knowledge of which tool is the right one for a given problem.
Arrays, lists, stacks, queues, trees, hash tables, graphs.
Oct 1, 2001
CSE 373