T******n
发帖数: 11 | 1 我用vector表示set，结果是一个vector的vector。不用recursion。
1. 把empty set加入结果；
2. 遍历set里的元素，每碰到一个都是把之前的结果复制一遍，然后把set里的新元素
加入，然后加入结果中；
vector > powerSet(vector& set) {
vector > subsets;
vector emptySet;
subsets.push_back(emptySet);
for(int i = 0; i < set.size(); i++) {
vector > add = subsets;
for(int j = 0; j < add.size(); j++) {
add[j].push_back(set[i]);
subsets.push_back(add[j]);
}
}
return subsets;
} |
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Q***5
发帖数: 994 | 2 Here is a simple counter example (hope I got it right):
Omega = {1,2,3,4}
P(i) = 1/4, i = 1,2,3,4
G = {{2},{1,3,4},Omega, EmptySet}
H = {{1,2},{3,4},Omega, EmptySet}
X(i) = 1 for i = 2,3; 0 otherwise
X is independent of H
E[X|G](i) = 1 for i = 2 and 1/3 otherwise
E(X|sigma(G,H))(i) = 1 for i = 2, 0 for i = 1 and 1/2 otherwise
provide |
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i*********n
发帖数: 58 | 3 Pseudocode and implementation needs to be optimized:
set PowerSet(set input)
if (input.empty())
return set.insert(EmptySet);
else
e = input.first();
input.removeFirst();
input = PowerSet(input);
for (iter = input.second(); iter != input.end(); ++iter)
set.insert(SetUnion(e, *iter));
return SetUnion(set, input);
|
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g**w
发帖数: 969 | 4 想了一个non recursion
set.add(EmptySet)
foreach (item in Set)
{
tmpset = empty;
foreach (s in set)
{
news = s.clone();
news.addelement(item);
tmpset.add(news);
}
set.addset(tmpset);
} |
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M*****e
发帖数: 11621 | 5 \forall h>0, F(x+h)-F(x) = P((x,x+h])
\lim_{h\to 0^+} = \lim_{h\to 0^+} P((x,x+h]) = P(\emptyset) = 0.
～～～～这一步得展开
right |
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z*****3
发帖数: 15515 | 6 第一个方法里lim_{hto 0^+} P((x,x+h]) = P(emptyset) 不懂
第二个方法里lim_{hto 0^+}F(x+h) <= F(x+g)不懂
that |
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g***e
发帖数: 1168 | 7 almost forgot :D no big deal, haha, but soren is written like \phi or \
emptyset or \O
http://en.wikipedia.org/wiki/S%C3%B8ren_Kierkegaard
haha, not sure if you write technical paper, but here's a handy iOS app for
tex user: Detexify
guilty |
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s*****g
发帖数: 5159 | 8 \emptyset in math environment. |
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D**o
发帖数: 2653 | 9 注意作者 \author{YHBKJ}
Atiyah-Bott Localization 1
2012-09-05 09:24:19
\documentclass[a4paper,12pt]{article}
\usepackage{amsfonts}
\usepackage{amsmath,amsthm,amssymb}
\usepackage{CJK,graphicx}
\usepackage{amscd}
\usepackage{amssymb}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{definition}{Definition}[section]
\newtheorem{lemma}{Lemma}[section]
\begin{document}
\title{\textbf{\Huge{Atiyah-Bott Localization 1}}}\author{YHBKJ}\date{}\
maketitle
\begin{ab... 阅读全帖 |
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