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
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
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
//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。
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。
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