洛谷P3690 【模板】Link Cut Tree （动态树）

【模板】Link Cut Tree （动态树）

题目传送门

解题思路

妈妈我终于学会LCT了。

代码如下

#include <bits/stdc++.h>

using namespace std;

const int N = 300005;

int v[N], fa[N], ch[N][2], sum[N];
bool lazy[N];

inline bool get(int x)
{
    return ch[fa[x]][1] == x;
}

inline void pushr(int x)
{
    swap(ch[x][1], ch[x][0]);
    lazy[x] ^= 1;
}

inline void push_down(int x)
{
    if(lazy[x]){
        pushr(ch[x][0]);
        pushr(ch[x][1]);
        lazy[x] = 0;
    }
}

inline void update(int x)
{
    sum[x] = sum[ch[x][0]] ^ sum[ch[x][1]] ^ v[x];
}

inline bool isroot(int x)
{
    return (!fa[x] || (ch[fa[x]][1] != x && ch[fa[x]][0] != x));
}

inline void rotate(int x)
{
    int y = fa[x], z = fa[y];
    bool u = get(x), v = get(y);
    ch[y][u] = ch[x][u^1], fa[ch[x][u^1]] = y;
    if(!isroot(y))
        ch[z][v] = x;
    fa[x] = z;
    ch[x][u^1] = y, fa[y] = x;
    update(y), update(x);
}

int sta[N];

inline void splay(int x)
{  
    int pos = 0;
    sta[++pos] = x;
    for(int i = x; !isroot(i); i = fa[i])
        sta[++pos] = fa[i];
    while(pos)
        push_down(sta[pos --]);
    while(!isroot(x)){
        int y = fa[x];
        if(!isroot(y)){
            get(x) == get(y) ? rotate(y): rotate(x);
        }
        rotate(x);
    }
}

void access(int x)
{
    for(int y = 0; x; y = x, x = fa[x])
        splay(x), ch[x][1] = y, update(x);
}

void make_root(int x)
{
    access(x);splay(x);
    pushr(x);
}

int find_root(int x)
{
    access(x);splay(x);
    while(ch[x][0]){
        push_down(x);
        x = ch[x][0];
    }
    splay(x);
    return x;
}

void link(int x, int y)
{
    make_root(x);
    if(find_root(y) != x)
        fa[x] = y;
}

void split(int x, int y)
{
    make_root(x);
    access(y);splay(y);
}

void cut(int x, int y)
{
    make_root(x);
    if(find_root(y) != x || fa[y] != x || ch[y][0])
        return;
    fa[y] = ch[x][1] = 0;
    update(x);
}

int main()
{
    int n, m;
    scanf("%d%d", &n, &m);
    for(int i = 1; i <= n; i ++){
        scanf("%d", &v[i]);
        sum[i] = v[i];
    }
    for(int i = 1; i <= m; i ++){
        int opt, x, y;
        scanf("%d%d%d", &opt, &x, &y);
        if(opt == 0){
            split(x, y);
            printf("%d\n", sum[y]);
        }
        else if(opt == 1){
            link(x, y);
        }
        else if(opt == 2){
            cut(x, y);
        }
        else {
            splay(x);
            v[x] = y;
            update(x);
        }
    }
    return 0;
}