go语言|数据结构:二叉树可视化(svg树形图改进版)

简介: go语言|数据结构:二叉树可视化(svg树形图改进版)

题目


以图形展示任意二叉树,如下图,一个中缀表达式表示的二叉树:3.14*r²*h/3

d3e5376008194f6281305ac02b2595d8.png



源代码

package main
import (
  "fmt"
  "io"
  "os"
  "os/exec"
  "strconv"
  "strings"
)
type any = interface{}
type btNode struct {
  Data   any
  Lchild *btNode
  Rchild *btNode
}
type biTree struct {
  Root *btNode
  Info *biTreeInfo
}
type biTreeInfo struct {
  Data                []any
  DataLevel           [][]any
  L, R                []bool
  X, Y, W             []int
  Index, Nodes        int
  Width, Height       int
  MarginX, MarginY    int
  SpaceX, SpaceY      int
  SvgWidth, SvgHeight int
  SvgXml              string
}
func Build(Data ...any) *biTree {
  if len(Data) == 0 || Data[0] == nil {
    return &biTree{}
  }
  node := &btNode{Data: Data[0]}
  Queue := []*btNode{node}
  for lst := Data[1:]; len(lst) > 0 && len(Queue) > 0; {
    cur, val := Queue[0], lst[0]
    Queue, lst = Queue[1:], lst[1:]
    if val != nil {
      cur.Lchild = &btNode{Data: val}
      Queue = append(Queue, cur.Lchild)
    }
    if len(lst) > 0 {
      val, lst = lst[0], lst[1:]
      if val != nil {
        cur.Rchild = &btNode{Data: val}
        Queue = append(Queue, cur.Rchild)
      }
    }
  }
  return &biTree{Root: node}
}
func BuildFromList(List []any) *biTree {
  return Build(List...)
}
func AinArray(sub int, array []int) int {
  for idx, arr := range array {
    if sub == arr {
      return idx
    }
  }
  return -1
}
func Pow2(x int) int { //x>=0
  res := 1
  for i := 0; i < x; i++ {
    res *= 2
  }
  return res
}
func Max(L, R int) int {
  if L > R {
    return L
  } else {
    return R
  }
}
func (bt *btNode) MaxDepth() int {
  if bt == nil {
    return 0
  }
  Lmax := bt.Lchild.MaxDepth()
  Rmax := bt.Rchild.MaxDepth()
  return 1 + Max(Lmax, Rmax)
}
func (bt *btNode) Coordinate(x, y, w int) []any {
  var res []any
  if bt != nil {
    L, R := bt.Lchild != nil, bt.Rchild != nil
    res = append(res, []any{bt.Data, L, R, x, y, w})
    res = append(res, bt.Lchild.Coordinate(x-w, y+1, w/2)...)
    res = append(res, bt.Rchild.Coordinate(x+w, y+1, w/2)...)
  }
  return res
}
func (bt *biTree) NodeInfo() []any {
  return bt.Root.Coordinate(0, 0, Pow2(bt.Root.MaxDepth()-2))
}
func (bt *biTree) TreeInfo() {
  height := bt.Root.MaxDepth()
  width := Pow2(height - 1)
  lsInfo := bt.NodeInfo()
  btInfo := &biTreeInfo{
    Height: height,
    Width:  width,
    Nodes:  len(lsInfo),
  }
  for _, data := range lsInfo {
    for i, info := range data.([]any) {
      switch i {
      case 0:
        btInfo.Data = append(btInfo.Data, info.(any))
      case 1:
        btInfo.L = append(btInfo.L, info.(bool))
      case 2:
        btInfo.R = append(btInfo.R, info.(bool))
      case 3:
        btInfo.X = append(btInfo.X, info.(int))
      case 4:
        btInfo.Y = append(btInfo.Y, info.(int))
      case 5:
        btInfo.W = append(btInfo.W, info.(int))
      }
    }
  }
  for j, k := 0, width*2; j < height; j++ {
    DLevel := []any{}
    for i := k / 2; i < width*2; i += k {
      index := AinArray(i-width, btInfo.X)
      if index > -1 {
        DLevel = append(DLevel, btInfo.Data[index])
      } else {
        DLevel = append(DLevel, nil)
      }
      DLevel = append(DLevel, []int{i, j})
      if k/4 == 0 {
        DLevel = append(DLevel, []int{0, 0})
        DLevel = append(DLevel, []int{0, 0})
      } else {
        DLevel = append(DLevel, []int{i - k/4, j + 1})
        DLevel = append(DLevel, []int{i + k/4, j + 1})
      }
    }
    k /= 2
    btInfo.DataLevel = append(btInfo.DataLevel, DLevel)
  }
  bt.Info = btInfo
}
func (bt *biTree) Info2SVG(Margin ...int) string {
  var res, Line, Color string
  info := bt.Info
  MarginX, MarginY := 0, 10
  SpaceX, SpaceY := 40, 100
  switch len(Margin) {
  case 0:
    break
  case 1:
    MarginX = Margin[0]
  case 2:
    MarginX, MarginY = Margin[0], Margin[1]
  case 3:
    MarginX, MarginY, SpaceX = Margin[0], Margin[1], Margin[2]
  default:
    MarginX, MarginY = Margin[0], Margin[1]
    SpaceX, SpaceY = Margin[2], Margin[3]
  }
  info.MarginX, info.MarginY = MarginX, MarginY
  info.SpaceX, info.SpaceY = SpaceX, SpaceY
  info.SvgWidth = Pow2(info.Height)*info.SpaceX + info.SpaceX
  info.SvgHeight = info.Height * info.SpaceY
  for i, Data := range info.Data {
    Node := "\n\t<g id=\"INDEX,M,N\">\n\t<CIRCLE/>\n\t<TEXT/>\n\t<LEAF/>\n\t</g>"
    DataStr := ""
    switch Data.(type) {
    case int:
      DataStr = strconv.Itoa(Data.(int))
    case float64:
      DataStr = strconv.FormatFloat(Data.(float64), 'g', -1, 64)
    case string:
      DataStr = Data.(string)
    default:
      DataStr = "Error Type"
    }
    Node = strings.Replace(Node, "INDEX", strconv.Itoa(info.Index), 1)
    Node = strings.Replace(Node, "M", strconv.Itoa(info.X[i]), 1)
    Node = strings.Replace(Node, "N", strconv.Itoa(info.Y[i]), 1)
    x0, y0 := (info.X[i]+info.Width)*SpaceX+MarginX, 50+info.Y[i]*SpaceY+MarginY
    x1, y1 := x0-info.W[i]*SpaceX, y0+SpaceY-30
    x2, y2 := x0+info.W[i]*SpaceX, y0+SpaceY-30
    Color = "orange"
    if info.L[i] && info.R[i] {
      Line = XmlLine(x0-21, y0+21, x1, y1) + "\n\t" + XmlLine(x0+21, y0+21, x2, y2)
    } else if info.L[i] && !info.R[i] {
      Line = XmlLine(x0-21, y0+21, x1, y1)
    } else if !info.L[i] && info.R[i] {
      Line = XmlLine(x0+21, y0+21, x2, y2)
    } else {
      Color = "lightgreen"
    }
    Node = strings.Replace(Node, "<CIRCLE/>", XmlCircle(x0, y0, Color), 1)
    Node = strings.Replace(Node, "<TEXT/>", XmlText(x0, y0, DataStr), 1)
    if info.L[i] || info.R[i] {
      Node = strings.Replace(Node, "<LEAF/>", Line, 1)
    }
    res += Node
  }
  info.SvgXml = res
  return res
}
func XmlCircle(X, Y int, Color string) string {
  Radius := 30
  Circle := "<circle cx=\"" + strconv.Itoa(X) + "\" cy=\"" + strconv.Itoa(Y) +
    "\" r=\"" + strconv.Itoa(Radius) + "\" stroke=\"black\" stroke-width=" +
    "\"2\" fill=\"" + Color + "\" />"
  return Circle
}
func XmlText(X, Y int, DATA string) string {
  iFontSize, tColor := 20, "red"
  Text := "<text x=\"" + strconv.Itoa(X) + "\" y=\"" + strconv.Itoa(Y) +
    "\" fill=\"" + tColor + "\" font-size=\"" + strconv.Itoa(iFontSize) +
    "\" text-anchor=\"middle\" dominant-baseline=\"middle\">" + DATA + "</text>"
  return Text
}
func XmlLine(X1, Y1, X2, Y2 int) string {
  Line := "<line x1=\"" + strconv.Itoa(X1) + "\" y1=\"" + strconv.Itoa(Y1) +
    "\" x2=\"" + strconv.Itoa(X2) + "\" y2=\"" + strconv.Itoa(Y2) +
    "\" style=\"stroke:black;stroke-width:2\" />"
  return Line
}
func (bt *biTree) ShowSVG(FileName ...string) {
  var file *os.File
  var err1 error
  Head := "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink" +
    "=\"http://www.w3.org/1999/xlink\" version=\"1.1\" width=" +
    "\"Width\" height=\"Height\">\nLINKCONTENT\n</svg>"
  Link := `<a xlink:href="https://blog.csdn.net/boysoft2002" target="_blank">
  <text x="5" y="20" fill="blue">Hann's CSDN Homepage</text></a>`
  Xml := strings.Replace(Head, "LINK", Link, 1)
  Xml = strings.Replace(Xml, "Width", strconv.Itoa(bt.Info.SvgWidth), 1)
  Xml = strings.Replace(Xml, "Height", strconv.Itoa(bt.Info.SvgHeight), 1)
  Xml = strings.Replace(Xml, "CONTENT", bt.Info.SvgXml, 1)
  svgFile := "biTree.svg"
  if len(FileName) > 0 {
    svgFile = FileName[0] + ".svg"
  }
  file, err1 = os.Create(svgFile)
  if err1 != nil {
    panic(err1)
  }
  _, err1 = io.WriteString(file, Xml)
  if err1 != nil {
    panic(err1)
  }
  file.Close()
  exec.Command("cmd", "/c", "start", svgFile).Start()
  //Linux 代码:
  //exec.Command("xdg-open", svgFile).Start()
  //Mac 代码:
  //exec.Command("open", svgFile).Start()
}
func main() {
  list := []any{"*", "*", "*", "/", 5, "*", 3.14, 1, 3, nil, nil, 6, 6}
  tree := Build(list...)
  tree.TreeInfo()
  tree.Info2SVG()
  tree.ShowSVG()
  fmt.Println(tree.Info.Data)
  fmt.Println(tree.Info.DataLevel)
}



做题思路

增加一个结构biTreeInfo,在遍历二叉树时把作图要用的信息存入此结构中,方便读取信息。

type any = interface{}
type btNode struct {
    Data   any
    Lchild *btNode
    Rchild *btNode
}
type biTree struct {
    Root *btNode
    Info *biTreeInfo
}
type biTreeInfo struct {
    Data                []any
    DataLevel           [][]any
    L, R                []bool
    X, Y, W             []int
    Index, Nodes        int
    Width, Height       int
    MarginX, MarginY    int
    SpaceX, SpaceY      int
    SvgWidth, SvgHeight int
    SvgXml              string
}
//数据域类型用 type any = interface{} 自定义类型,模拟成any数据类型。


遍历二叉树获取每个结点在svg图形中的坐标,使用先序递归遍历:

func (bt *btNode) Coordinate(x, y, w int) []any {
    var res []any
    if bt != nil {
        L, R := bt.Lchild != nil, bt.Rchild != nil
        res = append(res, []any{bt.Data, L, R, x, y, w})
        res = append(res, bt.Lchild.Coordinate(x-w, y+1, w/2)...)
        res = append(res, bt.Rchild.Coordinate(x+w, y+1, w/2)...)
    }
    return res
}


二叉树的每个结点,转svg时有圆、文字、左或右直线(叶结点没有真线)。

func XmlCircle(X, Y int, Color string) string {
    Radius := 30
    Circle := "<circle cx=\"" + strconv.Itoa(X) + "\" cy=\"" + strconv.Itoa(Y) +
        "\" r=\"" + strconv.Itoa(Radius) + "\" stroke=\"black\" stroke-width=" +
        "\"2\" fill=\"" + Color + "\" />"
    return Circle
}
func XmlText(X, Y int, DATA string) string {
    iFontSize, tColor := 20, "red"
    Text := "<text x=\"" + strconv.Itoa(X) + "\" y=\"" + strconv.Itoa(Y) +
        "\" fill=\"" + tColor + "\" font-size=\"" + strconv.Itoa(iFontSize) +
        "\" text-anchor=\"middle\" dominant-baseline=\"middle\">" + DATA + "</text>"
    return Text
}
func XmlLine(X1, Y1, X2, Y2 int) string {
    Line := "<line x1=\"" + strconv.Itoa(X1) + "\" y1=\"" + strconv.Itoa(Y1) +
        "\" x2=\"" + strconv.Itoa(X2) + "\" y2=\"" + strconv.Itoa(Y2) +
        "\" style=\"stroke:black;stroke-width:2\" />"
    return Line
}


TreeInfo()写入二叉树结点信息,其中DataLevel是层序遍历的结果,也可以用它来作图。

Info2XML()就是把上述方法所得信息,转化成SVG的xml代码;

ShowSVG()生成并显示图形,svg的xml如下:

<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.1" width="680" height="400">
<a xlink:href="https://blog.csdn.net/boysoft2002" target="_blank">
    <text x="5" y="20" fill="blue">Hann's CSDN Homepage</text></a>
    <g id="0,0,0">
    <circle cx="320" cy="60" r="30" stroke="black" stroke-width="2" fill="orange" />
    <text x="320" y="60" fill="red" font-size="20" text-anchor="middle" dominant-baseline="middle">*</text>
    <line x1="299" y1="81" x2="160" y2="130" style="stroke:black;stroke-width:2" />
    <line x1="341" y1="81" x2="480" y2="130" style="stroke:black;stroke-width:2" />
    </g>
    <g id="0,-4,1">
    <circle cx="160" cy="160" r="30" stroke="black" stroke-width="2" fill="orange" />
    <text x="160" y="160" fill="red" font-size="20" text-anchor="middle" dominant-baseline="middle">*</text>
    <line x1="139" y1="181" x2="80" y2="230" style="stroke:black;stroke-width:2" />
    <line x1="181" y1="181" x2="240" y2="230" style="stroke:black;stroke-width:2" />
    </g>
    <g id="0,-6,2">
    <circle cx="80" cy="260" r="30" stroke="black" stroke-width="2" fill="orange" />
    <text x="80" y="260" fill="red" font-size="20" text-anchor="middle" dominant-baseline="middle">/</text>
    <line x1="59" y1="281" x2="40" y2="330" style="stroke:black;stroke-width:2" />
    <line x1="101" y1="281" x2="120" y2="330" style="stroke:black;stroke-width:2" />
    </g>
    <g id="0,-7,3">
    <circle cx="40" cy="360" r="30" stroke="black" stroke-width="2" fill="lightgreen" />
    <text x="40" y="360" fill="red" font-size="20" text-anchor="middle" dominant-baseline="middle">1</text>
    <LEAF/>
    </g>
    <g id="0,-5,3">
    <circle cx="120" cy="360" r="30" stroke="black" stroke-width="2" fill="lightgreen" />
    <text x="120" y="360" fill="red" font-size="20" text-anchor="middle" dominant-baseline="middle">3</text>
    <LEAF/>
    </g>
    <g id="0,-2,2">
    <circle cx="240" cy="260" r="30" stroke="black" stroke-width="2" fill="lightgreen" />
    <text x="240" y="260" fill="red" font-size="20" text-anchor="middle" dominant-baseline="middle">5</text>
    <LEAF/>
    </g>
    <g id="0,4,1">
    <circle cx="480" cy="160" r="30" stroke="black" stroke-width="2" fill="orange" />
    <text x="480" y="160" fill="red" font-size="20" text-anchor="middle" dominant-baseline="middle">*</text>
    <line x1="459" y1="181" x2="400" y2="230" style="stroke:black;stroke-width:2" />
    <line x1="501" y1="181" x2="560" y2="230" style="stroke:black;stroke-width:2" />
    </g>
    <g id="0,2,2">
    <circle cx="400" cy="260" r="30" stroke="black" stroke-width="2" fill="orange" />
    <text x="400" y="260" fill="red" font-size="20" text-anchor="middle" dominant-baseline="middle">*</text>
    <line x1="379" y1="281" x2="360" y2="330" style="stroke:black;stroke-width:2" />
    <line x1="421" y1="281" x2="440" y2="330" style="stroke:black;stroke-width:2" />
    </g>
    <g id="0,1,3">
    <circle cx="360" cy="360" r="30" stroke="black" stroke-width="2" fill="lightgreen" />
    <text x="360" y="360" fill="red" font-size="20" text-anchor="middle" dominant-baseline="middle">6</text>
    <LEAF/>
    </g>
    <g id="0,3,3">
    <circle cx="440" cy="360" r="30" stroke="black" stroke-width="2" fill="lightgreen" />
    <text x="440" y="360" fill="red" font-size="20" text-anchor="middle" dominant-baseline="middle">6</text>
    <LEAF/>
    </g>
    <g id="0,6,2">
    <circle cx="560" cy="260" r="30" stroke="black" stroke-width="2" fill="lightgreen" />
    <text x="560" y="260" fill="red" font-size="20" text-anchor="middle" dominant-baseline="middle">3.14</text>
    <LEAF/>
    </g>
</svg>



扩展

多棵二叉树同时展示,Info2SVG()可以设置起始位置



左右并列展示

  tree2 := Build("*", "*", 3.14, 6, 6)
  tree2.TreeInfo()
  tree2.Info2SVG()
  tree2.ShowSVG("tree2")
  //左右并列展示
  tree2.Info2SVG(tree.Info.SvgWidth, tree.Info.SpaceY)
  tree.Info.SvgXml += tree2.Info.SvgXml
  tree.Info.SvgWidth += tree2.Info.SvgWidth
  tree.ShowSVG("tree12")
  tree.Info2SVG() //恢复tree原状

265042bf86be421a81c23c959ff92794.png




上下并列展示

  //上下并列展示
  tree2.Info2SVG(tree.Info.SvgWidth-tree2.Info.SvgWidth, tree.Info.SvgHeight)
  tree.Info.SvgXml += tree2.Info.SvgXml
  tree.Info.SvgHeight += tree2.Info.SvgHeight
  tree.ShowSVG("tree123")
  tree.Info2SVG() //恢复tree原状

以上2段代码放在前文源代码的main()函数中测试。


60f665e58e2b461d8a067d9b6e776683.png




总结回顾


结点显示的代码固定了文字和圆形的大小颜色,如果读者愿意自己动手的话,可以尝试把这些要素设成参数或者增加biTreeInfo结构的属性。


ac17f04147fc4162b4e70de9b25eaaa3.png





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