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【題解】HNOI2014世界樹

清醒 space 小時 swa print bsp min 節點 建立

  腦子不清醒的時候千萬別寫題。寫題寫不下去了千萬別死扛,重構才是你唯一的出路QAQ

  昨天很想快點寫道題,思路沒有很清晰的時候就寫了,結果……今天一怒之下決定重整思路重構代碼,其實不過是半個小時的事情……

  提示很明顯,總點數限制了範圍。建立出虛樹,在虛樹上面 dp。 在虛樹上面我們dp兩遍,兩遍一起處理出每一個(虛樹上的)節點被誰管轄,在連接兩者的路徑上找到管理的分界點即可。處理兩點之間的距離一定要上 ST 表啊……

#include <bits/stdc++.h>
using namespace std;
#define maxn 350000
#define CNST 20
int n, dep[maxn], gra[maxn][CNST];
int size[maxn], hson[maxn], ans[maxn];
int top, S[maxn], a[maxn], b[maxn];
int timer, dfn[maxn], sum[maxn];
bool mark[maxn], vis[maxn];
int T, Log[maxn * 2], bit[21], ST[maxn * 2][CNST], pos[maxn];

int read()
{
int x = 0, k = 1;
char c;
c = getchar();
while(c < ‘0‘ || c > ‘9‘) { if(c == ‘-‘) k = -1; c = getchar(); }
while(c >= ‘0‘ && c <= ‘9‘) x = x * 10 + c - ‘0‘, c = getchar();
return x * k;
}

struct edge
{
int cnp, to[maxn * 2], last[maxn * 2], head[maxn];
edge() { cnp = 1; }
void add(int u, int v)
{
if(u == v) return;
to[cnp] = v, last[cnp] = head[u], head[u] = cnp ++;
to[cnp] = u, last[cnp] = head[v], head[v] = cnp ++;
}
}E1, E2;

bool cmp(int x, int y) { return dfn[x] < dfn[y]; }

void dfs(int u, int fa)
{
size[u] = 1; dfn[u] = ++ timer;
gra[u][0] = fa; dep[u] = dep[fa] + 1; ST[++ T][0] = dep[u]; pos[u] = T;
for(int i = 1; i < CNST; i ++) gra[u][i] = gra[gra[u][i - 1]][i - 1];
for(int i = E1.head[u]; i; i = E1.last[i])
{
int v = E1.to[i];
if(v == fa) return;
dfs(v, u); size[u] += size[v];
ST[++ T][0] = dep[u];
}
}

int LCA(int x, int y)
{
if(dep[x] < dep[y]) swap(x, y);
for(int i = CNST - 1; ~i; i --)
if(dep[gra[x][i]] >= dep[y]) x = gra[x][i];
for(int i = CNST - 1; ~i; i --)
if(gra[x][i] != gra[y][i]) x = gra[x][i], y = gra[y][i];
return (x == y) ? x : gra[x][0];
}

int Get_Dis(int x, int y)
{
int ret = dep[x] + dep[y];
if(!x) return dep[y]; else if(!y) return dep[x];
x = pos[x], y = pos[y];
if(x > y) swap(x, y);
int k = Log[y - x + 1];
ret = ret - 2 * min(ST[x][k], ST[y - bit[k] + 1][k]);
return ret;
}

int Get_Gra(int x, int y)
{
for(int i = CNST - 1; ~i; i --)
if(dep[gra[x][i]] > dep[y]) x = gra[x][i];
return x;
}

int Work(int u, int v, int k)
{
bool flag = 0;
int x = u;
for(int i = CNST - 1; i >= 0; i --)
{
int tem = gra[x][i]; if(dep[tem] < dep[k]) continue;
int d1 = Get_Dis(u, tem), d2 = Get_Dis(v, tem);
if(d1 < d2) x = gra[x][i];
else if(d1 == d2 && u < v) x = gra[x][i];
}
return x;
}

void DP(int u, int fa)
{
hson[u] = 0; sum[u] = 0;
for(int i = E2.head[u]; i; i = E2.last[i])
{
int v = E2.to[i]; if(!v) continue;
if(v == fa) continue;
DP(v, u);
int t = hson[v];
int dis = Get_Dis(u, t), dis2 = Get_Dis(u, hson[u]);
if(dis < dis2) hson[u] = t;
else if(dis == dis2 && t < hson[u]) hson[u] = t;
if(!hson[u]) hson[u] = t;
}
if(mark[u]) hson[u] = u;
}

void DP2(int u, int fa)
{
int tot = 0;
if(hson[fa])
{
int t = hson[fa];
int dis = Get_Dis(u, t), dis2 = Get_Dis(u, hson[u]);
if(dis < dis2) hson[u] = t;
else if(dis == dis2 && t < hson[u]) hson[u] = t;
if(!hson[u]) hson[u] = t;
}
for(int i = E2.head[u]; i; i = E2.last[i])
{
int v = E2.to[i];
if(v == fa) continue; DP2(v, u);
int y = Get_Gra(v, u);
int x = Work(hson[v], hson[u], u);
int tem = size[x] - size[v];
ans[hson[v]] += tem, ans[hson[u]] += size[y] - size[x];
tot += size[y];
}
ans[hson[u]] += size[u] - tot;
E2.head[u] = 0;
}

void Solve()
{
int K = read();
for(int i = 1; i <= K; i ++) b[i] = a[i] = read(), mark[a[i]] = 1;
sort(a + 1, a + 1 + K, cmp); S[top = 1] = 1; E2.cnp = 1; ans[0] = 0;
for(int i = 1; i <= K; i ++)
{
int lca = LCA(S[top], a[i]);
while(2333)
{
if(dep[S[top - 1]] <= dep[lca])
{
E2.add(lca, S[top --]);
if(lca != S[top]) S[++ top] = lca;
break;
}
else E2.add(S[top], S[top - 1]), top --;
}
S[++ top] = a[i];
}
while(top > 1) E2.add(S[top], S[top - 1]), top --;
sum[1] = 0; DP(1, 0); DP2(1, 0);
for(int i = 1; i <= K; i ++) printf("%d ", ans[b[i]]), mark[b[i]] = 0, ans[b[i]] = 0;
puts("");
}

void init()
{
bit[0] = 1; for(int i = 1; i <= 20; i ++) bit[i] = bit[i - 1] << 1;
Log[0] = -1; for(int i = 1; i < maxn * 2; i ++) Log[i] = Log[i >> 1] + 1;
}

int main()
{
init(); n = read();
for(int i = 1; i < n; i ++)
{
int x = read(), y = read();
E1.add(x, y);
}
dfs(1, 0);
for(int i = 1; i <= Log[T]; i ++)
for(int j = 1; j + bit[i - 1] <= T; j ++)
ST[j][i] = min(ST[j][i - 1], ST[j + bit[i - 1]][i - 1]);
int q = read();
for(int i = 1; i <= q; i ++) Solve();
return 0;
}

【題解】HNOI2014世界樹