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
源代码
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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。
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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：
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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）。
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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：
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<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
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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 |
上下并列展示
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//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。
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。
