[bzoj5329][Sdoi2018]战略游戏

题目大意：多组数据，每组数据给一张图，多组询问，每个询问给一个点集，要求删除一个点，使得至少点集中的两个点互不连通，输出方案数

题解：圆方树，发现使得两个点不连通的方案数就是它们路径上的原点个数。如何处理重复？可以按圆方树的$dfn$序排序，相邻两点求一下贡献，这样贡献就被重复计算了两次，除去$k$个询问点就行了。还有每次计算中$lca$没有被统计，发现排序后第一个点和最后一个点的$lca$一定是深度最浅的，所以只有这个点没有被统计答案，加上即可

卡点：1.圆方树$dfn$数组没赋值

2.$LCA$的$log$太小

C++ Code：

#include <cstdio>
#include <algorithm>
#include <cstring>
#define maxn 200010
#define maxm 200010
int Tim, n, m, LCA;
inline int min(int a, int b) {return a < b ? a : b;}
inline void swap(int &a, int &b) {a ^= b ^= a ^= b;}
struct Tree {
	#define root 1
	#define fa(u) dad[u][0]
	#define M 18
	int head[maxn], cnt;
	struct Edge {
		int to, nxt;
	} e[maxm << 1];
	inline void addE(int a, int b) {e[++cnt] = (Edge) {b, head[a]}; head[a] = cnt;}
	inline void add(int a, int b) {
		addE(a, b);
		addE(b, a);
	}

	int dad[maxn][M], dep[maxn], sz[maxn];
	int dfn[maxn], idx;
	void dfs(int u = root) {
		dfn[u] = ++idx;
		for (int i = 1; i < M; i++) dad[u][i] = dad[dad[u][i - 1]][i - 1];
		for (int i = head[u]; i; i = e[i].nxt) {
			int v = e[i].to;
			if (v != fa(u)) {
				sz[v] = sz[u] + int(v <= n);
				dep[v] = dep[u] + 1;
				fa(v) = u;
				dfs(v);
			}
		}
	}
	inline int LCA(int x, int y) {
		if (dep[x] < dep[y]) swap(x, y);
		for (int i = dep[x] - dep[y]; i; i &= i - 1) x = dad[x][__builtin_ctz(i)];
		if (x == y) return x;
		for (int i = M - 1; ~i; i--) if (dad[x][i] != dad[y][i]) x = dad[x][i], y = dad[y][i];
		return fa(x);
	}

	inline int len(int x, int y) {
		return sz[x] + sz[y] - (sz[::LCA = LCA(x, y)] << 1);
	}

	inline void init() {
		memset(head, 0, sizeof head); cnt = 0;
		memset(dfn, 0, sizeof dfn); idx = 0;
		sz[root] = 0;
	}
	#undef root
	#undef fa
	#undef M
} T;

struct Graph {
	#define root 1
	int head[maxn], cnt;
	struct Edge {
		int to, nxt;
	} e[maxm << 1];
	inline void addE(int a, int b) {e[++cnt] = (Edge) {b, head[a]}; head[a] = cnt;}
	inline void add(int a, int b) {
		addE(a, b);
		addE(b, a);
	}

	int DFN[maxn], low[maxn], idx, CNT;
	int S[maxn], top, tmp;
	void tarjan(int u = root) {
		DFN[u] = low[u] = ++idx;
		S[++top] = u;
		for (int i = head[u]; i; i = e[i].nxt) {
			int v = e[i].to;
			if (!DFN[v]) {
				tarjan(v);
				low[u] = min(low[u], low[v]);
				if (low[v] >= DFN[u]) {
					CNT++;
					T.add(CNT, u);
					do {
						T.add(CNT, tmp = S[top--]);
					} while (tmp != v);
				}
			} else low[u] = min(low[u], DFN[v]);
		}
	}

	inline void init(int n) {
		memset(head, 0, sizeof head); cnt = 0;
		memset(DFN, 0, sizeof DFN); idx = 0;
		CNT = n;
	}
	#undef root
} G;

#define Online_Judge
#define read() R::READ()
#include <cctype>
namespace R {
    int x;
    #ifdef Online_Judge
    char *ch, op[1 << 26];
    inline void init() {
        fread(ch = op, 1, 1 << 26, 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 s[maxn];
inline bool cmp(int a, int b) {return T.dfn[a] < T.dfn[b];}
int main() {
    #ifdef Online_Judge
    R::init();
    #endif
	Tim = read();
	while (Tim --> 0) {
		G.init(n = read()), T.init();
		for (int i = m = read(); i; i--) G.add(read(), read());
		G.tarjan();
		T.dfs();
		int Q = read();
		while (Q --> 0) {
			int k = read(), ans = 0;
			for (int i = 0; i < k; i++) s[i] = read();
			std::sort(s, s + k, cmp);
			s[k] = s[0];
			for (int i = 0; i < k; i++) ans += T.len(s[i], s[i + 1]);
			printf("%d\n", (ans >> 1) - k + int(LCA <= n));
		}
	}
	return 0;
}

原文地址：https://www.cnblogs.com/Memory-of-winter/p/9650984.html