洛谷P4606 [SDOI2018]战略游戏 【圆方树 + 虚树】
题目链接
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;
}
