转置图

有向图 G 的转置是同一组顶点上的另一个有向图，其中所有边与 G 中相应边的方向相反。也就是说，如果 G 包含边 (u, v)，则相反/ G的转置/反转包含一条边（v，u），反之亦然。
给定一个图（表示为邻接表），我们需要找到另一个图，它是给定图的转置。

例子：

转置图

Input : figure (i) is the input graph.
Output : figure (ii) is the transpose graph of the given graph.

我们遍历邻接表，当我们在顶点 u 的邻接表中找到一个顶点 v 表示主图中从 u 到 v 的一条边时，我们只需在转置图中添加一条从 v 到 u 的边，即在邻接中添加 u新图的顶点 v 列表。因此遍历主图所有顶点的列表，我们可以得到转置图。因此，算法的总时间复杂度为 O(V+E)，其中 V 是图的顶点数，E 是图的边数。
注意：获取以邻接矩阵格式存储的图形的转置很简单，您只需要获取该矩阵的转置即可。

C++

// CPP program to find transpose of a graph.
#include 
using namespace std;
  
// function to add an edge from vertex source to vertex dest
void addEdge(vector adj[], int src, int dest)
{
    adj[src].push_back(dest); 
}
  
// function to print adjacency list of a graph
void displayGraph(vector adj[], int v)
{
    for (int i = 0; i < v; i++) {
        cout << i << "--> ";
        for (int j = 0; j < adj[i].size(); j++)
            cout << adj[i][j] << "  ";
        cout << "\n";
    }
}
  
// function to get Transpose of a graph taking adjacency
// list of given graph and that of Transpose graph
void transposeGraph(vector adj[], 
                     vector transpose[], int v)
{
    // traverse the adjacency list of given graph and
    // for each edge (u, v) add an edge (v, u) in the
    // transpose graph's adjacency list
    for (int i = 0; i < v; i++)
        for (int j = 0; j < adj[i].size(); j++)
            addEdge(transpose, adj[i][j], i);
}
  
int main()
{
    int v = 5;
    vector adj[v];
    addEdge(adj, 0, 1);
    addEdge(adj, 0, 4);
    addEdge(adj, 0, 3);
    addEdge(adj, 2, 0);
    addEdge(adj, 3, 2);
    addEdge(adj, 4, 1);
    addEdge(adj, 4, 3);
  
    // Finding transpose of graph represented
    // by adjacency list adj[]
    vector transpose[v];
    transposeGraph(adj, transpose, v);
  
    // displaying adjacency list of transpose 
    // graph i.e. b
    displayGraph(transpose, v);
  
    return 0;
}

Java

// Java program to find the transpose of a graph
import java.util.*;
import java.lang.*;
import java.io.*;
  
class Graph
{
    // Total number of vertices
    private static int vertices = 5;
      
    // Find transpose of graph represented by adj
    private static ArrayList[] adj = new ArrayList[vertices];
     
    // Store the transpose of graph represented by tr
    private static ArrayList[] tr = new ArrayList[vertices];
  
    // Function to add an edge from source vertex u to 
    // destination vertex v, if choice is false the edge is added
    // to adj otherwise the edge is added to tr
    public static void addedge(int u, int v, boolean choice)
    {
        if(!choice)
            adj[u].add(v);
        else
            tr[u].add(v);
    }
  
    // Function to print the graph representation
    public static void printGraph()
    {
        for(int i = 0; i < vertices; i++)
        {
            System.out.print(i + "--> ");
            for(int j = 0; j < tr[i].size(); j++)
                System.out.print(tr[i].get(j) + " ");
            System.out.println();
        }
    }
  
    // Function to print the transpose of 
    // the graph represented as adj and store it in tr
    public static void getTranspose()
    {
  
        // Traverse the graph and for each edge u, v 
        // in graph add the edge v, u in transpose
        for(int i = 0; i < vertices; i++)
            for(int j = 0; j < adj[i].size(); j++)
                addedge(adj[i].get(j), i, true);
    }
  
    public static void main (String[] args) throws java.lang.Exception
    {
        for(int i = 0; i < vertices; i++)
        {
            adj[i] = new ArrayList();
            tr[i] = new ArrayList();
        }
        addedge(0, 1, false);
        addedge(0, 4, false);
        addedge(0, 3, false);
        addedge(2, 0, false);
        addedge(3, 2, false);
        addedge(4, 1, false);
        addedge(4, 3, false);
          
        // Finding transpose of the graph 
        getTranspose();
          
        // Printing the graph representation
        printGraph();
    }
}
  
// This code is contributed by code_freak

Python3

# Python3 program to find transpose of a graph. 
  
# function to add an edge from vertex 
# source to vertex dest 
def addEdge(adj, src, dest):
    adj[src].append(dest)
  
# function to pradjacency list 
# of a graph 
def displayGraph(adj, v):
    for i in range(v):
        print(i, "--> ", end = "")
        for j in range(len(adj[i])):
            print(adj[i][j], end = " ") 
        print()
  
# function to get Transpose of a graph 
# taking adjacency list of given graph
# and that of Transpose graph 
def transposeGraph(adj, transpose, v):
      
    # traverse the adjacency list of given 
    # graph and for each edge (u, v) add 
    # an edge (v, u) in the transpose graph's
    # adjacency list
    for i in range(v):
        for j in range(len(adj[i])):
            addEdge(transpose, adj[i][j], i)
  
# Driver Code
if __name__ == '__main__':
  
    v = 5
    adj = [[] for i in range(v)] 
    addEdge(adj, 0, 1) 
    addEdge(adj, 0, 4) 
    addEdge(adj, 0, 3) 
    addEdge(adj, 2, 0) 
    addEdge(adj, 3, 2) 
    addEdge(adj, 4, 1) 
    addEdge(adj, 4, 3) 
  
    # Finding transpose of graph represented 
    # by adjacency list adj[] 
    transpose = [[]for i in range(v)]
    transposeGraph(adj, transpose, v) 
  
    # displaying adjacency list of 
    # transpose graph i.e. b 
    displayGraph(transpose, v)
  
# This code is contributed by PranchalK

C#

// C# program to find the transpose of a graph
using System;
using System.Collections.Generic;
  
class Graph
{
    // Total number of vertices
    private static int vertices = 5;
      
    // Find transpose of graph represented by adj
    private static List[] adj = new List[vertices];
      
    // Store the transpose of graph represented by tr
    private static List[] tr = new List[vertices];
  
    // Function to add an edge from source vertex u to 
    // destination vertex v, if choice is false the edge is added
    // to adj otherwise the edge is added to tr
    public static void addedge(int u, int v, bool choice)
    {
        if(!choice)
            adj[u].Add(v);
        else
            tr[u].Add(v);
    }
  
    // Function to print the graph representation
    public static void printGraph()
    {
        for(int i = 0; i < vertices; i++)
        {
            Console.Write(i + "--> ");
            for(int j = 0; j < tr[i].Count; j++)
                Console.Write(tr[i][j] + " ");
            Console.WriteLine();
        }
    }
  
    // Function to print the transpose of 
    // the graph represented as adj and store it in tr
    public static void getTranspose()
    {
  
        // Traverse the graph and for each edge u, v 
        // in graph add the edge v, u in transpose
        for(int i = 0; i < vertices; i++)
            for(int j = 0; j < adj[i].Count; j++)
                addedge(adj[i][j], i, true);
    }
  
    // Driver code
    public static void Main(String[] args)
    {
        for(int i = 0; i < vertices; i++)
        {
            adj[i] = new List();
            tr[i] = new List();
        }
        addedge(0, 1, false);
        addedge(0, 4, false);
        addedge(0, 3, false);
        addedge(2, 0, false);
        addedge(3, 2, false);
        addedge(4, 1, false);
        addedge(4, 3, false);
          
        // Finding transpose of the graph 
        getTranspose();
          
        // Printing the graph representation
        printGraph();
    }
}
  
  
// This code is contributed by Rajput-Ji

输出：

0--> 2  
1--> 0  4  
2--> 3  
3--> 0  4  
4--> 0