没有合适的资源?快使用搜索试试~ 我知道了~
首页具体数学 repertoire方法讲解
资源详情
资源评论
资源推荐
Notes on the Repertoire Method for Solving
Recurrences
Geoffrey Matthews
2004
The repertoire method is presented in Concrete Mathematics, a Foundation
for Computer Science, by Graham, Knuth, and Patashnik, Addison-Wesley,
1989.
This is the greatest book on discrete math ever written.
1
Solve:
r
0
= 1
r
n
= r
n−1
+ 3n+ 5
2
First, get some cases
r
0
= 1
r
n
= r
n−1
+ 3n+ 5
r
1
= r
0
+ 3(1) + 5 = 1+ 3+ 5 = 9
r
2
= r
1
+ 3(2) + 5 = 9+ 6+ 5 = 20
r
3
= r
2
+ 3(3) + 5 = 20+ 9+ 5 = 34
It’s easy enough to do this by hand,
or write a little throw-away program to calculate them for you.
n 0 1 2 3 4 5
r
n
1 9 20 34 51 71
Quick, what’s the next number in this sequence?
Hmmm... nothing occurs to me.
3
Unsimplified cases.
r
0
= 1
r
n
= r
n−1
+ 3n+ 5
Let’s try that a little slower:
r
1
= r
0
+ 3(1) + 5 = 1+ 3+ 5
r
2
= r
1
+ 3(2) + 5
= 1+ 3+ 5+ 3(2) + 5
= 1+ 3(3) + 5(2)
r
3
= r
2
+ 3(3) + 5
= 1+ 3(3) + 5(2) + 3(3) + 5
= 1+ 3(6) + 5(3)
r
4
= r
3
+ 3(4) + 5
= 1+ 3(6) + 5(3) + 3(4) + 5
= 1+ 3(10) + 5(4)
4
A pattern in the unsimplified cases.
r
0
= 1
r
n
= r
n−1
+ 3n+ 5
r
0
= 1(1) + 3(0) + 5(0)
r
1
= 1(1) + 3(1) + 5(1)
r
2
= 1(1) + 3(3) + 5(2)
r
3
= 1(1) + 3(6) + 5(3)
r
4
= 1(1) + 3(10) + 5(4)
It looks like our solution could be:
r
n
= 1A(n) + 3B(n) + 5C(n)
where A, B and C are simple functions of n.
5
剩余66页未读,继续阅读
simplebutperfect
- 粉丝: 0
- 资源: 1
上传资源 快速赚钱
- 我的内容管理 收起
- 我的资源 快来上传第一个资源
- 我的收益 登录查看自己的收益
- 我的积分 登录查看自己的积分
- 我的C币 登录后查看C币余额
- 我的收藏
- 我的下载
- 下载帮助
会员权益专享
最新资源
- zigbee-cluster-library-specification
- JSBSim Reference Manual
- c++校园超市商品信息管理系统课程设计说明书(含源代码) (2).pdf
- 建筑供配电系统相关课件.pptx
- 企业管理规章制度及管理模式.doc
- vb打开摄像头.doc
- 云计算-可信计算中认证协议改进方案.pdf
- [详细完整版]单片机编程4.ppt
- c语言常用算法.pdf
- c++经典程序代码大全.pdf
- 单片机数字时钟资料.doc
- 11项目管理前沿1.0.pptx
- 基于ssm的“魅力”繁峙宣传网站的设计与实现论文.doc
- 智慧交通综合解决方案.pptx
- 建筑防潮设计-PowerPointPresentati.pptx
- SPC统计过程控制程序.pptx
资源上传下载、课程学习等过程中有任何疑问或建议,欢迎提出宝贵意见哦~我们会及时处理!
点击此处反馈
安全验证
文档复制为VIP权益,开通VIP直接复制
信息提交成功
评论3