使用 Lua 自动进行 BFS 绘图

Question

我尝试用 TeX 来学习 Lua。为此，我尝试以某种方式实现 BFS，以便它可以自动创建 Tikz 图片。下面是我所做的一个简短示例：

\documentclass{article}

\usepackage{luacode}
\usepackage{tikz}
\usetikzlibrary{graphs,graphdrawing}
\usegdlibrary{force}

\begin{luacode}
    tp=tex.print
    
    bfs_initial_graph = {}
    bfs_current = {}
    bfs_visited = {}
    bfs_in_queue = {}
    bfs_unvisited = {}
    
    function bfs_init(graph, start)
        -- initialize bfs_current with start node
        bfs_current = {start}
    
        -- initialize bfs_visited as an empty set
        bfs_visited = {}
    
        -- initialize bfs_in_queue with nodes reachable from start node
        bfs_in_queue = {}
        for _, neighbor in ipairs(graph[start]) do
            table.insert(bfs_in_queue, neighbor)
        end
    
        bfs_unvisited = {}
            for node, neighbors in pairs(graph) do
                if node ~= start then
                table.insert(bfs_unvisited, node)
            end
        end
    end
    
    function bfs_step()
        -- check if bfs_in_queue is empty
        if #bfs_in_queue == 0 then
            return false
        end
        -- move current node from bfs_current to bfs_visited
        local current_node = table.remove(bfs_current, 1)
        table.insert(bfs_visited, current_node)
        
        -- move first node from bfs_in_queue to bfs_current
        local next_node = table.remove(bfs_in_queue, 1)
        table.insert(bfs_current, next_node)
        
        -- update bfs_unvisited and bfs_in_queue
        for _, neighbor in ipairs(bfs_initial_graph[next_node]) do
            if bfs_unvisited[neighbor] then
                bfs_unvisited[neighbor] = nil
                table.insert(bfs_in_queue, neighbor)
            end
        end
        
        return true
    end
    
    function bfs_draw_graph()
        -- start TikZ picture
        tp("\\begin{tikzpicture}[>=stealth, every node/.style={circle, draw, minimum size=0.75cm}]")
        
        -- loop through nodes in the initial graph and draw them
        for node, neighbors in pairs(bfs_initial_graph) do
            -- determine color based on BFS list membership
            local color = "gray"
            if node == bfs_current[1] then
                color = "red"
            elseif table.contains(bfs_in_queue, node) then
                color = "yellow"
            elseif table.contains(bfs_visited, node) then
                color = "green"
            end
        
            -- draw node with appropriate color
            tp(string.format("%s [color=%s]", node, color))
        
            -- draw edges to neighbors
            for _, neighbor in ipairs(neighbors) do
                tp(string.format("%s -- %s", node, neighbor))
            end
        end
        -- end TikZ picture
        tp("\\end{tikzpicture}")
    end
    
    function bfs_run()
        -- run BFS until bfs_in_queue is empty
        while #bfs_in_queue > 0 do
            bfs_next_step()
        end
    end
\end{luacode}

\newcommand{\BfsInit}[2]{\luaexec{bfs_init(#1, #2)}}
\newcommand{\BfsNextStep}{\luaexec{bfs_draw_graph()}}
\newcommand{\BfsAllSteps}{\luaexec{bfs_run()}}

\begin{document}

    \BfsInit{
            a -- {b,c},
            b -- {a,c},
            c -- {a,b},}
            {a}
            
    \BfsNextStep

\end{document}

遗憾的是它无法运行，我不知道如何让它运行。对于我这个初学者来说，它看起来是正确的，但我不知道错误在哪里。有人能帮我运行并向我解释我的错误在哪里吗？非常感谢！！！