1. Introduction to Intractability

recall model of computation: DFA
a univeral model of computation: turing machine
→ no more powerful model of computation.
Turing machine can compute any function that can be computed by a physically harnessable process of the natural world.

bottom line: turing machine is a simple and universal …

simplex algo: top 10 algo of the 20th century (ever?).

what is linear programming:
a general problem-solving model that works for:
shortest-path, maxflow, MST, matching, assignment, ...

1. Brewer-'s Problem

toy example: choose products to maximize profit.
...
feasible region: a convex polygon.

⇒ optimum solution appears at an extreme point.

standard form …

Goal: classify problems according to computational requirements.
bad new: for huge number of pbs we don't know...

1. Introduction to Reductions

shifing gears:

  • from individual problems to problem-solving models.
  • from linear/quard to polynomial/exponential pbs
  • from implementation details to conceptual framwork

suppose we could (not) solve pb X efficiently …

1. Introduction to Data Compression

pb: reduce the size of a file, to save space/time for storing/transmitting.
applications: generic file compression(gzip), multimedia (mp3), communication(skype).

From binary data B, ⇒ generate a compressed representation C(B).

lossless compression: get exactly B from C(B)
compression ratio: |C(B …

I. 工作

学业

三月初结束了在X的最后几门考试, X的课从来都不简单, 但我真的很享受, 尤其是那些数学课.
(不过刚考完就sb了: 陪伴我两年的杯子丢了...)

Polytechnique, 从憧憬 …

1. Regular Expressions

pb: pattern matching.

regular expression

Is a notation to specify a set of strings.
basic operations:

  • concatenation
  • or
  • closure: "0 or more appearances of chars"
  • parentheses


additional operations (added for convinence):

ex. [A-C]+ is equivalent to (A|B|C)(A|B|C)*.

吐槽名句:

2 …

今天简单介绍一下优先队列(priority queue, 以下简称PQ)这个数据结构的实现.

PQ又叫"堆"(heap), 但是可能优先队列这个名字更容易记忆它的 …