动态树

Link-Cut Tree

洛谷 P3690 【模板】Link Cut Tree （动态树）

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using p = pair<int, int>;
const int maxn(1e5 + 10);

struct node {
    int l, r;
    int ch[2], fa;
    int val, sum;
    bool rev;
} tree[maxn];

template<typename T = int>
inline const T read()
{
    T x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' or ch > '9') {
        if (ch == '-') f = -1;
        ch = getchar();
    }
    while (ch >= '0' and ch <= '9') {
        x = (x << 3) + (x << 1) + ch - '0';
        ch = getchar();
    }
    return x * f;
}

template<typename T>
inline void write(T x, bool ln)
{
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    if (x > 9) write(x / 10, false);
    putchar(x % 10 + '0');
    if (ln) putchar(10);
}

inline int& ls(int cur)
{
    return tree[cur].ch[0];
}

inline int& rs(int cur)
{
    return tree[cur].ch[1];
}

inline bool get_rel(int cur, int fa)
{
    return tree[fa].ch[1] == cur;
}

inline void connect(int cur, int fa, bool rel)
{
    tree[fa].ch[rel] = cur;
    tree[cur].fa = fa;
}

inline bool is_root(int cur)
{
    return ls(tree[cur].fa) not_eq cur and rs(tree[cur].fa) not_eq cur;
}

inline void push_up(int cur)
{
    tree[cur].sum = tree[cur].val xor tree[ls(cur)].sum xor tree[rs(cur)].sum;
}

inline void reverse(int cur)
{
    swap(ls(cur), rs(cur));
    tree[cur].rev xor_eq 1;
}

inline void push_down(int cur)
{
    if (tree[cur].rev) {
        reverse(ls(cur));
        reverse(rs(cur));
        tree[cur].rev = false;
    }
}

inline void rotate(int cur)
{
    int fa = tree[cur].fa;
    int gf = tree[fa].fa;
    bool rel = get_rel(cur, fa);
    connect(tree[cur].ch[rel xor 1], fa, rel);
    tree[cur].fa = gf;
    if (not is_root(fa)) {
        tree[gf].ch[get_rel(fa, gf)] = cur;
    }
    connect(fa, cur, rel xor 1);
    push_up(fa);
    push_up(cur);
}

inline void push_all(int cur)
{
    if (not is_root(cur)) {
        push_all(tree[cur].fa);
    }
    push_down(cur);
}

inline void splaying(int cur)
{
    push_all(cur);
    while (not is_root(cur)) {
        int fa = tree[cur].fa;
        int gf = tree[fa].fa;
        if (not is_root(fa)) {
            get_rel(cur, fa) xor get_rel(fa, gf) ? rotate(cur) : rotate(fa);
        }
        rotate(cur);
    }
}

inline void access(int cur)
{
    for (int pre = 0; cur; cur = tree[cur].fa) {
        splaying(cur);
        rs(cur) = pre;
        push_up(cur);
        pre = cur;
    }
}

inline void make_root(int cur)
{
    access(cur);
    splaying(cur);
    reverse(cur);
}

inline int find_root(int cur)
{
    access(cur);
    splaying(cur);
    while (ls(cur)) {
        push_down(cur);
        cur = ls(cur);
    }
    splaying(cur);
    return cur;
}

inline void link(int u, int v)
{
    make_root(u);
    if (find_root(v) not_eq u) {
        tree[u].fa = v;
    }
}

inline void cut(int u, int v)
{
    make_root(u);
    if (find_root(v) == u and tree[v].fa == u and not ls(v)) {
        rs(u) = tree[v].fa = 0;
        push_up(u);
    }
}

inline void split(int u, int v)
{
    make_root(u);
    access(v);
    splaying(v);
}

int main()
{
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
#endif
    int n = read(), m = read();
    for (int i = 1; i <= n; ++i) {
        tree[i].val = read();
    }
    while (m--) {
        int op = read(), x = read(), y = read();
        if (op == 0) {
            split(x, y);
            write(tree[y].sum, true);
        } else if (op == 1) {
            link(x, y);
        } else if (op == 2) {
            cut(x, y);
        } else {
            splaying(x);
            tree[x].val = y;
            push_up(x);
        }
    }
    return 0;
}