算法精粹(algorithm-essentials)

感谢soulmachine@github提供内容
## Clone Graph


### 描述

Clone an undirected graph. Each node in the graph contains a `label` and a list of its `neighbours`.


OJ's undirected graph serialization:
Nodes are labeled uniquely.

We use `#` as a separator for each node, and `,` as a separator for node label and each neighbour of the node.
As an example, consider the serialized graph `{0,1,2#1,2#2,2}`.

The graph has a total of three nodes, and therefore contains three parts as separated by `#`.


1. First node is labeled as 0. Connect node 0 to both nodes 1 and 2.
1. Second node is labeled as 1. Connect node 1 to node 2.
1. Third node is labeled as 2. Connect node 2 to node 2 (itself), thus forming a self-cycle.

Visually, the graph looks like the following:

```
1
/ \
/ \
0 --- 2
/ \
\_/
```

### 分析

广度优先遍历或深度优先遍历都可以。


### DFS

{% if book.java %}
```java
// Clone Graph
// DFS,时间复杂度O(n),空间复杂度O(n)
public class Solution {
public UndirectedGraphNode cloneGraph(UndirectedGraphNode node) {
if(node == null) return null;
// key is original node,value is copied node
HashMap visited = new HashMap<>();
clone(node, visited);
return visited.get(node);
}
// DFS
private static UndirectedGraphNode clone(UndirectedGraphNode node,
HashMap UndirectedGraphNode> visited) {
// a copy already exists
if (visited.containsKey(node)) return visited.get(node);

UndirectedGraphNode new_node = new UndirectedGraphNode(node.label);
visited.put(node, new_node);
for (UndirectedGraphNode nbr : node.neighbors)
new_node.neighbors.add(clone(nbr, visited));
return new_node;
}
}
```
{% endif %}

{% if book.cpp %}
```cpp
// Clone Graph
// DFS,时间复杂度O(n),空间复杂度O(n)
class Solution {
public:
UndirectedGraphNode *cloneGraph(const UndirectedGraphNode *node) {
if(node == nullptr) return nullptr;
// key is original node,value is copied node
unordered_map UndirectedGraphNode *> visited;
clone(node, visited);
return visited[node];
}
private:
// DFS
static UndirectedGraphNode* clone(const UndirectedGraphNode *node,
unordered_map UndirectedGraphNode *> &visited) {
// a copy already exists
if (visited.find(node) != visited.end()) return visited[node];

UndirectedGraphNode *new_node = new UndirectedGraphNode(node->label);
visited[node] = new_node;
for (auto nbr : node->neighbors)
new_node->neighbors.push_back(clone(nbr, visited));
return new_node;
}
};
```
{% endif %}


### BFS

{% if book.java %}
```java
// Clone Graph
// BFS,时间复杂度O(n),空间复杂度O(n)
public class Solution {
public UndirectedGraphNode cloneGraph(UndirectedGraphNode node) {
if (node == null) return null;
// key is original node,value is copied node
HashMap visited = new HashMap<>();
// each node in queue is already copied itself
// but neighbors are not copied yet
Queue q = new LinkedList<>();
q.offer(node);
visited.put(node, new UndirectedGraphNode(node.label));
while (!q.isEmpty()) {
UndirectedGraphNode cur = q.poll();
for (UndirectedGraphNode nbr : cur.neighbors) {
// a copy already exists
if (visited.containsKey(nbr)) {
visited.get(cur).neighbors.add(visited.get(nbr));
} else {
UndirectedGraphNode new_node =
new UndirectedGraphNode(nbr.label);
visited.put(nbr, new_node);
visited.get(cur).neighbors.add(new_node);
q.offer(nbr);
}
}
}
return visited.get(node);
}
}
```
{% endif %}

{% if book.cpp %}
```cpp
// Clone Graph
// BFS,时间复杂度O(n),空间复杂度O(n)
class Solution {
public:
UndirectedGraphNode *cloneGraph(const UndirectedGraphNode *node) {
if (node == nullptr) return nullptr;
// key is original node,value is copied node
unordered_map UndirectedGraphNode *> copied;
// each node in queue is already copied itself
// but neighbors are not copied yet
queue q;
q.push(node);
copied[node] = new UndirectedGraphNode(node->label);
while (!q.empty()) {
const UndirectedGraphNode *cur = q.front();
q.pop();
for (auto nbr : cur->neighbors) {
// a copy already exists
if (copied.find(nbr) != copied.end()) {
copied[cur]->neighbors.push_back(copied[nbr]);
} else {
UndirectedGraphNode *new_node =
new UndirectedGraphNode(nbr->label);
copied[nbr] = new_node;
copied[cur]->neighbors.push_back(new_node);
q.push(nbr);
}
}
}
return copied[node];
}
};
```
{% endif %}