【题解】HNOI2016网络

　　整体二分是个好东西！可我忘记了它QAQ其实当你知道这题可以整体二分的时候就已经不难了（个人觉得这是最难想到的一点啊）。整体二分的话，我们就可以把问题转化为是否有一条权值 \(>= k\) 的链经过某一点，这个可以通过树上差分做到 \(logn\) 的复杂度。而由于每次二分答案之后，都可以将询问和操作分成两个部分，所以是满足整体二分的性质的。

　　以及自己的代码能力还有待提升啊……(；д；)

#include <bits/stdc++.h>
using namespace std;
#define lowbit(i) (i & (-i))
#define maxn 1000000
#define INF 99999999
#define CNST 20
int n, m, tot, book[maxn];
int b[maxn], id[maxn];
int C[maxn], Ans[maxn], pos[maxn];
int dfn[maxn], size[maxn], f[maxn];
int timer, cnt, ST[maxn * 2][CNST];
int bit[CNST], Log[maxn * 2];
map <int, int> Map;

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 node
{
    int opt, x, y, w, mark, id, rec;
}Q[maxn], ql[maxn], qr[maxn];

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

void Update(int x, int y) 
{ 
    if(!x) return;
    for(; x <= n; x += lowbit(x)) C[x] += y; 
}

int Query(int x)
{
    int ret = 0;
    for(; x; x -= lowbit(x)) ret += C[x];
    return ret;
}

void dfs(int u, int fa)
{
    dfn[u] = ++ timer; size[u] = 1; f[dfn[u]] = dfn[fa];
    ST[++ cnt][0] = dfn[u]; pos[u] = cnt;
    for(int i = E1.head[u]; i; i = E1.last[i])
    {
        int v = E1.to[i];
        if(v == fa) continue;
        dfs(v, u); size[u] += size[v];
        ST[++ cnt][0] = dfn[u];
    }
}

int RMQ(int u, int v)
{
    u = pos[u], v = pos[v];
    if(u > v) swap(u, v);
    int k = Log[v - u + 1];
    return min(ST[u][k], ST[v - bit[k] + 1][k]);
}

void Check(int l, int r, int ll, int rr)
{
    if(l == r)
    {
        for(int i = ll; i <= rr; i ++)
            if(Q[i].opt == 2) 
                Ans[Q[i].id] = l ? id[l] : -1;
        return;
    }
    if(l > r) return;
    int mid = (l + r) >> 1, sum = 0;
    for(int i = ll; i <= rr; i ++)
    {
        int x = Q[i].x, y = Q[i].y;
        if(!Q[i].opt && Q[i].rec > mid)
        {
            Update(dfn[x], 1), Update(dfn[y], 1);
            int K = RMQ(x, y);
            Update(K, -1), Update(f[K], -1); sum ++;
        }
        else if(Q[i].opt == 1 && Q[i].rec > mid) 
        {
            Update(dfn[x], -1), Update(dfn[y], -1);
            int K = RMQ(x, y);
            Update(K, 1), Update(f[K], 1); sum --;
        }
        else if(Q[i].opt == 2)
        {
            int x = Query(dfn[Q[i].x] + size[Q[i].x] - 1) - Query(dfn[Q[i].x] - 1);
            if(x < sum) Q[i].mark = 1;
        }
    }
    for(int i = ll; i <= rr; i ++)
    {
        int x = Q[i].x, y = Q[i].y;
        if(!Q[i].opt && Q[i].rec > mid && !book[Q[i].id])
        {
            Update(dfn[x], -1), Update(dfn[y], -1);
            int K = RMQ(x, y);
            Update(K, 1), Update(f[K], 1);
        }
    }
    int L = 0, R = 0;
    for(int i = ll; i <= rr; i ++)
    {
        if(Q[i].opt == 2) 
        {
            if(Q[i].mark) Q[i].mark = 0, qr[++ R] = Q[i];
            else ql[++ L] = Q[i];
        }
        else if(Q[i].rec > mid) qr[++ R] = Q[i]; 
        else ql[++ L] = Q[i];
    }
    int rec = ll - 1, ls = 1, rs = 1;
    while(ls <= L) Q[++ rec] = ql[ls], ls ++;
    while(rs <= R) Q[++ rec] = qr[rs], rs ++;
    
    Check(l, mid, ll, ll + ls - 2);
    Check(mid + 1, r, ll + ls - 1, rr);
}

void init()
{
    bit[0] = 1; for(int i = 1; i < CNST; 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(), m = read();
    for(int i = 1; i <= m; i ++) Ans[i] = -INF;
    for(int i = 1; i < n; i ++)
    {
        int u = read(), v = read();
        E1.add(u, v);
    }
    dfs(1, 0);
    for(int i = 1; i <= Log[cnt]; i ++)
        for(int j = 1; j + bit[i - 1] <= cnt; j ++)
            ST[j][i] = min(ST[j][i - 1], ST[j + bit[i - 1]][i - 1]);
    for(int i = 1; i <= m; i ++)
    {
        Q[i].opt = read(); Q[i].id = i; 
        if(Q[i].opt == 0) 
        {
            Q[i].x = read(), Q[i].y = read(), Q[i].w = read();
            b[++ tot] = Q[i].w;
        }
        else if(Q[i].opt == 1)
        {
            int t = read(); book[t] = 1;
            Q[i] = Q[t], Q[i].opt = 1;  Q[i].id = i;
        }
        else if(Q[i].opt == 2) Q[i].x = read();
    }
    sort(b + 1, b + 1 + tot); int tem = 0;
    for(int i = 1; i <= tot; i ++)
        if(b[i] != b[i - 1]) Map[b[i]] = ++ tem, id[tem] = b[i];
    tot = tem;
    for(int i = 1; i <= m; i ++)
        if(!Q[i].opt || Q[i].opt == 1) Q[i].rec = Map[Q[i].w];
    Check(0, tot, 1, m);
    for(int i = 1; i <= m; i ++)
        if(Ans[i] != -INF) printf("%d\n", Ans[i]);
    return 0;
}