Introduction to Algorithms演算法導論筆記

演算法導論Lesson1

課程簡介：

內容主要包括：

• 演算法的含義、意義的簡要介紹；
• 演算法的分析；
• 插入排序、合併排序
• 如下圖：
  如下圖：

preface
Analysis of Algorithms
The theoretical study of computer program
performance and resource usage

What’s more important than perf?
cost, ux
Why study algs and perf?
infeasable ->feasable
perf like the currency in economy
Perf is the precondition to have good ux.
bottom of heap
Speed is always fun.

Problem Sorting
input sequence [a1,a2,…,an] of numbers
output permutation[a1’,a2’,…,an’] to sorted as smaller->bigger

Insertion Sort

Running time:
- depends on input(e.g. sorted already)
- depends on input size( 6 elem. vs 6*10**9)

Kinds of analysis

• Worst-case(usually)

  T(n) =max time on any input of size n

• Average-case:(sometimes)

  T(n)=expected time over all inputs of size n
  (Need assumption of stat. distr.)

• Best-case:(bogus)
  cheat

What’s my sort’s worst time?
Depends on computer

• relative speed(on same machine)

• absolute speed(on different machines)
  BIG DATA
  漸進分析
  look at the growth of time when n->infinity
  Asymptotic notation:

  O(n**3) Drop low-order such as n**2,n,constant and leading constant.

  arithmetic series（算術級數，等差級數）
  教授居然說，我們這裡有高手知道算數級數，溝通就好辦了。
  Merge Sort

  

  1. If n=1, done
  2. Recursively sort
     a[1,…n/2] and
     a[n/2+1,…n]
  3. Merge 2 sorted lists.
     Key Subroutine: Merge
     20 12
     13 11
     7 9
     2 1
     1 2 7 9 11 13 12 20

小結：
兩種排序演算法
對於排序問題，本節課提供了兩種演算法，分別是插入排序和合並排序。

插入排序是O(n*n)，合併排序是O(nlgn)

其中合併排序運用了遞迴呼叫和分治策略，這兩個內容將分別在後續兩節中介紹。