省队集训Day1 睡觉困难综合征

传送门：https://www.luogu.org/problem/show?pid=3613

【题解】

按二进制位分开，对于每一位，用“起床困难综合征”的方法贪心做。

写棵LCT，维护正反两种权值，每个维护2种，代表全0的输出和全1的输出。

然后直接上LCT即可。

权值的合并有点trick，可以参考代码，需要压位。

# include <stdio.h>
# include <string.h>
# include <iostream>
# include <algorithm>
// # include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
const int M = 1e5 + ;
const int mod = 1e9+;

int n, m, K;

struct node {
    ull p0, p1;
    node () {}
    node (ull p0, ull p1) : p0(p0), p1(p1) {}
    friend node operator + (node a, node b) {
        return node( (a.p0 & b.p1) | ((~a.p0) & b.p0), (a.p1 & b.p1) | ((~a.p1) & b.p0) );
    }
};

inline node deal(int op, ull x) {
    if(op == ) return node(, x);
    if(op == ) return node(x, ull(-));
    if(op == ) return node(x, ~x);
}

struct LCT {
    int ch[M][], fa[M];
    bool rev[M];
    node w[M][], val[M];
    # define ls ch[x][]
    # define rs ch[x][]
    inline void up(int x) {
        if(!x) return ;
        w[x][] = w[x][] = val[x];
        if(ls) w[x][] = w[ls][] + w[x][], w[x][] = w[x][] + w[ls][];
        if(rs) w[x][] = w[x][] + w[rs][], w[x][] = w[rs][] + w[x][];
    }
    inline void pushrev(int x) {
        if(!x) return ;
        rev[x] ^= ;
        swap(ch[x][], ch[x][]);
        swap(w[x][], w[x][]);
    }
    inline void down(int x) {
        if(!x || !rev[x]) return ;
        pushrev(ls); pushrev(rs);
        rev[x] = ;
    }
    # undef ls
    # undef rs
    inline bool isrt(int x) {
        return ch[fa[x]][] != x && ch[fa[x]][] != x;
    }
    inline void rotate(int x) {
        int y = fa[x], z = fa[y], ls = ch[y][] == x, rs = ls^;
        if(!isrt(y)) ch[z][ch[z][] == y] = x;
        fa[ch[x][rs]] = y, fa[y] = x, fa[x] = z;
        ch[y][ls] = ch[x][rs]; ch[x][rs] = y;
        up(y); up(x);
    }
    int st[M];
    inline void splay(int x) {
        int stn = , tx = x;
        while(!isrt(tx)) st[++stn] = tx, tx = fa[tx];
        st[++stn] = tx;
        for (int i=stn; i; --i) down(st[i]);
        while(!isrt(x)) {
            int y = fa[x], z = fa[y];
            if(!isrt(y)) {
                if((ch[z][] == y)^(ch[y][] == x)) rotate(x);
                else rotate(y);
            }
            rotate(x);
        }
    }

    inline int access(int x) {
        int t = ;
        for (; x; t = x, x = fa[x]) {
            splay(x);
            ch[x][] = t;
            up(x);
        }
        return t;
    }

    inline void makeroot(int x) {
        access(x); splay(x); pushrev(x);
    }

    inline void link(int x, int y) {
        makeroot(y); fa[y] = x;
    }
}T;

# define bit(x, i) (((x) >> (i)) & ) 

int main() {
//    freopen("sleep.in", "r", stdin);
//    freopen("sleep.out", "w", stdout);
    scanf("%d%d%d", &n, &m, &K);
    for (int i=, op; i<=n; ++i) {
        ull x;
        scanf("%d%llu", &op, &x);
        T.val[i] = T.w[i][] = T.w[i][] = deal(op, x);
        T.ch[i][] = T.ch[i][] = T.fa[i] = T.rev[i] = ;
    }
    for (int i=, u, v; i<n; ++i) {
         scanf("%d%d", &u, &v);
        T.link(u, v);
    }
    int op, x, y; ull z, tx, ty, ans, t;
    while(m--) {
        scanf("%d%d%d%llu", &op, &x, &y, &z);
        if(op == ) {
            ans = ; t = ;
            T.makeroot(x); T.access(y); T.splay(y);
            tx = T.w[y][].p0, ty = T.w[y][].p1;
            for (int i=; ~i; --i) {
                if(bit(tx, i)) ans |= (1ull << i);
                else if(bit(ty, i)) {
                    if(t + (1ull << i) <= z) t = t + (1ull << i), ans |= (1ull << i);
                }
            }
            printf("%llu\n", ans);
        } else {
            T.splay(x);
            T.val[x] = deal(y, z);
            T.up(x);
        }
    }
    return ;
}