洛谷P4606 [SDOI2018]战略游戏 【圆方树 + 虚树】

题目链接

洛谷P4606

双倍经验：弱化版

题解

两点之间必经的点就是圆方树上两点之间的圆点

所以只需建出圆方树

每次询问建出虚树，统计一下虚树边上有多少圆点即可

还要讨论一下经不经过根\(1\)的情况

P4606

#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<map>
#define Redge(u) for (int k = h[u],to; k; k = ed[k].nxt)
#define REP(i,n) for (int i = 1; i <= (n); i++)
#define mp(a,b) make_pair<int,int>(a,b)
#define cls(s) memset(s,0,sizeof(s))
#define cp pair<int,int>
#define LL long long int
using namespace std;
const int maxn = 200005,maxm = 100005,INF = 1000000000;
inline int read(){
	int out = 0,flag = 1; char c = getchar();
	while (c < 48 || c > 57){if (c == '-') flag = -1; c = getchar();}
	while (c >= 48 && c <= 57){out = (out << 3) + (out << 1) + c - 48; c = getchar();}
	return out * flag;
}
int h[maxn],ne = 1,hh[maxn],Ne = 1;
struct EDGE{int to,nxt;}ed[maxn << 2],e[maxn << 2];
inline void build(int u,int v){
	e[++Ne] = (EDGE){v,hh[u]}; hh[u] = Ne;
	e[++Ne] = (EDGE){u,hh[v]}; hh[v] = Ne;
}
inline void add(int u,int v){
	ed[++ne] = (EDGE){v,h[u]}; h[u] = ne;
	ed[++ne] = (EDGE){u,h[v]}; h[v] = ne;
}
int n,m,N,dfn[maxn],low[maxn],st[maxn],top,cnt;
void dfs(int u,int last){
	dfn[u] = low[u] = ++cnt;
	st[++top] = u;
	for (int k = hh[u],to; k; k = e[k].nxt){
		if (k == last) continue;
		if (!dfn[to = e[k].to]){
			dfs(to,k ^ 1);
			low[u] = min(low[u],low[to]);
			if (low[to] >= dfn[u]){
				++N;
				do{add(st[top],N);}while (st[top--] != to);
				add(N,u);
			}
		}
		else low[u] = min(low[u],dfn[to]);
	}
}
int K,a[maxn],fa[maxn][20],d[maxn][20],Dfn[maxn],dep[maxn],dfc;
void DFS(int u){
	Dfn[u] = ++dfc; d[u][0] = (u <= n);
	REP(i,19){
		fa[u][i] = fa[fa[u][i - 1]][i - 1];
		d[u][i] = d[u][i - 1] + d[fa[u][i - 1]][i - 1];
	}
	Redge(u) if ((to = ed[k].to) != fa[u][0]){
		fa[to][0] = u; dep[to] = dep[u] + 1; DFS(to);
	}
}
inline int lca(int u,int v){
	if (dep[u] < dep[v]) swap(u,v);
	for (int i = 0,D = dep[u] - dep[v]; (1 << i) <= D; i++)
		if (D & (1 << i)) u = fa[u][i];
	if (u == v) return u;
	for (int i = 19; ~i; i--)
		if (fa[u][i] != fa[v][i]){
			u = fa[u][i];
			v = fa[v][i];
		}
	return fa[u][0];
}
inline int getup(int u,int v){
	if (u == v) return 0;
	int re = -(u <= n);
	for (int i = 19; ~i; i--)
		if (fa[u][i] && dep[fa[u][i]] >= dep[v]){
			re += d[u][i];
			u = fa[u][i];
		}
	return re;
}
inline bool cmp(const int& a,const int& b){
	return Dfn[a] < Dfn[b];
}
int pre[maxn];
void work(){
	st[top = 1] = 1; int tot = 0,M = K;
	sort(a + 1,a + 1 + K,cmp);
	for (int i = 1; i <= K; i++){
		int u = a[i],p = lca(u,st[top]);
		if (u == 1) tot = INF;
		if (p == st[top]) {if (u != st[top]) st[++top] = u;}
		else {
			while (true){
				if (dep[p] >= dep[st[top - 1]]){
					pre[st[top--]] = p; if (p == 1) tot++;
					if (st[top] != p) st[++top] = p,a[++M] = p;
					break;
				}
				pre[st[top]] = st[top - 1];
				if (st[top - 1] == 1) tot++;
				top--;
			}
			if (u != st[top]) st[++top] = u;
		}
	}
	while (top > 1){
		pre[st[top]] = st[top - 1];
		if (st[top - 1] == 1) tot++;
		top--;
	}
	if (tot < INF) a[++M] = 1;
	int ans = 0;
	for (int i = 1; i <= M; i++){
		int u = a[i];
		if (u == 1){
			if (i > K && tot > 1) ans++;
			continue;
		}
		if (pre[u] != 1 || (pre[u] == 1 && tot > 1)) ans += getup(u,pre[u]);
		if (i > K) ans += (u <= n);
		pre[u] = 0;
	}
	printf("%d\n",ans);
}
int main(){
	int T = read();
	while (T--){
		cls(dfn); cls(h); cls(hh);
		ne = Ne = 1; cnt = dfc = top = 0;
		N = n = read(); m = read();
		REP(i,m) build(read(),read());
		dfs(1,0); DFS(1);
		int q = read();
		while (q--){
			K = read();
			REP(i,K) a[i] = read();
			work();
		}
	}
	return 0;
}

P4320

#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<map>
#define Redge(u) for (int k = h[u],to; k; k = ed[k].nxt)
#define REP(i,n) for (int i = 1; i <= (n); i++)
#define mp(a,b) make_pair<int,int>(a,b)
#define cls(s) memset(s,0,sizeof(s))
#define cp pair<int,int>
#define LL long long int
using namespace std;
const int maxn = 1000005,maxm = 100005,INF = 1000000000;
inline int read(){
	int out = 0,flag = 1; char c = getchar();
	while (c < 48 || c > 57){if (c == '-') flag = -1; c = getchar();}
	while (c >= 48 && c <= 57){out = (out << 3) + (out << 1) + c - 48; c = getchar();}
	return out * flag;
}
int h[maxn],ne = 1,hh[maxn],Ne = 1;
struct EDGE{int to,nxt;}ed[maxn << 2],e[maxn << 2];
inline void build(int u,int v){
	e[++Ne] = (EDGE){v,hh[u]}; hh[u] = Ne;
	e[++Ne] = (EDGE){u,hh[v]}; hh[v] = Ne;
}
inline void add(int u,int v){
	ed[++ne] = (EDGE){v,h[u]}; h[u] = ne;
	ed[++ne] = (EDGE){u,h[v]}; h[v] = ne;
}
int n,m,N,val[maxn];
int dfn[maxn],low[maxn],st[maxn],top,cnt;
void dfs(int u,int last){
	dfn[u] = low[u] = ++cnt;
	st[++top] = u;
	for (int k = hh[u],to; k; k = e[k].nxt){
		if (k == last) continue;
		if (!dfn[to = e[k].to]){
			dfs(to,k ^ 1);
			low[u] = min(low[u],low[to]);
			if (low[to] >= dfn[u]){
				++N;
				do{add(st[top],N);}while (st[top--] != to);
				add(N,u);
			}
		}
		else low[u] = min(low[u],dfn[to]);
	}
}
int fa[maxn][20],d[maxn][20],Dfn[maxn],dep[maxn],dfc;
void DFS(int u){
	Dfn[u] = ++dfc; d[u][0] = (u <= n);
	REP(i,19){
		fa[u][i] = fa[fa[u][i - 1]][i - 1];
		d[u][i] = d[u][i - 1] + d[fa[u][i - 1]][i - 1];
	}
	Redge(u) if ((to = ed[k].to) != fa[u][0]){
		fa[to][0] = u; dep[to] = dep[u] + 1; DFS(to);
	}
}
int dis(int u,int v){
	int re = 0;
	if (dep[u] < dep[v]) swap(u,v);
	for (int i = 0,D = dep[u] - dep[v]; (1 << i) <= D; i++)
		if (D & (1 << i)){
			re += d[u][i];
			u = fa[u][i];
		}
	if (u == v) return re + 1;
	for (int i = 19; ~i; i--)
		if (fa[u][i] != fa[v][i]){
			re += d[u][i] + d[v][i];
			u = fa[u][i];
			v = fa[v][i];
		}
	re += d[u][0] + d[v][0];
	if (fa[u][0] <= n) re++;
	return re;
}
int main(){
	N = n = read(); m = read();
	REP(i,m) build(read(),read());
	dfs(1,0);
	DFS(1);
	int q = read(),u,v;
	while (q--){
		u = read(); v = read();
		printf("%d\n",dis(u,v));
	}
	return 0;
}