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最新推荐文章于 2023-08-03 16:10:53 发布

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本文介绍了一种基于最大流最小割原理的算法实现过程，该算法通过特定的增量路径选择来逐步逼近网络中的最大流，并确保在限定次数内完成迭代求解。

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\documentclass[a4paper,12pt]{cctart}
\usepackage{amsmath,amssymb,graphicx,subfigure}
\usepackage{algorithm}
\usepackage{algorithmic}
\title{}
\author{}
\date{}
\textheight=25cm \textwidth=15cm \topmargin=-2cm
\oddsidemargin=0cm \evensidemargin=0cm

\begin{document}\begin{algorithm}[H]\renewcommand{\algorithmicrequire}{\textbf{Input:}}\renewcommand{\algorithmicensure}{\textbf{Output:}}\begin{algorithmic}[1]\REQUIRE a network $N:=N(x,y)$ and a zero flow $f$ in $N$\ENSURE a maximum flow $f$ returned by $2M+1$ iterations\STATE  set $k=0$ and $s=0$\IF {$k=0$}\STATE choose the increment path shown in figure 8-1-1-b\STATE set $s=s+1$\ELSE\STATE choose the increment path shown in figure 8-1-1-c\STATE set $s=s+1$\ENDIF\IF {either $f((u,y))$ or $f((v,y))$ is less than $M$}\STATE set $k=1-k$\RETURN to step 2\ELSE\STATE do the Max-Flow Min-Cut Algorithm to show that $f$ is a maximum flow\STATE set $s=s+1$\ENDIF\RETURN $(f,s)$ where $s$ means the number of iterations used\end{algorithmic}\end{algorithm}\end{document}

$\begin{document} \begin{algorithm}[H] \renewcommand{\algorithmicrequire}{\textbf{Input:}} \renewcommand{\algorithmicensure}{\textbf{Output:}} \begin{algorithmic}[1] \REQUIRE a network $N:=N(x,y)$ and a zero flow $f$ in $N$ \ENSURE a maximum flow $f$ returned by $2M+1$ iterations \STATE set $k=0$ and $s=0$ \IF {$k=0$} \STATE choose the increment path shown in figure 8-1-1-b \STATE set $s=s+1$ \ELSE \STATE choose the increment path shown in figure 8-1-1-c \STATE set $s=s+1$ \ENDIF \IF {either $f((u,y))$ or $f((v,y))$ is less than $M$} \STATE set $k=1-k$ \RETURN to step 2 \ELSE \STATE do the Max-Flow Min-Cut Algorithm to show that $f$ is a maximum flow \STATE set $s=s+1$ \ENDIF \RETURN $(f,s)$ where $s$ means the number of iterations used \end{algorithmic} \end{algorithm} \end{document}$