Dado un gráfico dirigido, un vértice de origen ‘s’ y un vértice de destino ‘d’, imprima todas las rutas desde la ‘s’ dada hasta la ‘d’.
Considere el siguiente gráfico dirigido. Sea s 2 y d 3. Hay 3 caminos diferentes de 2 a 3.
Acercarse:
- La idea es hacer el primer recorrido en profundidad de un gráfico dirigido dado.
- Inicie el recorrido DFS desde el origen.
- Siga almacenando los vértices visitados en una array o HashMap diga ‘ruta []’.
- Si se alcanza el vértice de destino, imprime el contenido de ruta[].
- Lo importante es marcar los vértices actuales en el camino [] como visitados también para que el recorrido no vaya en un ciclo.
A continuación se muestra la implementación de la idea anterior.
C++14
// C++ program to print all paths
// from a source to destination.
#include <iostream>
#include <list>
using namespace std;
// A directed graph using
// adjacency list representation
class Graph {
int V; // No. of vertices in graph
list<int>* adj; // Pointer to an array containing
// adjacency lists
// A recursive function used by printAllPaths()
void printAllPathsUtil(int, int, bool[], int[], int&);
public:
Graph(int V); // Constructor
void addEdge(int u, int v);
void printAllPaths(int s, int d);
};
Graph::Graph(int V)
{
this->V = V;
adj = new list<int>[V];
}
void Graph::addEdge(int u, int v)
{
adj[u].push_back(v); // Add v to u’s list.
}
// Prints all paths from 's' to 'd'
void Graph::printAllPaths(int s, int d)
{
// Mark all the vertices as not visited
bool* visited = new bool[V];
// Create an array to store paths
int* path = new int[V];
int path_index = 0; // Initialize path[] as empty
// Initialize all vertices as not visited
for (int i = 0; i < V; i++)
visited[i] = false;
// Call the recursive helper function to print all paths
printAllPathsUtil(s, d, visited, path, path_index);
}
// A recursive function to print all paths from 'u' to 'd'.
// visited[] keeps track of vertices in current path.
// path[] stores actual vertices and path_index is current
// index in path[]
void Graph::printAllPathsUtil(int u, int d, bool visited[],
int path[], int& path_index)
{
// Mark the current node and store it in path[]
visited[u] = true;
path[path_index] = u;
path_index++;
// If current vertex is same as destination, then print
// current path[]
if (u == d) {
for (int i = 0; i < path_index; i++)
cout << path[i] << " ";
cout << endl;
}
else // If current vertex is not destination
{
// Recur for all the vertices adjacent to current
// vertex
list<int>::iterator i;
for (i = adj[u].begin(); i != adj[u].end(); ++i)
if (!visited[*i])
printAllPathsUtil(*i, d, visited, path,
path_index);
}
// Remove current vertex from path[] and mark it as
// unvisited
path_index--;
visited[u] = false;
}
// Driver program
int main()
{
// Create a graph given in the above diagram
Graph g(4);
g.addEdge(0, 1);
g.addEdge(0, 2);
g.addEdge(0, 3);
g.addEdge(2, 0);
g.addEdge(2, 1);
g.addEdge(1, 3);
int s = 2, d = 3;
cout << "Following are all different paths from " << s
<< " to " << d << endl;
g.printAllPaths(s, d);
return 0;
}
Java
// JAVA program to print all
// paths from a source to
// destination.
import java.util.ArrayList;
import java.util.List;
// A directed graph using
// adjacency list representation
public class Graph {
// No. of vertices in graph
private int v;
// adjacency list
private ArrayList<Integer>[] adjList;
// Constructor
public Graph(int vertices)
{
// initialise vertex count
this.v = vertices;
// initialise adjacency list
initAdjList();
}
// utility method to initialise
// adjacency list
@SuppressWarnings("unchecked")
private void initAdjList()
{
adjList = new ArrayList[v];
for (int i = 0; i < v; i++) {
adjList[i] = new ArrayList<>();
}
}
// add edge from u to v
public void addEdge(int u, int v)
{
// Add v to u's list.
adjList[u].add(v);
}
// Prints all paths from
// 's' to 'd'
public void printAllPaths(int s, int d)
{
boolean[] isVisited = new boolean[v];
ArrayList<Integer> pathList = new ArrayList<>();
// add source to path[]
pathList.add(s);
// Call recursive utility
printAllPathsUtil(s, d, isVisited, pathList);
}
// A recursive function to print
// all paths from 'u' to 'd'.
// isVisited[] keeps track of
// vertices in current path.
// localPathList<> stores actual
// vertices in the current path
private void printAllPathsUtil(Integer u, Integer d,
boolean[] isVisited,
List<Integer> localPathList)
{
if (u.equals(d)) {
System.out.println(localPathList);
// if match found then no need to traverse more till depth
return;
}
// Mark the current node
isVisited[u] = true;
// Recur for all the vertices
// adjacent to current vertex
for (Integer i : adjList[u]) {
if (!isVisited[i]) {
// store current node
// in path[]
localPathList.add(i);
printAllPathsUtil(i, d, isVisited, localPathList);
// remove current node
// in path[]
localPathList.remove(i);
}
}
// Mark the current node
isVisited[u] = false;
}
// Driver program
public static void main(String[] args)
{
// Create a sample graph
Graph g = new Graph(4);
g.addEdge(0, 1);
g.addEdge(0, 2);
g.addEdge(0, 3);
g.addEdge(2, 0);
g.addEdge(2, 1);
g.addEdge(1, 3);
// arbitrary source
int s = 2;
// arbitrary destination
int d = 3;
System.out.println(
"Following are all different paths from "
+ s + " to " + d);
g.printAllPaths(s, d);
}
}
// This code is contributed by Himanshu Shekhar.
Python3
# Python program to print all paths from a source to destination.
from collections import defaultdict
# This class represents a directed graph
# using adjacency list representation
class Graph:
def __init__(self, vertices):
# No. of vertices
self.V = vertices
# default dictionary to store graph
self.graph = defaultdict(list)
# function to add an edge to graph
def addEdge(self, u, v):
self.graph[u].append(v)
'''A recursive function to print all paths from 'u' to 'd'.
visited[] keeps track of vertices in current path.
path[] stores actual vertices and path_index is current
index in path[]'''
def printAllPathsUtil(self, u, d, visited, path):
# Mark the current node as visited and store in path
visited[u]= True
path.append(u)
# If current vertex is same as destination, then print
# current path[]
if u == d:
print (path)
else:
# If current vertex is not destination
# Recur for all the vertices adjacent to this vertex
for i in self.graph[u]:
if visited[i]== False:
self.printAllPathsUtil(i, d, visited, path)
# Remove current vertex from path[] and mark it as unvisited
path.pop()
visited[u]= False
# Prints all paths from 's' to 'd'
def printAllPaths(self, s, d):
# Mark all the vertices as not visited
visited =[False]*(self.V)
# Create an array to store paths
path = []
# Call the recursive helper function to print all paths
self.printAllPathsUtil(s, d, visited, path)
# Create a graph given in the above diagram
g = Graph(4)
g.addEdge(0, 1)
g.addEdge(0, 2)
g.addEdge(0, 3)
g.addEdge(2, 0)
g.addEdge(2, 1)
g.addEdge(1, 3)
s = 2 ; d = 3
print ("Following are all different paths from % d to % d :" %(s, d))
g.printAllPaths(s, d)
# This code is contributed by Neelam Yadav
C#
// C# program to print all
// paths from a source to
// destination.
using System;
using System.Collections.Generic;
// A directed graph using
// adjacency list representation
public class Graph {
// No. of vertices in graph
private int v;
// adjacency list
private List<int>[] adjList;
// Constructor
public Graph(int vertices)
{
// initialise vertex count
this.v = vertices;
// initialise adjacency list
initAdjList();
}
// utility method to initialise
// adjacency list
private void initAdjList()
{
adjList = new List<int>[v];
for (int i = 0; i < v; i++) {
adjList[i] = new List<int>();
}
}
// add edge from u to v
public void addEdge(int u, int v)
{
// Add v to u's list.
adjList[u].Add(v);
}
// Prints all paths from
// 's' to 'd'
public void printAllPaths(int s, int d)
{
bool[] isVisited = new bool[v];
List<int> pathList = new List<int>();
// add source to path[]
pathList.Add(s);
// Call recursive utility
printAllPathsUtil(s, d, isVisited, pathList);
}
// A recursive function to print
// all paths from 'u' to 'd'.
// isVisited[] keeps track of
// vertices in current path.
// localPathList<> stores actual
// vertices in the current path
private void printAllPathsUtil(int u, int d,
bool[] isVisited,
List<int> localPathList)
{
if (u.Equals(d)) {
Console.WriteLine(string.Join(" ", localPathList));
// if match found then no need
// to traverse more till depth
return;
}
// Mark the current node
isVisited[u] = true;
// Recur for all the vertices
// adjacent to current vertex
foreach(int i in adjList[u])
{
if (!isVisited[i]) {
// store current node
// in path[]
localPathList.Add(i);
printAllPathsUtil(i, d, isVisited,
localPathList);
// remove current node
// in path[]
localPathList.Remove(i);
}
}
// Mark the current node
isVisited[u] = false;
}
// Driver code
public static void Main(String[] args)
{
// Create a sample graph
Graph g = new Graph(4);
g.addEdge(0, 1);
g.addEdge(0, 2);
g.addEdge(0, 3);
g.addEdge(2, 0);
g.addEdge(2, 1);
g.addEdge(1, 3);
// arbitrary source
int s = 2;
// arbitrary destination
int d = 3;
Console.WriteLine("Following are all different"
+ " paths from " + s + " to " + d);
g.printAllPaths(s, d);
}
}
// This code contributed by Rajput-Ji
Javascript
<script>
// JavaScript program to print all
// paths from a source to
// destination.
let v;
let adjList;
// A directed graph using
// adjacency list representation
function Graph(vertices)
{
// initialise vertex count
v = vertices;
// initialise adjacency list
initAdjList();
}
// utility method to initialise
// adjacency list
function initAdjList()
{
adjList = new Array(v);
for (let i = 0; i < v; i++) {
adjList[i] = [];
}
}
// add edge from u to v
function addEdge(u,v)
{
// Add v to u's list.
adjList[u].push(v);
}
// Prints all paths from
// 's' to 'd'
function printAllPaths(s,d)
{
let isVisited = new Array(v);
for(let i=0;i<v;i++)
isVisited[i]=false;
let pathList = [];
// add source to path[]
pathList.push(s);
// Call recursive utility
printAllPathsUtil(s, d, isVisited, pathList);
}
// A recursive function to print
// all paths from 'u' to 'd'.
// isVisited[] keeps track of
// vertices in current path.
// localPathList<> stores actual
// vertices in the current path
function printAllPathsUtil(u,d,isVisited,localPathList)
{
if (u == (d)) {
document.write(localPathList+"<br>");
// if match found then no need to
// traverse more till depth
return;
}
// Mark the current node
isVisited[u] = true;
// Recur for all the vertices
// adjacent to current vertex
for (let i=0;i< adjList[u].length;i++) {
if (!isVisited[adjList[u][i]]) {
// store current node
// in path[]
localPathList.push(adjList[u][i]);
printAllPathsUtil(adjList[u][i], d,
isVisited, localPathList);
// remove current node
// in path[]
localPathList.splice(localPathList.indexOf
(adjList[u][i]),1);
}
}
// Mark the current node
isVisited[u] = false;
}
// Driver program
// Create a sample graph
Graph(4);
addEdge(0, 1);
addEdge(0, 2);
addEdge(0, 3);
addEdge(2, 0);
addEdge(2, 1);
addEdge(1, 3);
// arbitrary source
let s = 2;
// arbitrary destination
let d = 3;
document.write(
"Following are all different paths from "
+ s + " to " + d+"<Br>");
printAllPaths(s, d);
// This code is contributed by avanitrachhadiya2155
</script>
Producción
Following are all different paths from 2 to 3 2 0 1 3 2 0 3 2 1 3
Análisis de Complejidad:
- Complejidad de tiempo: O(V^V), La complejidad de tiempo es exponencial. De cada vértice hay v vértices que se pueden visitar desde el vértice actual.
- Espacio auxiliar: O(V^V), Para almacenar las rutas se necesita espacio V^V.
Este artículo es una contribución de Shivam Gupta . Escriba comentarios si encuentra algo incorrecto o si desea compartir más información sobre el tema tratado anteriormente.
Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA