2014
11-29

LeetCode-Clone Graph[图论]

Clone Graph

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

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 neighbor 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.
2. Second node is labeled as 1. Connect node 1 to node 2.
3. 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
/ \
\_/

BFS

// LeetCode, 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<const UndirectedGraphNode *,
UndirectedGraphNode *> copied;
clone(node, copied);
return copied[node];
}
private:
// DFS
static UndirectedGraphNode* clone(const UndirectedGraphNode *node,
unordered_map<const UndirectedGraphNode *,
UndirectedGraphNode *> &copied) {
// a copy already exists
if (copied.find(node) != copied.end()) return copied[node];

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

DFS

// LeetCode, 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<const UndirectedGraphNode *,
UndirectedGraphNode *> copied;
// each node in queue is already copied itself
// but neighbors are not copied yet
queue<const UndirectedGraphNode *> 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];
}
};

1. 一开始就规定不相邻节点颜色相同，可能得不到最优解。我想个类似的算法，也不确定是否总能得到最优解：先着一个点，随机挑一个相邻点，着第二色，继续随机选一个点，但必须至少有一个边和已着点相邻，着上不同色，当然尽量不增加新色，直到完成。我还找不到反例验证他的错误。。希望LZ也帮想想, 有想法欢迎来邮件。谢谢

2. 学算法中的数据结构学到一定程度会乐此不疲的，比如其中的2－3树，类似的红黑树，我甚至可以自己写个逻辑文件系统结构来。

3. Thanks for using the time to examine this, I truly feel strongly about it and enjoy finding out far more on this subject matter. If achievable, as you achieve knowledge

4. 代码是给出了，但是解析的也太不清晰了吧！如 13 abejkcfghid jkebfghicda
第一步拆分为 三部分 (bejk, cfghi, d) * C(13,3)，为什么要这样拆分，原则是什么？

5. 约瑟夫也用说这么长……很成熟的一个问题了，分治的方法解起来o(n)就可以了，有兴趣可以看看具体数学的第一章，关于约瑟夫问题推导出了一系列的结论，很漂亮