「LuoguP3979」遥远的国度

标签：space   res   http   const   代码   第一个   直接   就是   amp   

传送门
Luogu

解题思路

带换根操作的树剖。
换根只会影响更新或查询子树信息的操作。
我们始终保持初始的根不变，然后只要分类讨论一下：
假设当前被查询的节点是 \(u\)

1. 如果 \(u\) 就是根节点，直接询问整棵树；
2. 如果 \(u\) 不是根，且不是初始根的祖先，直接查询子树即可；
3. 如果 \(u\) 是根的祖先，那么我们就找到 \(u\) 到根这条路径上的第一个儿子，然后分开查询即可
   至于怎么分开查询，自己yy一下就好了。

细节注意事项

• 咕咕咕

参考代码

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <cctype>
#include <cmath>
#include <ctime>
#define rg register
using namespace std;
template < typename T > inline void read(T& s) {
    s = 0; int f = 0; char c = getchar();
    while (!isdigit(c)) f |= (c == '-'), c = getchar();
    while (isdigit(c)) s = s * 10 + (c ^ 48), c = getchar();
    s = f ? -s : s;
}

const int _ = 100010;

int tot, head[_], nxt[_ << 1], ver[_ << 1];
inline void Add_edge(int u, int v)
{ nxt[++tot] = head[u], head[u] = tot, ver[tot] = v; }

int n, m, rt, val[_];
int dep[_], siz[_], son[_], fa[_];
int top[_], dfn[_], rev[_];
int mn[_ << 2], tag[_ << 2];

inline int lc(int p) { return p << 1; }

inline int rc(int p) { return p << 1 | 1; }

inline void pushup(int p) { mn[p] = min(mn[lc(p)], mn[rc(p)]); }

inline void f(int p, int v) { mn[p] = tag[p] = v; }

inline void pushdown(int p)
{ if (tag[p]) f(lc(p), tag[p]), f(rc(p), tag[p]), tag[p] = 0; }

inline void build(int p = 1, int l = 1, int r = n) {
    tag[p] = 0; if (l == r) { mn[p] = val[rev[l]]; return ; }
    int mid = (l + r) >> 1;
    build(lc(p), l, mid), build(rc(p), mid + 1, r), pushup(p);
}

inline void update(int ql, int qr, int v, int p = 1, int l = 1, int r = n) {
    if (ql <= l && r <= qr) return f(p, v);
    int mid = (l + r) >> 1;
    pushdown(p);
    if (ql <= mid) update(ql, qr, v, lc(p), l, mid);
    if (qr > mid) update(ql, qr, v, rc(p), mid + 1, r);
    pushup(p);
}

inline int query(int ql, int qr, int p = 1, int l = 1, int r = n) {
    if (ql <= l && r <= qr) return mn[p];
    int mid = (l + r) >> 1, res = 2147483647;
    pushdown(p);
    if (ql <= mid) res = min(res, query(ql, qr, lc(p), l, mid));
    if (qr > mid) res = min(res, query(ql, qr, rc(p), mid + 1, r));
    return res;
}

inline void dfs1(int u, int f) {
    siz[u] = 1, fa[u] = f, dep[u] = dep[f] + 1;
    for (rg int v, i = head[u]; i; i = nxt[i])
        if (!dep[v = ver[i]]) {
            dfs1(v, u), siz[u] += siz[v];
            if (siz[son[u]] < siz[v]) son[u] = v;
        }
}

inline void dfs2(int u, int topf) {
    top[rev[dfn[u] = ++dfn[0]] = u] = topf;
    if (!son[u]) return; dfs2(son[u], topf);
    for (rg int v, i = head[u]; i; i = nxt[i])
        if (!top[v = ver[i]]) dfs2(v, v);
}

inline int pson(int x, int y){
    int fx = top[x], fy = top[y];
    while (fx != fy){
        if (dep[fx] < dep[fy]) swap(x, y), swap(fx, fy);
        if (fa[fx] == y) return fx; x = fa[fx], fx = top[x];
    }
    return dep[x] < dep[y] ? son[x] : son[y];
}

inline int LCA(int x, int y) {
    int fx = top[x], fy = top[y];
    while (fx != fy) {
        if (dep[fx] < dep[fy]) swap(x, y), swap(fx, fy);
        x = fa[fx], fx = top[x];
    }
    return dep[x] < dep[y] ? x : y;
}

inline void uptRange(int x, int y, int v) {
    int fx = top[x], fy = top[y];
    while (fx != fy) {
        if (dep[fx] < dep[fy]) swap(x, y), swap(fx, fy);
        update(dfn[fx], dfn[x], v), x = fa[fx], fx = top[x];
    }
    if (dep[x] > dep[y]) swap(x, y);
    return update(dfn[x], dfn[y], v);
}

inline int qSon(int x) {
    if (rt == x) return query(1, n);
    int lca = LCA(rt, x);
    if (lca != x) return query(dfn[x], dfn[x] + siz[x] - 1);
    int t = pson(rt, x);
    return min(query(1, dfn[t] - 1), query(dfn[t] + siz[t], n));
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("in.in", "r", stdin);
#endif
    read(n), read(m);
    for (rg int u, v, i = 1; i < n; ++i)
        read(u), read(v), Add_edge(u, v), Add_edge(v, u);
    for (rg int i = 1; i <= n; ++i) read(val[i]);
    read(rt), dfs1(rt, 0), dfs2(rt, rt), build();
    for (int opt, x, y, v; m--; ) {
        read(opt);
        if (opt == 1) read(rt);
        else if (opt == 2) read(x), read(y), read(v), uptRange(x, y, v);
        else if (opt == 3) read(x), printf("%d\n", qSon(x));
    }
    return 0;
}

完结撒花 \(qwq\)

「LuoguP3979」遥远的国度

标签：space   res   http   const   代码   第一个   直接   就是   amp   

原文地址：https://www.cnblogs.com/zsbzsb/p/11746535.html