Introduction to Algorithms算法导论笔记-Lecture1

Introduction to Algorithms算法导论笔记

算法导论Lesson1

课程简介：

内容主要包括：

算法的含义、意义的简要介绍；

算法的分析；

插入排序、合并排序

如下图：

如下图：



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

渐进分析

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（算术级数，等差级数）

教授居然说，我们这里有高手知道算数级数，沟通就好办了。

Merge Sort



If n=1, done

Recursively sort

a[1,…n/2] and

a[n/2+1,…n]

Merge 2 sorted lists.

Key Subroutine: Merge

20 12

13 11

7 9

2 1

1 2 7 9 11 13 12 20

小结：

两种排序算法

对于排序问题，本节课提供了两种算法，分别是插入排序和合并排序。

插入排序是O(n*n)，合并排序是O(nlgn)

其中合并排序运用了递归调用和分治策略，这两个内容将分别在后续两节中介绍。