LaTeX 中最便宜成本的动态规划

Question

从我如何才能自动生成这个动态规划图？，Jubobs 帮助开发了一个foreach绘制路径的方案。我想知道 LaTeX 是否可以通过实施动态规划来找到最便宜的路径。

\documentclass{article}

\usepackage{tikz}

\newcounter{rowcount}
\newcounter{columncount}

\begin{document}
\begin{tikzpicture}[scale=2]
\begin{scope}[rotate=-45]
    % rows
    \foreach[count=\y from 0] \W in
    {{7,8,6},{8,8,8},{6,9,7},{7,8,10}} % row-wise weights
    {
      \stepcounter{rowcount}
      \foreach \w [count=\x, remember=\x as \lastx (initially 0)] in \W
        \draw (\lastx,\y) -- (\x,\y)
          node[above,pos=0.5] {\w};
    }
    % columns
    \foreach[count=\x from 0] \W in
    {{5,6,10},{7,10,5},{10,5,6},{7,9,11}} % column-wise weights
    {
      \stepcounter{columncount}
      \foreach \w [count=\y, remember=\y as \lasty (initially 0)] in \W
        \draw (\x,\lasty) -- (\x,\y)
          node[above,pos=0.5] {\w};
  }
  \fill (0,0) circle (0.1em) node[below left] {A};
  \fill ({\value{columncount}-1},{\value{rowcount}-1}) circle (0.1em) node[below right] {B};
\end{scope}
\end{tikzpicture}
\end{document}

1. LaTeX 有这个能力吗？
2. 如果确实如此，那么这样的事情是如何做到的？