【题解】HNOI2014世界树

  脑子不清醒的时候千万别写题。写题写不下去了千万别死扛,重构才是你唯一的出路QAQ

  昨天很想快点写道题,思路没有很清晰的时候就写了,结果……今天一怒之下决定重整思路重构代码,其实不过是半个小时的事情……

  提示很明显,总点数限制了范围。建立出虚树,在虚树上面 dp。 在虚树上面我们dp两遍,两遍一起处理出每一个(虚树上的)节点被谁管辖,在连接两者的路径上找到管理的分界点即可。处理两点之间的距离一定要上 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;
}

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转载自www.cnblogs.com/twilight-sx/p/9420478.html
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