dado un gráfico no dirigido conectado representado por lista de adyacencia listaadj[][] con norte nodos y metro bordes con cada nodo teniendo un etiqueta distinta de 0 a n-1 y cada adj[i] representa la lista de vértices conectados al vértice i.
Crear un clon del gráfico donde cada nodo del gráfico contiene un número entero vale y una matriz ( vecinos ) de nodos que contiene nodos que son adyacentes al nodo actual.
clase Nodo {
valor: entero
vecinos: Lista[Nodo]
}
Su tarea es clonar el gráfico dado y devolver una referencia al gráfico clonado.
Nota: Si devuelve una copia correcta del gráfico dado, el resultado será verdadero; de lo contrario, si la copia es incorrecta, se imprimirá falsa.
Ejemplos
Aporte: n = 4 ListaAdj[][] = [[1 2] [0 2] [0 1 3] [2]]
Producción: verdadero
Explicación:
Dado que el gráfico clonado es idéntico al original, el resultado será verdadero.Aporte: n = 3 ListaAdj[][] = [[1 2] [0] [0]]
Producción: verdadero
Explicación:
Dado que el gráfico clonado es idéntico al original, el resultado será verdadero.
Tabla de contenido
- ¿Por qué necesitamos realizar un seguimiento de los nodos visitados/clonados?
- ¿Cómo realizar un seguimiento de los nodos visitados/clonados?
- ¿Cómo conectar nodos clonados?
- ¿Cómo verificar si el gráfico clonado es correcto?
- [Método 1] Uso del recorrido BFS: tiempo O(V+E) y espacio O(V)
- [Método 2] Uso del recorrido DFS: tiempo O(V+E) y espacio O(V)
¿Por qué necesitamos realizar un seguimiento de los nodos visitados/clonados?
Necesitamos realizar un seguimiento de los nodos visitados o clonados para evitar la recursividad infinita y el trabajo redundante al clonar un gráfico. Dado que los gráficos pueden contener ciclos (donde un nodo puede apuntar a un nodo visitado anteriormente) sin realizar un seguimiento de los nodos que ya hemos clonado, la función de clonación volvería a visitar interminablemente los mismos nodos, lo que provocaría un desbordamiento de la pila o una duplicación incorrecta.
¿Cómo realizar un seguimiento de los nodos visitados/clonados?
Se requiere un HashMap/Map para mantener todos los nodos que ya se han creado. Tiendas clave : Referencia/Dirección del Nodo original Tiendas de valor : Referencia/Dirección del Nodo clonado Se ha realizado una copia de todos los nodos del gráfico.
¿Cómo conectar nodos clonados?
Al visitar los vértices vecinos de un nodo en conseguir el clonado correspondiente nodo para ti llamemos a eso EN ahora visite todos los nodos vecinos para en y para cada vecino busque el nodo clon correspondiente (si no lo encuentra, cree uno) y luego presione el vector vecino de EN nodo.
¿Cómo verificar si el gráfico clonado es correcto?
Realice un recorrido BFS en el gráfico original antes de la clonación y luego nuevamente en el gráfico clonado una vez completada la clonación. Durante cada recorrido, imprima el valor de cada nodo junto con su dirección (o referencia). Para verificar la exactitud de la clonación, compare el orden de los nodos visitados en ambos recorridos. Si los valores de los nodos aparecen en el mismo orden pero sus direcciones (o referencias) difieren, confirma que el gráfico se ha clonado exitosa y correctamente.
Explora cómo clonar un gráfico no dirigido que incluye gráficos con múltiples componentes conectados utilizando BFS o DFS para garantizar una copia profunda completa de todos los nodos y bordes.
[Método 1] Uso del recorrido BFS: tiempo O(V+E) y espacio O(V)
C++En el enfoque BFS, el gráfico se clona de forma iterativa mediante una cola. Comenzamos clonando el nodo inicial y colocándolo en la cola. A medida que procesamos cada nodo de la cola, visitamos a sus vecinos. Si un vecino aún no ha sido clonado, creamos un clon, lo almacenamos en un mapa y lo ponemos en cola para su posterior procesamiento. Luego agregamos el clon del vecino a la lista de vecinos del clon del nodo actual. Este proceso continúa nivel por nivel asegurando que todos los nodos sean visitados en orden de amplitud. BFS es particularmente útil para evitar la recursividad profunda y manejar gráficos grandes o anchos de manera eficiente.
#include
import java.util.*; // Definition for a Node class Node { public int val; public ArrayList<Node> neighbors; public Node() { neighbors = new ArrayList<>(); } public Node(int val) { this.val = val; neighbors = new ArrayList<>(); } } public class GfG { // Clone the graph public static Node cloneGraph(Node node) { if (node == null) return null; Map<Node Node> mp = new HashMap<>(); Queue<Node> q = new LinkedList<>(); // Clone the starting node Node clone = new Node(node.val); mp.put(node clone); q.offer(node); while (!q.isEmpty()) { Node current = q.poll(); for (Node neighbor : current.neighbors) { // Clone neighbor if it hasn't been cloned yet if (!mp.containsKey(neighbor)) { mp.put(neighbor new Node(neighbor.val)); q.offer(neighbor); } // Add the clone of the neighbor to the current node's clone mp.get(current).neighbors.add(mp.get(neighbor)); } } return mp.get(node); } // Build graph public static Node buildGraph() { Node node1 = new Node(0); Node node2 = new Node(1); Node node3 = new Node(2); Node node4 = new Node(3); node1.neighbors.addAll(new ArrayList<> (Arrays.asList(node2 node3))); node2.neighbors.addAll(new ArrayList<> (Arrays.asList(node1 node3))); node3.neighbors.addAll(new ArrayList<> (Arrays.asList(node1 node2 node4))); node4.neighbors.addAll(new ArrayList<> (Arrays.asList(node3))); return node1; } // Compare two graphs for structure and value public static boolean compareGraphs(Node n1 Node n2 HashMap<Node Node> visited) { if (n1 == null || n2 == null) return n1 == n2; if (n1.val != n2.val || n1 == n2) return false; visited.put(n1 n2); if (n1.neighbors.size() != n2.neighbors.size()) return false; for (int i = 0; i < n1.neighbors.size(); i++) { Node neighbor1 = n1.neighbors.get(i); Node neighbor2 = n2.neighbors.get(i); if (visited.containsKey(neighbor1)) { if (visited.get(neighbor1) != neighbor2) return false; } else { if (!compareGraphs(neighbor1 neighbor2 visited)) return false; } } return true; } public static void main(String[] args) { Node original = buildGraph(); Node cloned = cloneGraph(original); boolean isEqual = compareGraphs(original cloned new HashMap<>()); System.out.println(isEqual ? 'true' : 'false'); } }
from collections import deque # Definition for a Node class Node: def __init__(self val=0): self.val = val self.neighbors = [] # Clone the graph def cloneGraph(node): if not node: return None # Map to hold original nodes as keys and their clones as values mp = {} # Initialize BFS queue q = deque([node]) # Clone the starting node mp[node] = Node(node.val) while q: current = q.popleft() for neighbor in current.neighbors: # If neighbor not cloned yet if neighbor not in mp: mp[neighbor] = Node(neighbor.val) q.append(neighbor) # Link clone of neighbor to the clone of the current node mp[current].neighbors.append(mp[neighbor]) return mp[node] # Build graph def buildGraph(): node1 = Node(0) node2 = Node(1) node3 = Node(2) node4 = Node(3) node1.neighbors = [node2 node3] node2.neighbors = [node1 node3] node3.neighbors = [node1 node2 node4] node4.neighbors = [node3] return node1 # Compare two graphs structurally and by values def compareGraphs(n1 n2 visited): if not n1 or not n2: return n1 == n2 if n1.val != n2.val or n1 is n2: return False visited[n1] = n2 if len(n1.neighbors) != len(n2.neighbors): return False for i in range(len(n1.neighbors)): neighbor1 = n1.neighbors[i] neighbor2 = n2.neighbors[i] if neighbor1 in visited: if visited[neighbor1] != neighbor2: return False else: if not compareGraphs(neighbor1 neighbor2 visited): return False return True # Driver if __name__ == '__main__': original = buildGraph() cloned = cloneGraph(original) result = compareGraphs(original cloned {}) print('true' if result else 'false')
using System; using System.Collections.Generic; // Definition for a Node public class Node { public int val; public List<Node> neighbors; public Node() { neighbors = new List<Node>(); } public Node(int val) { this.val = val; neighbors = new List<Node>(); } } class GfG { // Clone the graph public static Node CloneGraph(Node node) { if (node == null) return null; var mp = new Dictionary<Node Node>(); var q = new Queue<Node>(); // Clone the starting node var clone = new Node(node.val); mp[node] = clone; q.Enqueue(node); while (q.Count > 0) { var current = q.Dequeue(); foreach (var neighbor in current.neighbors) { // If neighbor not cloned clone it and enqueue if (!mp.ContainsKey(neighbor)) { mp[neighbor] = new Node(neighbor.val); q.Enqueue(neighbor); } // Add clone of neighbor to clone of current mp[current].neighbors.Add(mp[neighbor]); } } return mp[node]; } // Build graph public static Node BuildGraph() { var node1 = new Node(0); var node2 = new Node(1); var node3 = new Node(2); var node4 = new Node(3); node1.neighbors.AddRange(new[] { node2 node3 }); node2.neighbors.AddRange(new[] { node1 node3 }); node3.neighbors.AddRange(new[] { node1 node2 node4 }); node4.neighbors.AddRange(new[] { node3 }); return node1; } // Compare two graphs for structure and value public static bool CompareGraphs(Node n1 Node n2 Dictionary<Node Node> visited) { if (n1 == null || n2 == null) return n1 == n2; if (n1.val != n2.val || ReferenceEquals(n1 n2)) return false; visited[n1] = n2; if (n1.neighbors.Count != n2.neighbors.Count) return false; for (int i = 0; i < n1.neighbors.Count; i++) { var neighbor1 = n1.neighbors[i]; var neighbor2 = n2.neighbors[i]; if (visited.ContainsKey(neighbor1)) { if (!ReferenceEquals(visited[neighbor1] neighbor2)) return false; } else { if (!CompareGraphs(neighbor1 neighbor2 visited)) return false; } } return true; } public static void Main() { var original = BuildGraph(); var cloned = CloneGraph(original); var visited = new Dictionary<Node Node>(); Console.WriteLine(CompareGraphs(original cloned visited) ? 'true' : 'false'); } }
// Definition for a Node class Node { constructor(val = 0) { this.val = val; this.neighbors = []; } } // Clone the graph function cloneGraph(node) { if (!node) return null; const mp = new Map(); const q = [node]; // Clone the initial node mp.set(node new Node(node.val)); while (q.length > 0) { const current = q.shift(); for (const neighbor of current.neighbors) { if (!mp.has(neighbor)) { mp.set(neighbor new Node(neighbor.val)); q.push(neighbor); } // Link clone of neighbor to clone of current mp.get(current).neighbors.push(mp.get(neighbor)); } } return mp.get(node); } // Build graph function buildGraph() { const node1 = new Node(0); const node2 = new Node(1); const node3 = new Node(2); const node4 = new Node(3); node1.neighbors = [node2 node3]; node2.neighbors = [node1 node3]; node3.neighbors = [node1 node2 node4]; node4.neighbors = [node3]; return node1; } // Compare two graphs structurally and by value function compareGraphs(n1 n2 visited = new Map()) { if (!n1 || !n2) return n1 === n2; if (n1.val !== n2.val || n1 === n2) return false; visited.set(n1 n2); if (n1.neighbors.length !== n2.neighbors.length) return false; for (let i = 0; i < n1.neighbors.length; i++) { const neighbor1 = n1.neighbors[i]; const neighbor2 = n2.neighbors[i]; if (visited.has(neighbor1)) { if (visited.get(neighbor1) !== neighbor2) return false; } else { if (!compareGraphs(neighbor1 neighbor2 visited)) return false; } } return true; } // Driver const original = buildGraph(); const cloned = cloneGraph(original); const result = compareGraphs(original cloned); console.log(result ? 'true' : 'false');
Producción
true
[Método 2] Uso del recorrido DFS: tiempo O(V+E) y espacio O(V)
C++En el enfoque DFS, el gráfico se clona mediante recursividad. Comenzamos desde el nodo dado y exploramos lo más lejos posible a lo largo de cada rama antes de retroceder. Se utiliza un mapa (o diccionario) para realizar un seguimiento de los nodos ya clonados para evitar procesar el mismo nodo varias veces y manejar ciclos. Cuando encontramos un nodo por primera vez, creamos un clon del mismo y lo almacenamos en el mapa. Luego, para cada vecino de ese nodo, lo clonamos recursivamente y agregamos el vecino clonado al clon del nodo actual. Esto garantiza que todos los nodos se visiten profundamente antes de regresar y que la estructura del gráfico se copie fielmente.
#include
import java.util.*; // Definition for a Node class Node { int val; ArrayList<Node> neighbors; Node() { neighbors = new ArrayList<>(); } Node(int val) { this.val = val; neighbors = new ArrayList<>(); } } public class GfG { // Map to hold original node to its copy static HashMap<Node Node> copies = new HashMap<>(); // Function to clone the graph using DFS public static Node cloneGraph(Node node) { // If the node is NULL return NULL if (node == null) return null; // If node is not yet cloned clone it if (!copies.containsKey(node)) { Node clone = new Node(node.val); copies.put(node clone); // Recursively clone neighbors for (Node neighbor : node.neighbors) { clone.neighbors.add(cloneGraph(neighbor)); } } // Return the clone return copies.get(node); } // Build graph public static Node buildGraph() { Node node1 = new Node(0); Node node2 = new Node(1); Node node3 = new Node(2); Node node4 = new Node(3); node1.neighbors.addAll(Arrays.asList(node2 node3)); node2.neighbors.addAll(Arrays.asList(node1 node3)); node3.neighbors.addAll(Arrays.asList(node1node2 node4)); node4.neighbors.addAll(Arrays.asList(node3)); return node1; } // Compare two graphs for structural and value equality public static boolean compareGraphs(Node node1 Node node2 HashMap<Node Node> visited) { if (node1 == null || node2 == null) return node1 == node2; if (node1.val != node2.val || node1 == node2) return false; visited.put(node1 node2); if (node1.neighbors.size() != node2.neighbors.size()) return false; for (int i = 0; i < node1.neighbors.size(); i++) { Node n1 = node1.neighbors.get(i); Node n2 = node2.neighbors.get(i); if (visited.containsKey(n1)) { if (visited.get(n1) != n2) return false; } else { if (!compareGraphs(n1 n2 visited)) return false; } } return true; } // Driver Code public static void main(String[] args) { Node original = buildGraph(); // Clone the graph Node cloned = cloneGraph(original); // Compare original and cloned graph boolean result = compareGraphs(original cloned new HashMap<>()); System.out.println(result ? 'true' : 'false'); } }
# Definition for a Node class Node: def __init__(self val=0 neighbors=None): self.val = val self.neighbors = neighbors if neighbors is not None else [] # Map to hold original node to its copy copies = {} # Function to clone the graph def cloneGraph(node): # If the node is None return None if not node: return None # If node is not yet cloned clone it if node not in copies: # Create a clone of the node clone = Node(node.val) copies[node] = clone # Recursively clone neighbors for neighbor in node.neighbors: clone.neighbors.append(cloneGraph(neighbor)) # Return the clone return copies[node] def buildGraph(): node1 = Node(0) node2 = Node(1) node3 = Node(2) node4 = Node(3) node1.neighbors = [node2 node3] node2.neighbors = [node1 node3] node3.neighbors = [node1 node2 node4] node4.neighbors = [node3] return node1 # Compare two graphs for structural and value equality def compareGraphs(node1 node2 visited): if not node1 or not node2: return node1 == node2 if node1.val != node2.val or node1 is node2: return False visited[node1] = node2 if len(node1.neighbors) != len(node2.neighbors): return False for i in range(len(node1.neighbors)): n1 = node1.neighbors[i] n2 = node2.neighbors[i] if n1 in visited: if visited[n1] != n2: return False else: if not compareGraphs(n1 n2 visited): return False return True # Driver Code if __name__ == '__main__': original = buildGraph() # Clone the graph using DFS cloned = cloneGraph(original) # Compare original and cloned graph visited = {} print('true' if compareGraphs(original cloned visited) else 'false')
using System; using System.Collections.Generic; public class Node { public int val; public List<Node> neighbors; public Node() { val = 0; neighbors = new List<Node>(); } public Node(int _val) { val = _val; neighbors = new List<Node>(); } } class GfG { // Dictionary to hold original node to its copy static Dictionary<Node Node> copies = new Dictionary<Node Node>(); // Function to clone the graph using DFS public static Node CloneGraph(Node node) { // If the node is NULL return NULL if (node == null) return null; // If node is not yet cloned clone it if (!copies.ContainsKey(node)) { Node clone = new Node(node.val); copies[node] = clone; // Recursively clone neighbors foreach (Node neighbor in node.neighbors) { clone.neighbors.Add(CloneGraph(neighbor)); } } // Return the clone return copies[node]; } // Build graph public static Node BuildGraph() { Node node1 = new Node(0); Node node2 = new Node(1); Node node3 = new Node(2); Node node4 = new Node(3); node1.neighbors.Add(node2); node1.neighbors.Add(node3); node2.neighbors.Add(node1); node2.neighbors.Add(node3); node3.neighbors.Add(node1); node3.neighbors.Add(node2); node3.neighbors.Add(node4); node4.neighbors.Add(node3); return node1; } // Compare two graphs for structural and value equality public static bool CompareGraphs(Node node1 Node node2 Dictionary<Node Node> visited) { if (node1 == null || node2 == null) return node1 == node2; if (node1.val != node2.val || node1 == node2) return false; visited[node1] = node2; if (node1.neighbors.Count != node2.neighbors.Count) return false; for (int i = 0; i < node1.neighbors.Count; i++) { Node n1 = node1.neighbors[i]; Node n2 = node2.neighbors[i]; if (visited.ContainsKey(n1)) { if (visited[n1] != n2) return false; } else { if (!CompareGraphs(n1 n2 visited)) return false; } } return true; } // Driver Code public static void Main() { Node original = BuildGraph(); // Clone the graph using DFS Node cloned = CloneGraph(original); // Compare original and cloned graph bool isEqual = CompareGraphs(original cloned new Dictionary<Node Node>()); Console.WriteLine(isEqual ? 'true' : 'false'); } }
// Definition for a Node class Node { constructor(val = 0) { this.val = val; this.neighbors = []; } } // Map to hold original node to its copy const copies = new Map(); // Function to clone the graph using DFS function cloneGraph(node) { // If the node is NULL return NULL if (node === null) return null; // If node is not yet cloned clone it if (!copies.has(node)) { const clone = new Node(node.val); copies.set(node clone); // Recursively clone neighbors for (let neighbor of node.neighbors) { clone.neighbors.push(cloneGraph(neighbor)); } } // Return the clone return copies.get(node); } // Build graph function buildGraph() { const node1 = new Node(0); const node2 = new Node(1); const node3 = new Node(2); const node4 = new Node(3); node1.neighbors.push(node2 node3); node2.neighbors.push(node1 node3); node3.neighbors.push(node1 node2 node4); node4.neighbors.push(node3); return node1; } // Compare two graphs for structural and value equality function compareGraphs(node1 node2 visited = new Map()) { if (!node1 || !node2) return node1 === node2; if (node1.val !== node2.val || node1 === node2) return false; visited.set(node1 node2); if (node1.neighbors.length !== node2.neighbors.length) return false; for (let i = 0; i < node1.neighbors.length; i++) { const n1 = node1.neighbors[i]; const n2 = node2.neighbors[i]; if (visited.has(n1)) { if (visited.get(n1) !== n2) return false; } else { if (!compareGraphs(n1 n2 visited)) return false; } } return true; } // Driver Code const original = buildGraph(); // Clone the graph using DFS const cloned = cloneGraph(original); // Compare original and cloned graph console.log(compareGraphs(original cloned) ? 'true' : 'false');
Producción
true