2024-07-12
한어Русский языкEnglishFrançaisIndonesianSanskrit日本語DeutschPortuguêsΕλληνικάespañolItalianoSuomalainenLatina
In adiacentiis notae repraesentationis in unumquodque vertex conexum vvv Est index coniunctus, et uterque nodi in indice coniuncto servum repraesentat vvv ora incipiens.ut ratio GTG^TGT, opus est percurrere GGG pro quolibet ore , et aversa directione crepidinis, adde to GTG^TGT in album coniunctum respondentem.
Ite linguam exsecutionem：
package main
import (
"fmt"
)
// Graph 使用邻接链表表示
type Graph struct {
vertices int
adjList map[int][]int
}
// NewGraph 创建一个新的图
func NewGraph(vertices int) *Graph {
return &Graph{
vertices: vertices,
adjList: make(map[int][]int),
}
}
// AddEdge 添加一条边到图中
func (g *Graph) AddEdge(u, v int) {
g.adjList[u] = append(g.adjList[u], v)
}
// Transpose 计算图的转置
func (g *Graph) Transpose() *Graph {
gT := NewGraph(g.vertices)
for u, adj := range g.adjList {
for _, v := range adj {
gT.AddEdge(v, u) // 反转边的方向
}
}
return gT
}
func main() {
g := NewGraph(4)
g.AddEdge(0, 1)
g.AddEdge(0, 2)
g.AddEdge(1, 2)
g.AddEdge(2, 0)
g.AddEdge(2, 3)
gT := g.Transpose()
fmt.Println("Original Graph:")
for u, adj := range g.adjList {
fmt.Printf("%d -> %vn", u, adj)
}
fmt.Println("nTransposed Graph:")
for u, adj := range gT.adjList {
fmt.Printf("%d -> %vn", u, adj)
}
}
tempus complexionem：
In adiacentiis matricis repraesentatio utimur duo dimensiva ordinata ad informationem marginem reponendam, ubi matrix[u][v] Indicat an sit linea e* uu*u****** venire vvv latus.ut ratio GTG^TGTsuperiorem triangulum (seu triangulum inferiorem, secundum matrix repraesentationis habitum) percurrimus matricis, et convertimus directionem orarum, id est; matrix[u][v] De valore assignatamatrixT[v][u]。
Ite linguam exsecutionem(versio simplicior, solum existentiam considerat et ora pondera non considerat);
// 假设使用二维布尔切片表示邻接矩阵
type GraphMatrix [][]bool
// Transpose 计算图的转置
func (g GraphMatrix) Transpose() GraphMatrix {
n := len(g)
gT := make(GraphMatrix, n)
for i := range gT {
gT[i] = make([]bool, n)
}
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
gT[j][i] = g[i][j] // 反转边的方向
}
}
return gT
}
// 注意：这里没有完整的GraphMatrix类型实现，因为示例仅关注Transpose函数
tempus complexionem：
Nam graphi directi per album adiacentii repraesentati, vertices cuiusque vertex adiacentes adiacenti addere possumus album vertex transpositi novi graphi percurso adiacentiis cuiusvis vertex. Imprimis gradus sunt haec:
Tempus complexionem analysis: percurso verticem originalis graph requirit O ( V ) O (|V|)O********************(∣V∣) Tempus requiritur ad percurrendum adiacentiam index cuiusque vertex est O ( E ) O ( | E | )O********************(∣E∣) tempus, sic totum tempus complexionis est O ( V + E ) O (|V| + |E|)O********************(∣V∣+∣E∣)。
Ad graphum directum, quod matrix adiacentia repraesentatum est, consequi possumus adiacentia matrix novi graphi, transponendo adiacentia matrix graphi originalis. Imprimis gradus sunt haec:
Tempus multiplicitatis analysis: percurso adiacentia matrix graphi originalis requirit O ( V 2 ) O ( | V | ^ 2 )O********************(∣V∣2) tempus, sic totum tempus complexionis est O ( V 2 ) O ( | V | ^ 2 )O********************(∣V∣2)。
Sequentia est codicem in lingua Go implendum:
// 邻接链表表示的有向图转置
func transposeAdjList(G map[int][]int) map[int][]int {
GT := make(map[int][]int)
for v, neighbors := range G {
for _, u := range neighbors {
GT[u] = append(GT[u], v)
}
}
return GT
}
// 邻接矩阵表示的有向图转置
func transposeAdjMatrix(G [][]int) [][]int {
n := len(G)
GT := make([][]int, n)
for i := range GT {
GT[i] = make([]int, n)
}
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
GT[j][i] = G[i][j]
}
}
return GT
}
In album adiacentiis repraesentatio, imaginem originalem directe percurrere possumus GGGIndicem adiacentiae cuiuslibet nodi tunc additur novo grapho post directionem cuiusque marginem convertendo. GTG^{T}GTin nodi correspondentes.
type Graph struct {
Vertices []*Node // 存储图中所有节点的指针
}
type Node struct {
Value int
Adjacent []*Node // 存储与该节点相邻的所有节点的指针
}
func (g *Graph) Transpose() *Graph {
transposed := &Graph{make([]*Node, len(g.Vertices))}
for i, node := range g.Vertices {
transposed.Vertices[i] = &Node{node.Value, make([]*Node, 0)}
}
for _, node := range g.Vertices {
for _, adj := range node.Adjacent {
// 将边反向添加到转置图中
transposed.Vertices[adj.Value].Adjacent = append(transposed.Vertices[adj.Value].Adjacent, transposed.Vertices[node.Value])
}
}
return transposed
}
ergo totum tempus complexionis est O ( V + E ) O (|V| + |E|)O********************(∣V∣+∣E∣)。
In notatione matricis adiacentia novam matricem adiacentiam creare possumus ac deinde imaginem originalem percurrere GGGmatrix adiacentia, quodlibet elementum in matrice ( i , j )(ego,j)assignata novae matricis ( j , i )(j,ego)situm, sicque inversionem in marginem complens.
type MatrixGraph struct {
Matrix [][]bool // 存储邻接矩阵
}
func (mg *MatrixGraph) Transpose() *MatrixGraph {
transposed := &MatrixGraph{make([][]bool, len(mg.Matrix))}
for i := range mg.Matrix {
transposed.Matrix[i] = make([]bool, len(mg.Matrix))
for j := range mg.Matrix[i] {
// 将边反向赋值到转置矩阵中
transposed.Matrix[i][j] = mg.Matrix[j][i]
}
}
return transposed
}
ergo totum tempus complexionis est O ( V 2 ) O ( | V | ^ 2 )O********************(∣V∣2)。
Ad adiacentiam coniunctio repraesentatio indice, tempus complexionis algorithmi transpositi est O ( V + E ) O (|V| + |E|)O********************(∣V∣+∣E∣)ac pro adiacentiis matricis repraesentatio, tempus complexionis transpositi algorithmus est O ( V 2 ) O ( | V | ^ 2 )O********************(∣V∣2) .In applicationibus, si graph est sparsum (i.e. E |E|∣E∣multo minus V 2 |V|^2∣V∣2 ), efficacius esset ut album repraesentationem adiacentiam coniunctum adhiberet.Si graph est densa (i.e. E |E|∣E∣prope V 2 |V|^2∣V∣2), tunc repraesentatio matrix adiacentia aptior esse potest.
In graphe repraesentatione, adiacentia connexae tabulae et adiacentia matrices sunt ambo modi communiter usi. Indices adiacentia coniunctorum adhibentur ad graphas indirectas et directas repraesentandas, cum matrices adiacentia consueverunt graphs indedirectos repraesentare. Pro transposito graphi directi, possumus operari in album adiacentia coniunctum et matrix adiacentia separatim.
Ad graphum directum, quod per adiacentiis coniunctum indicem repraesentatum est, graphum transponendo effici potest per singulas graphi originalis vertices permensus et modificando extremas graphi originalis in oras ineuntes.
package main
import (
"fmt"
)
// 定义图的顶点结构
type Vertex struct {
Name string
Edges []*Vertex
Visited bool
}
// 计算图的转置
func Transpose(g *Vertex) {
for _, v := range g.Edges {
// 遍历顶点v的所有出边
for _, w := range v.Edges {
// 在原图中查找顶点w指向顶点v的边，并反转
for i, e := range w.Edges {
if e == v {
w.Edges[i] = v
break
}
}
}
}
}
func main() {
// 创建顶点
a := &Vertex{Name: "A"}
b := &Vertex{Name: "B"}
c := &Vertex{Name: "C"}
// 建立有向图关系
a.Edges = []*Vertex{b, c}
b.Edges = []*Vertex{a}
c.Edges = []*Vertex{a}
// 打印原图
fmt.Println("原图：")
PrintGraph(a)
// 计算转置图
Transpose(a)
// 打印转置图
fmt.Println("转置图：")
PrintGraph(a)
}
// PrintGraph 用于打印图的邻接链表表示
func PrintGraph(g *Vertex) {
g.Visited = true
for _, v := range g.Edges {
if !v.Visited {
fmt.Println(g.Name, "->", v.Name)
PrintGraph(v)
}
}
}
Nam graphi directi, matricis adiacentiis repraesentati, graphum transponendo effici potest, convertendo unumquemque graphi originalis in debitam columnam novi graphi.
package main
import (
"fmt"
)
// 计算邻接矩阵的转置
func TransposeMatrix(mat [][]int) [][]int {
transposed := make([][]int, len(mat[0]))
for i := range transposed {
transposed[i] = make([]int, len(mat))
}
for i, row := range mat {
for j, val := range row {
if val == 1 {
transposed[j][i] = 1
}
}
}
return transposed
}
func main() {
// 创建邻接矩阵
originalMatrix := [][]int{
{0, 1, 1},
{0, 0, 1},
{1, 0, 0},
}
// 计算转置矩阵
transposedMatrix := TransposeMatrix(originalMatrix)
// 打印转置矩阵
fmt.Println("转置矩阵：")
for _, row := range transposedMatrix {
fmt.Println(row)
}
}
Pro transpositione adiacentis indicem coniunctum, tempus complexionis algorithmi est O(E), ubi E numerus marginum in grapho est. Hoc est, quia utraque ora semel percurri debet.
Pro transposito adiacentiae matricis, tempus algorithm multiplicitas est O(V^2), ubi V est numerus verticerum in grapho. Causa est, quia unumquodque matrix elementum semel pertransiri debet, et magnitudo matricis est VOV.
Haec algorithms sunt omnia efficientia et currunt
Ad efficiendum algorithmus graph directa computare GGG transpositio GTG^{T}GT , possumus procedere duas repraesentationes adiacentiis connexas album et adiacentiae matricis respective. Sub his duobus casibus algorithmos describemus, et exempla codicis Go lingua praebent.
newAdjList Adhibetur ad graphum transpositum reponendum.adjList。(u, v)Adde newAdjList[v] medium.newAdjList。type Graph struct {
vertices []*Vertex
}
type Vertex struct {
key int
adjacent []*Vertex
}
func (g *Graph) Transpose() *Graph {
gt := &Graph{make([]*Vertex, len(g.vertices))}
for i := range g.vertices {
gt.vertices[i] = &Vertex{key: i}
}
for _, u := range g.vertices {
for _, v := range u.adjacent {
// Add edge (v, u) to the transpose graph.
gt.vertices[v.key].adjacent = append(gt.vertices[v.key].adjacent, gt.vertices[u.key])
}
}
return gt
}
Tempus currens algorithm huius est O(|V| + |E|), ubi |V| . est numerus verticerum et |E| Hoc est, quia omnes vertices et oras semel lustrare necesse est.
newAdjMatrix Adhibetur ad graphum transpositum reponendum.adjMatrix。adjMatrix[i][j]Tribue eam newAdjMatrix[j][i]。newAdjMatrix。type Graph struct {
matrix [][]bool
}
func (g *Graph) Transpose() *Graph {
gt := &Graph{make([][]bool, len(g.matrix))}
for i := range gt.matrix {
gt.matrix[i] = make([]bool, len(g.matrix))
}
for i := range g.matrix {
for j := range g.matrix[i] {
// Copy the adjacency values with swapped indices.
gt.matrix[j][i] = g.matrix[i][j]
}
}
return gt
}
Tempus currens algorithmus hujus est O(|V|^2), ubi |V| est numerus verticerum. Hoc est, quia necesse est totam adiantiam matricis percurrere, et magnitudo adiacentiae matricis x |V|
Exemplum supra codicem solum nucleum algorithm est. Praeterea ad simpliciorem rationem codicis, supponitur nullas in graphi margines repetitas et numeros in graphio vertex continuos numerari ab 0 incipiendo.
Sequens est algorithmus in lingua Go scriptum ad G^T ex graphi G calculare, et adiacentia matrix repraesentationis album et adiacentiae correspondentia connexum methodi traduntur;
package main
import "fmt"
// 图的节点结构体
type Node struct {
Value int // 节点的值
Next *Node // 下一个节点指针
}
// 邻接链表表示法的图结构体
type Graph struct {
Vertices []*Node // 图中所有节点的数组
}
// 添加有向边到邻接链表
func (g *Graph) AddEdge(u, v int) {
newNode := &Node{Value: v}
if g.Vertices[u] == nil {
g.Vertices[u] = newNode
} else {
curr := g.Vertices[u]
for curr.Next != nil {
curr = curr.Next
}
curr.Next = newNode
}
}
// 输出邻接链表表示的图信息
func (g *Graph) Print() {
for i, node := range g.Vertices {
fmt.Printf("顶点 %d：", i)
for node != nil {
fmt.Printf("%d ", node.Value)
node = node.Next
}
fmt.Println()
}
}
// 获取图 G 的转置图 G^T 的邻接链表表示法
func GetTranspose(g *Graph) *Graph {
transpose := &Graph{
Vertices: make([]*Node, len(g.Vertices)),
}
for i, node := range g.Vertices {
for node != nil {
v := node.Value
// 在转置图中添加反向边
transpose.AddEdge(v, i)
node = node.Next
}
}
return transpose
}
// 输出邻接链表表示的转置图信息
func PrintTranspose(g *Graph) {
fmt.Println("转置图 G^T：")
g.Print()
}
// 邻接矩阵表示法的图结构体
type Matrix struct {
Vertices [][]int // 邻接矩阵，存储边的连接关系（0 表示无边，1 表示有边）
}
// 初始化邻接矩阵表示的图
func InitMatrix(numVertices int) *Matrix {
matrix := &Matrix{
Vertices: make([][]int, numVertices),
}
for i := range matrix.Vertices {
matrix.Vertices[i] = make([]int, numVertices)
}
return matrix
}
// 添加有向边到邻接矩阵
func (m *Matrix) AddEdge(u, v int) {
m.Vertices[u][v] = 1
}
// 获取图 G 的转置图 G^T 的邻接矩阵表示法
func GetTransposeMatrix(m *Matrix) *Matrix {
numRows := len(m.Vertices)
numCols := len(m.Vertices[0])
transpose := InitMatrix(numRows)
for i := 0; i < numRows; i++ {
for j := 0; j < numCols; j++ {
if m.Vertices[i][j] == 1 {
// 在转置矩阵中添加反向边
transpose.AddEdge(j, i)
}
}
}
return transpose
}
// 输出邻接矩阵表示的转置图信息
func PrintTransposeMatrix(m *Matrix) {
numRows := len(m.Vertices)
numCols := len(m.Vertices[0])
fmt.Println("转置图 G^T：")
for i := 0; i < numRows; i++ {
fmt.Printf("顶点 %d：", i)
for j := 0; j < numCols; j++ {
if m.Vertices[i][j] == 1 {
fmt.Printf("%d ", j)
}
}
fmt.Println()
}
}
func main() {
// 邻接链表表示的有向图 G
g := &Graph{
Vertices: make([]*Node, 4),
}
g.AddEdge(0, 1)
g.AddEdge(1, 2)
g.AddEdge(2, 3)
g.AddEdge(3, 1)
// 输出原始图 G 的邻接链表表示法
fmt.Println("原始图 G：")
g.Print()
// 获取转置图 G^T 的邻接链表表示法并输出
transpose := GetTranspose(g)
PrintTranspose(transpose)
// 邻接矩阵表示的有向图 G
m := InitMatrix(4)
m.AddEdge(0, 1)
m.AddEdge(1, 2)
m.AddEdge(2, 3)
m.AddEdge(3, 1)
// 输出原始图 G 的邻接矩阵表示法
fmt.Println("原始图 G：")
for _, row := range m.Vertices {
fmt.Println(row)
}
// 获取转置图 G^T 的邻接矩阵表示法并输出
transposeMatrix := GetTransposeMatrix(m)
PrintTransposeMatrix(transposeMatrix)
}
Incomplexitas temporis huius algorithmi est O(V + E), ubi V est numerus verticerum et E numerus marginum. Constructio processus graphi transpositi postulat percurrendo omnes oras graphi archetypi et eas ad graphi transpositos transverso addens, ergo tota temporis complexio proportionalis est numero verticerum et orarum.
graphi graphi directi transpositi repraesentari possunt per duas structuras principales notitiarum: adiacentia conexae tabulae et adiacentia matrices. Subter algorithms in duobus casibus hisce respectivis introducam et codicem specimen praebebo in lingua Go.
Ad graphum per adiacentiis coniunctum indicem repraesentatum, graphum transponere possumus per adiacentiae uniuscuiusque verticem percurrendo, et deinde margini adiacentiis punctum cuique adiacenti addito. Huius methodi tempus intricatum est O(V + E), ubi V numerus verticerum est et E numerus marginum.
type Vertex struct {
Value int
Adj []Vertex
}
func transposeGraph(graph []Vertex) []Vertex {
transposed := make([]Vertex, len(graph))
for _, v := range graph {
for _, adjV := range v.Adj {
// 为邻接点添加反向边
found := false
for _, tV := range transposed[adjV.Value].Adj {
if tV.Value == v.Value {
found = true
break
}
}
if !found {
transposed[adjV.Value].Adj = append(transposed[adjV.Value].Adj, v)
}
}
}
return transposed
}
Nam lacinia, quam per adiacentia matrix repraesentata, transpositionem efficere possumus, permutando ordines et columnas matricis. Tempus complexionis huius methodi est O(V^2).
func transposeMatrix(matrix [][]int) [][]int {
n := len(matrix)
transposed := make([][]int, n)
for i := 0; i < n; i++ {
transposed[i] = make([]int, n)
for j := 0; j < n; j++ {
transposed[i][j] = matrix[j][i]
}
}
return transposed
}
In applicationibus practicis, quae algorithmus eligendi pendet a sparsitate graphi et memoriae promptae. Pro raris graphis, adiacentia connexis, plus possunt memoriae efficiens;
Calculari Aliquam lacinia purus G = ( V , E ) G=(V,E)G=(V,E) transpositio GT = ( V , ET ) G^T=(V,E^T)GT=(V,ET)algorithms correspondentes dare possumus pro duobus modis repraesentationis adiacentiae coniunctorum album et adiacentiae matricis respective, et tempus eorum currentem resolvere.
type Edge struct {
dest int
}
type AdjacencyList struct {
edges map[int][]Edge
}
func TransposeGraph(graph AdjacencyList) AdjacencyList {
transposed := AdjacencyList{edges: make(map[int][]Edge)}
for u, neighbors := range graph.edges {
for _, edge := range neighbors {
v := edge.dest
transposed.edges[v] = append(transposed.edges[v], Edge{dest: u})
}
}
return transposed
}
func main() {
// 示例图的邻接链表表示
graph := AdjacencyList{edges: map[int][]Edge{
0: {{dest: 1}},
1: {{dest: 2}},
2: {{dest: 0}},
}}
// 计算转置图
transposedGraph := TransposeGraph(graph)
// 打印转置图的邻接链表
for u, neighbors := range transposedGraph.edges {
fmt.Printf("Node %d -> Nodes: ", u)
for _, edge := range neighbors {
fmt.Printf("%d ", edge.dest)
}
fmt.Println()
}
}
In hoc codice definimus a Edge structuram repraesentet in marginibus, et aAdjacencyList Structuram adiacentiam coniunctum album repraesentare.TransposeGraph Munus accipit aAdjacencyList typus modulus et adiacentia remittit coniunctum album repraesentationis graphi transpositi.existmain munus, exemplum graphi conficimus, eius graphum transpositum calculare et imprimere debemus.
technologiae technologiae plus quam 30 annos operam dedit et in variis linguis proficit ut java, linux, javascript, php, css, etc. Multas contributiones in aperto fonte campo fecit elit documentorum statione ad communicandas quaestiones technologiarum progressus ad futuram referentiam
