用lua语言实现一下代码从确认起点出发遍历所有点的最短路径代码

以下是使用Lua语言实现的Dijkstra算法来求解从起点出发的最短路径的代码示例：

-- 图数据结构
local graph = {
  {0, 4, 0, 0, 0, 0, 0, 8, 0},
  {4, 0, 8, 0, 0, 0, 0, 11, 0},
  {0, 8, 0, 7, 0, 4, 0, 0, 2},
  {0, 0, 7, 0, 9, 14, 0, 0, 0},
  {0, 0, 0, 9, 0, 10, 0, 0, 0},
  {0, 0, 4, 14, 10, 0, 2, 0, 0},
  {0, 0, 0, 0, 0, 2, 0, 1, 6},
  {8, 11, 0, 0, 0, 0, 1, 0, 7},
  {0, 0, 2, 0, 0, 0, 6, 7, 0}
}

-- 获取图中的顶点数量
local function getVertexCount(graph)
  return #graph
end

-- 找到距离数组中最小距离的顶点
local function findMinDistance(distance, visited)
  local minDistance = math.huge
  local minIndex = -1
  for i = 1, #distance do
    if not visited[i] and distance[i] < minDistance then
      minDistance = distance[i]
      minIndex = i
    end
  end
  return minIndex
end

-- 打印最短路径
local function printPath(parent, vertex)
  if parent[vertex] == -1 then
    io.write(vertex, " ")
    return
  end
  printPath(parent, parent[vertex])
  io.write(vertex, " ")
end

-- Dijkstra算法
local function dijkstra(graph, start)
  local vertexCount = getVertexCount(graph)
  local distance = {}
  local visited = {}
  local parent = {}

  -- 初始化距离数组、访问数组和父节点数组
  for i = 1, vertexCount do
    distance[i] = math.huge
    visited[i] = false
    parent[i] = -1
  end

  -- 设置起点的距离为0
  distance[start] = 0

  -- 找到最短路径
  for _ = 1, vertexCount - 1 do
    local u = findMinDistance(distance, visited)
    visited[u] = true
    for v = 1, vertexCount do
      if not visited[v] and graph[u][v] ~= 0 and distance[u] + graph[u][v] < distance[v] then
        distance[v] = distance[u] + graph[u][v]
        parent[v] = u
      end
    end
  end

  -- 打印最短路径和距离
  for i = 1, vertexCount do
    if i ~= start then
      io.write("最短路径从 ", start, " 到 ", i, " 的路径为：")
      printPath(parent, i)
      io.write("，距离为 ", distance[i], "\n")
    end
  end
end

-- 测试
dijkstra(graph, 1)

这里的graph变量表示图的数据结构，其中的数字表示边的权重。dijkstra函数接受一个图和起点作为参数，并计算出从起点到所有其他顶点的最短路径。最后的测试代码会输出从起点到其他顶点的最短路径和距离