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 …

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 …

1. Introduction to substring search

"most ingenious algorithm we've seen so far"
pb. having two strings, pattern and text, len(pattern)=M << len(text)=N, try to find pattern in text.

ex. indexOf method of String in java.

2. Brute-Force Substring Search

function signature:
public static int search(String pat …

今天总结一下非常有用的快速排序(qsort)算法, 以及由此衍生的一些其他相关算法(Knuth shuffle, quick select, 3-way partition).

快速排序的算法可以用三 …