[洛谷P4630][APIO2018] Duathlon 铁人两项

题目大意：给一张无向图，求三元组$(u,v,w)$满足$u->v->w$为简单路径，求个数

题解：圆方树，缩点后$DP$，因为同一个点双中的点一定地位相同

卡点：1.$father$数组开小，一不小心就续到了下面的$bool$的$vis$数组中，然后就挂成$98$，因为发现去掉没用的$vis$数组变成$86$，才找到问题

C++ Code：

#include <cstdio>
#include <cstring>
#define maxn 100010
#define maxm 200010
#define N 200010

#define ONLINE_JUDGE
#define read() R::READ()
#include <cctype>
namespace R {
	int x;
	#ifdef ONLINE_JUDGE
	char *ch, op[1 << 28];
	inline void init() {
		fread(ch = op, 1, 1 << 28, stdin);
	}
	inline int READ() {
		while (isspace(*ch)) ch++;
		for (x = *ch & 15, ch++; isdigit(*ch); ch++) x = x * 10 + (*ch & 15);
		return x;
	}
	#else
	char ch;
	inline int READ() {
		ch = getchar();
		while (isspace(ch)) ch = getchar();
		for (x = ch & 15, ch = getchar(); isdigit(ch); ch = getchar()) x = x * 10 + (ch & 15);
		return x;
	}
	#endif
}

int n, m;
long long ans;
inline int min(int a, int b) {return a < b ? a : b;}

namespace Tree {
	int CNT;
	int head[N], cnt;
	struct Edge {
		int to, nxt;
	} e[N << 1];
	void add(int a, int b) {
		e[++cnt] = (Edge) {b, head[a]}; head[a] = cnt;
		e[++cnt] = (Edge) {a, head[b]}; head[b] = cnt;
	}
	
	long long w[N], f[N], sz[N], pointsz;
	int fa[N];
	void dfs(int u) {
		sz[u] = bool(u <= n);
		long long tmp = 0;
		for (int i = head[u]; i; i = e[i].nxt) {
			int v = e[i].to;
			if (v != fa[u]) {
				fa[v] = u;
				dfs(v);
				tmp += sz[v] * sz[u];
				sz[u] += sz[v];
			}
		}
		tmp += sz[u] * (pointsz - sz[u]);
		ans += w[u] * tmp << 1ll;
	}
}
namespace Graph {
	int head[maxn], cnt;
	struct Edge {
		int to, nxt;
	} e[maxm << 1];
	void add(int a, int b) {
		e[++cnt] = (Edge) {b, head[a]}; head[a] = cnt;
		e[++cnt] = (Edge) {a, head[b]}; head[b] = cnt;
	}
	
	int DFN[maxn], low[maxn], idx, fa[maxn];
	int S[maxn], top;
	void Tarjan(int u) {
		Tree::pointsz++;
		DFN[u] = low[u] = ++idx;
		Tree::w[S[++top] = u] = -1;
		int v;
		for (int i = head[u]; i; i = e[i].nxt) {
			v = e[i].to;
			if (!DFN[v]) {
				fa[v] = u;
				Tarjan(v);
				low[u] = min(low[u], low[v]);
				if (low[v] >= DFN[u]) {
					Tree::w[++Tree::CNT] = 1;
					Tree::add(Tree::CNT, u);
					do {
						v = S[top--];
						Tree::add(Tree::CNT, v);
						Tree::w[Tree::CNT]++;
					} while (v != e[i].to);
				}
			} else low[u] = min(low[u], DFN[v]);
		}
	}
	inline void tarjan(int n) {
		for (int i = 1; i <= n; i++) if (!DFN[i]) {
			Tree::pointsz = 0;
			Tarjan(i);
			Tree::dfs(i);
		}
	}
}

int main() {
	#ifdef ONLINE_JUDGE
	R::init();
	#endif
	Tree::CNT = n = read(), m = read();
	for (int i = 1; i <= m; i++) Graph::add(read(), read());
	Graph::tarjan(n);
	printf("%lld
", ans);
	return 0;
}