Ņemot vērā a savienots nevirzīts grafiks ko pārstāv blakus saraksts adjList[][] ar n mezgli un m malas, kurās katrā mezglā ir a atšķirīga etiķete no 0 līdz n-1 un katrs adj[i] apzīmē virsotņu sarakstu, kas savienotas ar virsotni i.
Izveidot a klons diagrammas, kur katrs diagrammas mezgls satur veselu skaitli val un masīvs ( kaimiņiem ) no mezgliem satur mezglus, kas atrodas blakus pašreizējam mezglam.
klases mezgls {
val: vesels skaitlis
kaimiņi: saraksts[mezgls]
}
Tavs uzdevums ir klonēt doto grafiku un atgriezt atsauci uz klonēto grafiku.
Piezīme: Ja atgriezīsit pareizu dotā grafika kopiju, izvade būs patiesa; pretējā gadījumā, ja kopija ir nepareiza, tā tiks izdrukāta nepatiesi.
Piemēri
Ievade: n = 4 adjList[][] = [[1 2] [0 2] [0 1 3] [2]]
Izvade: taisnība
Paskaidrojums:
Tā kā klonētais grafiks ir identisks oriģinālajam, izvade būs patiesa.Ievade: n = 3 adjList[][] = [[1 2] [0] [0]]
Izvade: taisnība
Paskaidrojums:
Tā kā klonētais grafiks ir identisks oriģinālajam, izvade būs patiesa.
Satura rādītājs
- Kāpēc mums ir jāseko apmeklētajiem/klonētajiem mezgliem?
- Kā sekot līdzi apmeklētajiem/klonētajiem mezgliem?
- Kā savienot klonu mezglus?
- Kā pārbaudīt, vai klonētais grafiks ir pareizs?
- [1. pieeja] Izmantojot BFS šķērsošanu — O(V+E) laiks un O(V) telpa
- [2. pieeja] Izmantojot DFS šķērsošanu — O(V+E) laiks un O(V) telpa
Kāpēc mums ir jāseko apmeklētajiem/klonētajiem mezgliem?
Mums ir jāizseko apmeklētie vai klonētie mezgli, lai izvairītos no bezgalīgas rekursijas un lieka darba, klonējot grafiku. Tā kā grafikos var būt cikli (kur mezgls var norādīt atpakaļ uz iepriekš apmeklētu mezglu), neizsekojot jau klonētajiem mezgliem, klonēšanas funkcija bezgalīgi atkārtoti apmeklētu tos pašus mezglus, kā rezultātā rodas steka pārpilde vai nepareiza dublēšana.
Kā sekot līdzi apmeklētajiem/klonētajiem mezgliem?
Lai uzturētu visus jau izveidotos mezglus, ir nepieciešama HashMap/Map. Atslēgu veikali : sākotnējā mezgla atsauce/adrese Vērtību veikali : Klonētā mezgla atsauce/adrese Ir izveidota visu grafika mezglu kopija.
Kā savienot klonu mezglus?
Apmeklējot a blakus esošās virsotnes mezgls iekšā iegūt atbilstošo klonētu mezgls jo sauksim to IN tagad apmeklējiet visus blakus esošos mezglus iekšā un katram kaimiņam atrodiet atbilstošo klona mezglu (ja nav atrasts, izveidojiet to) un pēc tam ievadiet blakus esošajā vektorā IN mezgls.
Kā pārbaudīt, vai klonētais grafiks ir pareizs?
Pirms klonēšanas veiciet BFS šķērsošanu sākotnējā grafikā un pēc klonēšanas pabeigšanas vēlreiz uz klonētā grafika. Katras šķērsošanas laikā izdrukājiet katra mezgla vērtību kopā ar tā adresi (vai atsauci). Lai pārbaudītu klonēšanas pareizību, salīdziniet abos šķērsojumos apmeklēto mezglu secību. Ja mezglu vērtības parādās tādā pašā secībā, bet to adreses (vai atsauces) atšķiras, tas apstiprina, ka grafiks ir veiksmīgi un pareizi klonēts.
Izpētiet, kā klonēt nevirzītu grafiku, ieskaitot grafikus ar vairākiem savienotiem komponentiem izmantojot BFS vai DFS, lai nodrošinātu visu mezglu un malu pilnīgu dziļu kopiju.
[1. pieeja] Izmantojot BFS šķērsošanu — O(V+E) laiks un O(V) telpa
C++BFS pieejā grafiks tiek klonēts iteratīvi, izmantojot rindu. Mēs sākam, klonējot sākotnējo mezglu un ievietojot to rindā. Apstrādājot katru rindas mezglu, mēs apmeklējam tā kaimiņus. Ja kaimiņš vēl nav klonēts, mēs izveidojam klonu, saglabājam to kartē un ievietojam rindā vēlākai apstrādei. Pēc tam mēs pievienojam kaimiņa klonu pašreizējā mezgla klona kaimiņu sarakstam. Šis process turpinās pakāpeniski, nodrošinot, ka visi mezgli tiek apmeklēti platuma pirmajā secībā. BFS ir īpaši noderīga, lai izvairītos no dziļas rekursijas un efektīvi apstrādātu lielus vai platus 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');
Izvade
true
[2. pieeja] Izmantojot DFS šķērsošanu — O(V+E) laiks un O(V) telpa
C++DFS pieejā grafiks tiek klonēts, izmantojot rekursiju. Mēs sākam no dotā mezgla un izpētām pēc iespējas tālāk pa katru atzaru pirms atkāpšanās. Karte (vai vārdnīca) tiek izmantota, lai izsekotu jau klonētiem mezgliem, lai izvairītos no viena mezgla vairākkārtējas apstrādes un apstrādātu ciklus. Kad mēs pirmo reizi sastopamies ar mezglu, mēs izveidojam tā klonu un saglabājam to kartē. Pēc tam katram šī mezgla kaimiņam mēs to rekursīvi klonējam un klonēto kaimiņu pievienojam pašreizējā mezgla klonam. Tas nodrošina, ka visi mezgli tiek rūpīgi apmeklēti pirms atgriešanās un grafika struktūra tiek precīzi kopēta.
#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');
Izvade
true