Luogu 3979 遥远的国度

树剖已经是人尽皆知的sb题了吗……

很早以前就想填掉这坑了……

考虑到树链唯一，进行操作并不会对换根产生影响，那么我们的换根操作只要记下root在哪里就好了

询问的时候分类讨论：

1：root == x 直接返回全树最大值就好了

2：lca（root， x） ！= x，那就和x没什么关系了，只要返回原子树最大值就好了

3：lca（root， x） ==  x，说明x在root的上方，那么找到x的儿子中root的祖先y，除了y的子树就都是x的子树了

跳树链和找lca可以用倍增实现

总复杂度 O(nlog²n) 

Code（写的很长……）：

#include <cstdio>
using namespace std;

const int N = 1e5 + 5;
const int Lg = 20;
const int inf = 1 << 30;

int n, qn, a[N], tot = 0, head[N], root;
int dfsc = 0, id[N], siz[N], top[N];
int w[N], dep[N], fa[N][Lg], son[N];

struct Edge {
    int to, nxt;
} e[N << 1];

inline void add(int from, int to) {
    e[++tot].to = to;
    e[tot].nxt = head[from];
    head[from] = tot;
}

inline void read(int &X) {
    X = 0;
    char ch = 0;
    int op = 1;
    for(; ch > '9' || ch < '0'; ch = getchar())
        if(ch == '-') op = -1;
    for(; ch >= '0' && ch <= '9'; ch = getchar())
        X = (X << 3) + (X << 1) + ch - 48;
    X *= op;
}

inline int min(int x, int y) {
    return x > y ? y : x;
}

inline void chkMin(int &x, int y) {
    if(y < x) x = y;
}

inline void swap(int &x, int &y) {
    int t = x;
    x = y;
    y = t;
}

void dfs1(int x, int fat, int depth) {
    siz[x] = 1, fa[x][0] = fat, dep[x] = depth;
    for(int i = 1; i <= 18; i++)
        fa[x][i] = fa[fa[x][i - 1]][i - 1];
    
    int maxson = -1;
    for(int i = head[x]; i; i = e[i].nxt) {
        int y = e[i].to;
        if(y == fat) continue;
        dfs1(y, x, depth + 1);
        siz[x] += siz[y];
        if(siz[y] > maxson) 
            maxson = siz[y], son[x] = y;
    }
}

void dfs2(int x, int topf) {
    w[id[x] = ++dfsc] = a[x], top[x] = topf;
    if(!son[x]) return;
    dfs2(son[x], topf);
    for(int i = head[x]; i; i = e[i].nxt) {
        int y = e[i].to;
        if(y == fa[x][0] || y == son[x]) continue;
        dfs2(y, y);
    }
}

inline int getLca(int x, int y) {
    if(dep[x] < dep[y]) swap(x, y);
    for(int i = 18; i >= 0; i--)
        if(dep[fa[x][i]] >= dep[y])
            x = fa[x][i];
    if(x == y) return x;
    for(int i = 18; i >= 0; i--)
        if(fa[x][i] != fa[y][i])
            x = fa[x][i], y = fa[y][i];
    return fa[x][0];
}

namespace SegT {
    int s[N << 2], tag[N << 2];
    
    #define lc p << 1
    #define rc p << 1 | 1
    #define mid ((l + r) >> 1)
    
    inline void up(int p) {
        if(p) s[p] = min(s[lc], s[rc]);
    }
    
    inline void down(int p) {
        if(tag[p] == inf) return;
        s[lc] = tag[lc] = s[rc] = tag[rc] = tag[p];
        tag[p] = inf;
    }
    
    void build(int p, int l, int r) {
        tag[p] = inf;
        if(l == r) {
            s[p] = w[l];
            return;
        }
        
        build(lc, l, mid);
        build(rc, mid + 1, r);
        up(p);
    }
    
    void modify(int p, int l, int r, int x, int y, int v) {
        if(x <= l && y >= r) {
            s[p] = tag[p] = v;
            return;
        }
        
        down(p);
        if(x <= mid) modify(lc, l, mid, x, y, v);
        if(y > mid) modify(rc, mid + 1, r, x, y, v);
        up(p); 
    }
    
    int query(int p, int l, int r, int x, int y) {
        if(x <= l && y >= r) return s[p];
        down(p);
        
        int res = inf;
        if(x <= mid) chkMin(res, query(lc, l, mid, x, y));
        if(y > mid) chkMin(res, query(rc, mid + 1, r, x, y));
        return res;
    }
    
} using namespace SegT;

inline void mtree(int x, int y, int v) {
    for(; top[x] != top[y]; ) {
        if(dep[top[x]] < dep[top[y]]) swap(x, y);
        modify(1, 1, n, id[top[x]], id[x], v);
        x = fa[top[x]][0];
    }
    if(dep[x] > dep[y]) swap(x, y);
    modify(1, 1, n, id[x], id[y], v);
}

inline int ask(int x) {
    if(root == x) return s[1];
    int y = getLca(x, root);
    if(y == x) {
        int z = root;
        for(int i = 18; i >= 0; i--)
            if(dep[fa[z][i]] > dep[y])
                z = fa[z][i];
        return min(query(1, 1, n, 1, id[z] - 1), query(1, 1, n, id[z] + siz[z], n));
    } else return query(1, 1, n, id[x], id[x] + siz[x] - 1);
}

int main() {
    read(n), read(qn);
    for(int x, y, i = 1; i < n; i++) {
        read(x), read(y);
        add(x, y), add(y, x);
    }
    dfs1(1, 0, 1);
    
    for(int i = 1; i <= n; i++) read(a[i]);
    dfs2(1, 1);
    build(1, 1, n);
    
    read(root);
    for(int op; qn--; ) {
        read(op);
        if(op == 1) read(root);
        if(op == 2) {
            int x, y, v;
            read(x), read(y), read(v);
            mtree(x, y, v);
        }
        if(op == 3) {
            int x;
            read(x);
            printf("%d
", ask(x));
        }
    }
    
    return 0;
}