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View Code? Open in Web Editor NEW何老师算法课笔记
License: MIT License
何老师算法课笔记
License: MIT License
这里给出了一些新手指引,帮助大家上手LaTeX
几处错误:
$\{ I_1, I_2, \ldots , I_k \}$
且令S到所有的$V_l$中的点均有路径
您好,我是来自西电计算机的一名学生,我最近也有做类似『算法笔记』的想法。
以上都是我这种脑子不太好使的人学习算法的态度,恩,所以所有的内容和讲解都想给出实际练习题和代码,不然理解纯概念确实有些累。
等我期末月过完且您方便的时间,可否讨论下?
与
中均使用fig1
, fig2
这样的label来标识图片,导致了build的过程中引用混乱。
计划:
\label{fig:network-flow1}
)example中的定理cp过来没删掉
algorithm-course-notes/src/Proof-of-Statute.tex
Lines 12 to 14 in dc249cf
图片太大了,scale一下(下面一个图也是)
辛苦 @qzylalala 改一下吧,当时没认真review(
一些离谱的错误:
继续使用 $f(n)=pn^2+qn+r$ 的例子,其中q 、p、 r 均为正常数,我们可以说具有任何这种形式的函数都是$\Omega(n)$。
证明如下:
\begin{proof}
\begin{align*}
\forall n \geq 1,t & hen\ qn\leq 0,r\geq 0 \\
\Longrightarrow f(n) & =pn^2+qn+r \\
& \geq pn^2+pn^2+rn^2 \\
& =(p+q+r)n^2
\end{align*}
\end{proof}
显然证明错误,上面说$q, p, r$都是正常数,下面又来个$qn<0$,然后$n > n^2$?咋放缩的?应当是将低阶项舍去,建议修改:
继续使用 $f(n)=pn^2+qn+r$ 的例子,其中q 、p、 r 均为正常数,我们可以说具有任何这种形式的函数都是$\Omega(n)$。
证明如下:
\begin{proof}
\begin{align*}
\forall n \geq 1\\
\Longrightarrow f(n) & =pn^2+qn+r \\
& \geq pn^2\\
& =pn^2
\end{align*}
\end{proof}
\section{渐进增长的一些性质}
下面将给出渐进增长的一些性质,对于性质的证明,可以自己证明,然后与\cite{textbook1}的P38-P40的证明进行对照
\begin{theorem}{Transitivity}{}
(a)\ If\ $f=O(g)$\ and\ $g=O(h)$, then $f=O(h)$\\
(b)\ If\ $f=\Omega(g)$\ and\ $g=\Omega(h)$, then $f=\Omega(h)$\\
(c)\ If\ $f=\Theta(g)$\ and\ $g=\Theta(h)$, then $f=\Theta(h)$
\end{theorem}
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