POJ3177 Redundant Paths 图的边双连通分量

题目大意：问一个图至少加多少边能使该图的边双连通分量成为它本身。

图的边双连通分量为极大的不存在割边的子图。图的边双连通分量之间由割边连接。求法如下：

1. 求出图的割边
2. 在每个边双连通分量内Dfs，标记每个节点所属于的双连通分量编号
3. 构建一新图Tree，一个节点代表一个双连通分量。原图中遍历割边，将割边连接的两个双连通分量在Tree中的对应节点连接。
4. Tree中算出每个节点的度数，如果一节点度数为1，则其为叶子节点。输出（叶子节点数+1/2）。（连接了叶子节点，就形成了环，Tree中不连接叶子节点的边因为在环内，所以不再是割边了。）

注意：如果一个边是割边，则其反向边也是割边。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <cassert>
using namespace std;

#define LOOP(i, n) for(int i=1; i<=n; i++)
const int MAX_NODE = 5010, MAX_EDGE = 10010 * 2;

struct G {
	struct Node;
	struct Edge;

	struct Node {
		int Id, DfsN, Low, InBlock, Degree;
		Edge *Head;
	}_nodes[MAX_NODE], *Root;

	struct Edge {
		bool IsCut;
		Node *From, *To;
		Edge *Next, *Rev;
		Edge(){}
		Edge(Node *from, Node *to, Edge *next):From(from),To(to),Next(next),IsCut(false){}
	}*_edges[MAX_EDGE];

	int _vCount, _eCount, DfsCnt, BlockCnt, LeafCnt;

	void Init() {
		memset(_nodes, 0, sizeof(_nodes));
		_vCount = _eCount = DfsCnt = LeafCnt = 0;
		BlockCnt = 0;
	}

	Edge *NewEdge() {
		_eCount++;
		return _edges[_eCount] ? _edges[_eCount] : _edges[_eCount] = new Edge();
	}

	Edge *AddEdge(Node *from, Node *to) {
		Edge *e = NewEdge();
		*e = Edge(from, to, from->Head);
		from->Head = e;
		return e;
	}

	void Build(int uId, int vId, bool is2d) {
		while (_vCount < uId || _vCount < vId)
			_vCount++;
		Node *u = uId + _nodes, *v = vId + _nodes;
		u->Id = uId;
		v->Id = vId;
		Edge *e1 = AddEdge(u, v);
		if (is2d) {
			Edge *e2 = AddEdge(v, u);
			e1->Rev = e2;
			e2->Rev = e1;
		}
	}

	void FindCutEdge(Node *u, Edge *Prev) {//易忘点：prev
		if (u->DfsN)
			return;
		u->DfsN = u->Low = ++DfsCnt;
		for (Edge *e = u->Head; e; e = e->Next) {
			if (!e->To->DfsN) {
				FindCutEdge(e->To, e);
				u->Low = min(u->Low, e->To->Low);
				if (u->DfsN < e->To->Low)
					e->IsCut = e->Rev->IsCut = true;//易忘点：e->Rev->IsCut
			}
			else if (e->Rev != Prev)
				u->Low = min(u->Low, e->To->DfsN);
		}
	}

	void FindCutEdge() {
		LOOP(i, _vCount) {//易忘点：图不一定连通，所以要循环。
			Root = i + _nodes;
			FindCutEdge(Root, NULL);
		}
	}

	void SetBlock(Node *u) {
		u->InBlock = BlockCnt;
		for (Edge *e = u->Head; e; e = e->Next)
			if (!e->IsCut && !e->To->InBlock)
				SetBlock(e->To);
	}

	void SetBlock() {
		LOOP(i, _vCount) {
			if (!_nodes[i].InBlock) {
				BlockCnt++;
				SetBlock(i + _nodes);
			}
		}
	}
	void SetLeafCnt() {//此处比较有技巧，注意看看
		LOOP(i, _eCount)
			_edges[i]->To->Degree++;
		LOOP(i, _vCount)
			if (_nodes[i].Degree <= 1)
				LeafCnt++;
	}
}Org, Tree;

int main() {
#ifdef _DEBUG
	freopen("c:\\noi\\source\\input.txt", "r", stdin);
	//freopen("c:\\noi\\source\\output.txt", "w", stdout);
#endif
	Org.Init();
	Tree.Init();
	int totNode, totEdge, uId, vId;
	scanf("%d%d", &totNode, &totEdge);
	LOOP(i, totEdge) {
		scanf("%d%d", &uId, &vId);
		Org.Build(uId, vId, true);
	}
	Org.FindCutEdge();
	Org.SetBlock();
	LOOP(i, Org._eCount)
		if (Org._edges[i]->IsCut)
			Tree.Build(Org._edges[i]->From->InBlock, Org._edges[i]->To->InBlock, false);
	Tree.SetLeafCnt();
	printf("%d\n", (Tree.LeafCnt + 1) / 2);
	return 0;
}