Go语言数据结构之二叉树可视化详解

2022-12-03 13:52 开发作者： Hann

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

Go语言数据结构之二叉树可视化详解

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]
 android   }
    info.MarginX, inf编程客栈o.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[编程客栈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/>",http://www.devze.com 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-siwww.devze.comze=\"" + 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-basel开发者_Go培训ine="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

Go语言数据结构之二叉树可视化详解

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。

Go语言数据结构之二叉树可视化详解

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。

Go语言数据结构之二叉树可视化详解

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继续阅读：Go 二叉树 Go语言二叉树 Go语言二叉树可视化

Go语言数据结构之二叉树可视化详解

目录

题目

源代码

做题思路

扩展

左右并列展示

上下并列展示

总结回顾

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