KLONIRAJTE NEUSMJERENI GRAF

Isprobajte na GfG Practice Klonirajte neusmjereni graf' title=

S obzirom na a povezani neusmjereni graf predstavljena popisom susjedstva AdjList[][] s n čvorovi i m rubovi pri čemu svaki čvor ima a posebna oznaka iz 0 do n-1 a svaki adj[i] predstavlja popis vrhova povezanih s vrhom i.

Stvorite a klon grafa gdje svaki čvor u grafu sadrži cijeli broj val i niz ( susjedi ) čvorova koji sadrži čvorove koji su susjedni trenutnom čvoru.

klasa čvor {
val: cijeli broj
susjedi: popis[čvor]
}

Vaš zadatak je klonirati dati graf i vratiti referencu na klonirani graf.

Bilješka: Ako vratite ispravnu kopiju danog grafa, izlaz će biti istinit; inače ako je kopija netočna, ispis će biti netočan.

Primjeri

Ulazni: n = 4 adjList[][] = [[1 2] [0 2] [0 1 3] [2]]
Izlaz: pravi
Obrazloženje:

Budući da je klonirani graf identičan originalu, izlaz će biti istinit.
Ulazni: n = 3 adjList[][] = [[1 2] [0] [0]]
Izlaz: pravi
Obrazloženje:
Budući da je klonirani graf identičan originalu, izlaz će biti istinit.

Sadržaj

Zašto moramo pratiti posjećene/klonirane čvorove?
Kako pratiti posjećene/klonirane čvorove?
Kako spojiti klonirane čvorove?
Kako provjeriti je li klonirani graf točan?
[Pristup 1] Korištenje BFS traversal - O(V+E) vrijeme i O(V) prostor
[Pristup 2] Korištenje DFS traversal - O(V+E) vrijeme i O(V) prostor

Zašto moramo pratiti posjećene/klonirane čvorove?

Moramo pratiti posjećene ili klonirane čvorove kako bismo izbjegli beskonačnu rekurziju i suvišni rad prilikom kloniranja grafa. Budući da grafikoni mogu sadržavati cikluse (gdje čvor može upućivati natrag na prethodno posjećeni čvor) bez praćenja čvorova koje smo već klonirali, funkcija kloniranja bi beskrajno ponovno posjećivala iste čvorove što bi rezultiralo prekoračenjem stoga ili netočnim dupliciranjem.

Kako pratiti posjećene/klonirane čvorove?

HashMap/Map je potreban kako bi se održali svi čvorovi koji su već stvoreni. Pohrana ključeva : Referenca/adresa izvornog čvora Pohrane vrijednosti : Referenca/Adresa kloniranog čvora Napravljena je kopija svih čvorova grafa.

Kako spojiti klonirane čvorove?

Prilikom obilaska susjednih vrhova a čvor u dobiti odgovarajući klon čvor za tebe nazovimo to U sada posjetite sve susjedne čvorove za u i za svakog susjeda pronađite odgovarajući čvor klona (ako nije pronađen, stvorite jedan) i zatim gurnite u susjedni vektor od U čvor.

Kako provjeriti je li klonirani graf točan?

Izvršite BFS obilazak na izvornom grafu prije kloniranja i zatim ponovo na kloniranom grafu nakon što je kloniranje završeno. Tijekom svakog obilaska ispišite vrijednost svakog čvora zajedno s njegovom adresom (ili referencom). Kako biste provjerili ispravnost kloniranja, usporedite redoslijed čvorova posjećenih u oba obilaska. Ako se vrijednosti čvorova pojavljuju istim redoslijedom, ali se njihove adrese (ili reference) razlikuju, to potvrđuje da je graf uspješno i ispravno kloniran.

Istražite kako klonirati neusmjereni graf uključujući grafove s više povezanih komponenti koristeći BFS ili DFS kako bi se osigurala potpuna dubinska kopija svih čvorova i rubova.

[Pristup 1] Korištenje BFS traversal - O(V+E) vrijeme i O(V) prostor

U BFS pristupu graf se iterativno klonira korištenjem reda čekanja. Počinjemo kloniranjem početnog čvora i stavljanjem u red čekanja. Dok obrađujemo svaki čvor iz reda čekanja posjećujemo njegove susjede. Ako susjed još nije kloniran, stvaramo klon, pohranjujemo ga na kartu i stavljamo u red za kasniju obradu. Zatim dodajemo klon susjeda na popis susjeda klonova trenutnog čvora. Ovaj se proces nastavlja od razine do razine osiguravajući da su svi čvorovi posjećeni redoslijedom u širinu. BFS je posebno koristan za izbjegavanje duboke rekurzije i učinkovito rukovanje velikim ili širokim grafovima.

C++

#include    #include  #include  #include  using namespace std; // Definition for a Node struct Node {  int val;  vector<Node*> neighbors; }; // Clone the graph  Node* cloneGraph(Node* node) {  if (!node) return nullptr;  map<Node* Node*> mp;  queue<Node*> q;    // Clone the source node  Node* clone = new Node();  clone->val = node->val;  mp[node] = clone;  q.push(node);  while (!q.empty()) {  Node* u = q.front();  q.pop();  for (auto neighbor : u->neighbors) {    // Clone neighbor if not already cloned  if (mp.find(neighbor) == mp.end()) {  Node* neighborClone = new Node();  neighborClone->val = neighbor->val;  mp[neighbor] = neighborClone;  q.push(neighbor);  }  // Link clone of neighbor to clone of current node  mp[u]->neighbors.push_back(mp[neighbor]);  }  }  return mp[node]; } // Build graph Node* buildGraph() {  Node* node1 = new Node(); node1->val = 0;  Node* node2 = new Node(); node2->val = 1;  Node* node3 = new Node(); node3->val = 2;  Node* node4 = new Node(); node4->val = 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 bool compareGraphs(Node* node1 Node* node2   map<Node* Node*>& visited) {  if (!node1 || !node2)   return node1 == node2;    if (node1->val != node2->val || node1 == node2)  return false;  visited[node1] = node2;  if (node1->neighbors.size() != node2->neighbors.size())   return false;  for (size_t i = 0; i < node1->neighbors.size(); ++i) {  Node* n1 = node1->neighbors[i];  Node* n2 = node2->neighbors[i];  if (visited.count(n1)) {  if (visited[n1] != n2)   return false;  } else {  if (!compareGraphs(n1 n2 visited))  return false;  }  }  return true; } // Driver Code int main() {  Node* original = buildGraph();  Node* cloned = cloneGraph(original);  map<Node* Node*> visited;  cout << (compareGraphs(original cloned visited) ?   'true' : 'false') << endl;  return 0; }

Java

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');  } }

Python

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');  } }

JavaScript

// 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');

Izlaz

true

[Pristup 2] Korištenje DFS traversal - O(V+E) vrijeme i O(V) prostor

U DFS pristupu graf se klonira pomoću rekurzije. Počinjemo od zadanog čvora i istražujemo što je dalje moguće duž svake grane prije povratka. Karta (ili rječnik) se koristi za praćenje već kloniranih čvorova kako bi se izbjegla obrada istog čvora više puta i za rukovanje ciklusima. Kada prvi put naiđemo na čvor, stvaramo njegov klon i pohranjujemo ga na kartu. Zatim za svakog susjeda tog čvora rekurzivno kloniramo i dodajemo kloniranog susjeda klonu trenutnog čvora. Ovo osigurava da su svi čvorovi dubinski posjećeni prije povratka i da je struktura grafa vjerno kopirana.

C++

#include    #include  #include  #include  using namespace std; // Definition for a Node struct Node {  int val;  vector<Node*> neighbors; }; // Map to hold original node to its copy unordered_map<Node* Node*> copies; // Function to clone the graph  Node* cloneGraph(Node* node) {    // If the node is NULL return NULL  if (!node) return NULL;  // If node is not yet cloned clone it  if (copies.find(node) == copies.end()) {  Node* clone = new Node();  clone->val = node->val;  copies[node] = clone;  // Recursively clone neighbors  for (Node* neighbor : node->neighbors) {  clone->neighbors.push_back(cloneGraph(neighbor));  }  }  // Return the clone  return copies[node]; } // Build graph Node* buildGraph() {  Node* node1 = new Node(); node1->val = 0;  Node* node2 = new Node(); node2->val = 1;  Node* node3 = new Node(); node3->val = 2;  Node* node4 = new Node(); node4->val = 3;  node1->neighbors = {node2 node3};  node2->neighbors = {node1 node3};  node3->neighbors = {node1node2 node4};  node4->neighbors = {node3};  return node1; } // Compare two graphs for structural and value equality bool compareGraphs(Node* node1 Node* node2 map<Node* Node*>& visited) {  if (!node1 || !node2)   return node1 == node2;  if (node1->val != node2->val || node1 == node2)  return false;  visited[node1] = node2;  if (node1->neighbors.size() != node2->neighbors.size())   return false;  for (size_t i = 0; i < node1->neighbors.size(); ++i) {  Node* n1 = node1->neighbors[i];  Node* n2 = node2->neighbors[i];  if (visited.count(n1)) {  if (visited[n1] != n2)   return false;  } else {  if (!compareGraphs(n1 n2 visited))  return false;  }  }  return true; } // Driver Code int main() {  Node* original = buildGraph();  // Clone the graph  Node* cloned = cloneGraph(original);  // Compare original and cloned graph  map<Node* Node*> visited;  cout << (compareGraphs(original cloned visited) ?   'true' : 'false') << endl;  return 0; }