Atsižvelgiant į a prijungtas neorientuotas grafikas atstovaujama gretimų sąraše adjList[][] su n mazgai ir m briaunos, kurių kiekvienas mazgas turi a išskirtinė etiketė iš nuo 0 iki n-1 ir kiekvienas adj[i] reiškia viršūnių, sujungtų su i viršūne, sąrašą.
Sukurti a klonas grafiko, kuriame kiekviename grafiko mazge yra sveikasis skaičius val ir masyvas ( kaimynai ) mazgų kuriuose yra mazgų, kurie yra greta dabartinio mazgo.
klasės mazgas {
val: sveikasis skaičius
kaimynai: sąrašas[mazgas]
}
Jūsų užduotis yra klonuoti pateiktą grafiką ir grąžinti nuorodą į klonuotą grafiką.
palindromas java
Pastaba: Jei grąžinsite teisingą pateikto grafiko kopiją, išvestis bus teisinga; Priešingu atveju, jei kopija bus neteisinga, ji išspausdins klaidingą.
Pavyzdžiai
Įvestis: n = 4 adjList[][] = [[1 2] [0 2] [0 1 3] [2]]
Išvestis: tiesa
Paaiškinimas:
Kadangi klonuotas grafikas yra identiškas originalui, išvestis bus teisinga.Įvestis: n = 3 adjList[][] = [[1 2] [0] [0]]
Išvestis: tiesa
Paaiškinimas:
Kadangi klonuotas grafikas yra identiškas originalui, išvestis bus teisinga.
Turinio lentelė
- Kodėl mums reikia sekti aplankytus / klonuotus mazgus?
- Kaip sekti aplankytus/klonuotus mazgus?
- Kaip sujungti klonų mazgus?
- Kaip patikrinti, ar klonuotas grafikas yra teisingas?
- [1 metodas] Naudojant BFS perėjimą – O(V+E) laikas ir O(V) erdvė
- [2 metodas] Naudojant DFS perėjimą – O(V+E) laikas ir O(V) erdvė
Kodėl mums reikia sekti aplankytus / klonuotus mazgus?
Turime sekti aplankytus arba klonuotus mazgus, kad išvengtume begalinės rekursijos ir perteklinio darbo klonuojant grafiką. Kadangi diagramose gali būti ciklų (kai mazgas gali nukreipti atgal į anksčiau aplankytą mazgą), nesaugodami jau klonuotų mazgų, klonavimo funkcija be galo iš naujo aplankys tuos pačius mazgus, o tai sukeltų krūvos perpildymą arba neteisingą dubliavimą.
Kaip sekti aplankytus/klonuotus mazgus?
Norint išlaikyti visus jau sukurtus mazgus, reikalingas HashMap / Map. Raktų parduotuvės : pradinio mazgo nuoroda / adresas Vertės parduotuvės : Klonuoto mazgo nuoroda / adresas Padaryta visų grafiko mazgų kopija.
Kaip sujungti klonų mazgus?
Lankantis gretimose a viršūnėse mazgas in gauti atitinkamą klonuotą mazgas nes tu tai vadinkim IN dabar aplankykite visus gretimus mazgus in ir kiekvienam kaimynui suraskite atitinkamą klono mazgą (jei nerastas, sukurkite jį) ir tada įstumkite į gretimą vektorių IN mazgas.
Kaip patikrinti, ar klonuotas grafikas yra teisingas?
Prieš klonavimą atlikite BFS perėjimą pirminiame grafike, o baigę klonuoti – dar kartą klonuotame grafike. Kiekvienos kelionės metu atspausdinkite kiekvieno mazgo vertę kartu su jo adresu (arba nuoroda). Norėdami patikrinti klonavimo teisingumą, palyginkite aplankytų mazgų tvarką abiejose kelionėse. Jei mazgų reikšmės rodomos ta pačia tvarka, bet skiriasi jų adresai (arba nuorodos), tai patvirtina, kad grafikas buvo sėkmingai ir teisingai klonuotas.
komanda mazge js
Ištirkite, kaip klonuoti neorientuotą grafiką, įskaitant grafikus su keliais sujungtais komponentais naudojant BFS arba DFS, kad būtų užtikrinta visa gili visų mazgų ir kraštų kopija.
[1 metodas] Naudojant BFS perėjimą – O(V+E) laikas ir O(V) erdvė
C++Taikant BFS metodą, grafikas klonuojamas iteratyviai naudojant eilę. Pradedame nuo pradinio mazgo klonavimo ir įtraukimo į eilę. Apdorodami kiekvieną mazgą iš eilės, aplankome jo kaimynus. Jei kaimynas dar nebuvo klonuotas, sukuriame kloną, išsaugome jį žemėlapyje ir įtraukiame į eilę vėlesniam apdorojimui. Tada pridedame kaimyno kloną į dabartinio mazgo klono kaimynų sąrašą. Šis procesas tęsiamas lygiu po lygių, užtikrinant, kad visi mazgai būtų lankomi pagal plotį. BFS ypač naudinga norint išvengti gilios rekursijos ir efektyviai valdyti didelius ar plačius grafikus.
#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');
Išvestis
true
[2 metodas] Naudojant DFS perėjimą – O(V+E) laikas ir O(V) erdvė
C++Taikant DFS metodą, grafikas klonuojamas naudojant rekursiją. Pradedame nuo nurodyto mazgo ir kiek įmanoma tyrinėjame kiekvieną šaką prieš grįžtant atgal. Žemėlapis (arba žodynas) naudojamas sekti jau klonuotus mazgus, kad būtų išvengta to paties mazgo apdorojimo kelis kartus ir tvarkyti ciklus. Kai pirmą kartą susiduriame su mazgu, sukuriame jo kloną ir saugome jį žemėlapyje. Tada kiekvienam to mazgo kaimynui mes jį rekursyviai klonuojame ir pridedame klonuotą kaimyną prie dabartinio mazgo klono. Taip užtikrinama, kad visi mazgai būtų giliai aplankomi prieš grįžtant, o grafiko struktūra būtų tiksliai nukopijuota.
#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');
Išvestis
true