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⭐算法OJ⭐克隆图【BFS】（C++实现）Clone Graph

news 来源：原创 2025/5/28 11:44:00

前情提要：图论入门【数据结构基础】：什么是图？如何表示图？

133. Clone Graph

Given a reference of a node in a connected undirected graph.
Return a deep copy (clone) of the graph.
Each node in the graph contains a value (int) and a list (List[Node]) of its neighbors.

class Node {
    public int val;
    public List<Node> neighbors;
}

Test case format:

For simplicity, each node’s value is the same as the node’s index (1-indexed). For example, the first node with val == 1, the second node with val == 2, and so on. The graph is represented in the test case using an adjacency list.

An adjacency list is a collection of unordered lists used to represent a finite graph. Each list describes the set of neighbors of a node in the graph.

The given node will always be the first node with val = 1. You must return the copy of the given node as a reference to the cloned graph.

Example 1:
在这里插入图片描述

Input: adjList = [[2,4],[1,3],[2,4],[1,3]]
Output: [[2,4],[1,3],[2,4],[1,3]]
Explanation: There are 4 nodes in the graph.
1st node (val = 1)'s neighbors are 2nd node (val = 2) and 4th node (val = 4).
2nd node (val = 2)'s neighbors are 1st node (val = 1) and 3rd node (val = 3).
3rd node (val = 3)'s neighbors are 2nd node (val = 2) and 4th node (val = 4).
4th node (val = 4)'s neighbors are 1st node (val = 1) and 3rd node (val = 3).

Example 2:
在这里插入图片描述

Input: adjList = [[]]
Output: [[]]
Explanation: Note that the input contains one empty list. The graph consists of only one node with val = 1 and it does not have any neighbors.

Example 3:

Input: adjList = []
Output: []
Explanation: This an empty graph, it does not have any nodes.

要克隆一个无向连通图，我们可以使用深度优先搜索（DFS） 或广度优先搜索（BFS） 来遍历图，并在遍历过程中创建每个节点的副本。为了确保每个节点只被复制一次，我们可以使用一个哈希表（或字典）来存储已经复制过的节点。

代码设计

Node类： 定义了图节点的结构，包含一个整数值val和一个邻居节点列表neighbors。
cloneGraph函数：
- 首先检查输入节点是否为空，如果为空则返回nullptr。
- 使用一个哈希表visited来存储原节点和克隆节点的映射。
- 使用队列q来进行BFS遍历。
- 克隆第一个节点并将其加入哈希表。
- 在BFS过程中，遍历每个节点的邻居，如果邻居节点还没有被克隆，则克隆它并加入哈希表和队列。
- 最后，返回克隆图的第一个节点。

代码实现

#include <unordered_map>
#include <queue>
#include <vector>

using namespace std;

// Definition for a Node.
class Node {
public:
    int val;
    vector<Node*> neighbors;
    Node() {
        val = 0;
        neighbors = vector<Node*>();
    }
    Node(int _val) {
        val = _val;
        neighbors = vector<Node*>();
    }
    Node(int _val, vector<Node*> _neighbors) {
        val = _val;
        neighbors = _neighbors;
    }
};

class Solution {
public:
    Node* cloneGraph(Node* node) {
        if (!node) return nullptr;

        // 创建一个哈希表来存储原节点和克隆节点的映射
        unordered_map<Node*, Node*> visited;

        // 创建一个队列用于BFS
        queue<Node*> q;
        q.push(node);

        // 克隆第一个节点
        visited[node] = new Node(node->val);

        // 开始BFS
        while (!q.empty()) {
            Node* current = q.front();
            q.pop();

            // 遍历当前节点的邻居
            for (Node* neighbor : current->neighbors) {
                // 如果邻居节点还没有被克隆
                if (visited.find(neighbor) == visited.end()) {
                    // 克隆邻居节点并加入哈希表
                    visited[neighbor] = new Node(neighbor->val);
                    // 将邻居节点加入队列
                    q.push(neighbor);
                }
                // 将克隆的邻居节点加入当前克隆节点的邻居列表
                visited[current]->neighbors.push_back(visited[neighbor]);
            }
        }

        // 返回克隆图的第一个节点
        return visited[node];
    }
};