CS 101

Computer Science Theory and Conclusions

Announcements

Final is on Monday, December 10, 8:30AM-11:30AM in 200-203. If you have an exam accommodation and haven't received an email from Shreya, please email both of us.
Practice final exam materials are posted on the website (same reference sheet as last time)
Final review session on Thursday! Come with questions
Please give us EOQ feedback
Shreya will move her OH from Wednesday to this weekend. Stay tuned!

Wrap-up of the quarter

Recall: traditional computers have bits - either 0 or 1
Superposition allows a qubit to be a combination of 0 and 1. Note: when measuring or looking at a bit, it'll still be 0 or 1. For example, we could set it so that 50% of the time, the qubit is measured as a 1
Entanglement connects two bits together (so coming out of superposition, entangled bits will always have the same value)
Interference: can amplify the right answer to increase probability of getting the right answer or destructively decrease the likelihood of following a path to the wrong answer
Good for simulating nature
Idea: can simulate many things simultaneously
Example: break popular encryption schemes

Developed the Universal Turing Machine to prove that some problems are unsolvable
- One example: finding the cheapest sequence of flights for a trip
- Another example: we can't tell if a program will ever end
Broke Enigma encryption
Turing Test in Artificial Intelligence
Turing Award ("Nobel Prize of CS") named after him

Algorithm: way to solve a problem
Two main resources: time and space (memory)
Good algorithms run faster with respect to input size
- Getting the red value of a pixel always takes the same amount of time (constant)
- Studying an exam requires reading every slide (linear)
- Green screen: double the width and height of the image, quadruple the number of pixels to look at (polynomial)
- Listing all the two digit numbers takes one-tenth the time as listing all the three digit numbers (exponential)

We want to see if a certain value is in a sorted list of elements
Could look through all the values one by one (linear)
Binary Search
- Look at the middle value
- Only need to look at the left values if it's too big
- Only need to look at the right values if it's too large

Bogosort: randomly pick all the elements, then check if the list is in order (really, really slow)
Insertion Sort: Add the elements one-by-one
Bucket sort: pick categories for the data, then put each item in one of those buckets
- Commonly used with exams
- Idea: faster if we relax our definition of "sorted"

Biggest unsolved question in Computer Science (million dollar prize)
Basic idea: is it just as fast to solve a problem as it is to check that the solution is correct?
NP: guess a solution (very fast) and check that it's correct
P: actually find a solution

Abstractions can help computer scientists think about problems differently.
Some problems in computer science don't have any solutions (computers are not all-powerful).
Some problems don't have any "good" solutions.
There are lots of ways to solve problems! Computer scientists constantly try to find better ways.

Improve technical literacy, understanding computer terminology.
Understand how computer code is written.
Describe how computers and the internet works behind the scenes.
Understand the technologies most discussed in the news and how technology affects society.

It's a hard course, and you all have done very well. Good luck on the final!