bzoj3786

splay维护dfs序

我们发现有移动子树这种操作,树剖是做不了了,又要实现子树加,lct又维护不了了,这时我们用splay维护入栈出栈序来支持这些操作。我们记录每个点的入栈时间和出栈时间,这样一个闭合的区间就表示了一个节点的子树,于是我们可以支持更换父亲了。然后是子树加,这里我们把要加的区间提取出来,打标记,但是我们还得维护一个符号总和,因为入栈时间加,出栈时间要减去加的值,因为出栈时间之后得序列就不属于这棵子树了。最后是查询,查询我们只要把查询节点的入栈时间和1号节点提取出来,然后总和就是答案。注意提取区间时不是in[x]-1,out[x]+1,虽然这里节点编号就是对应排名,但是因为这里是出栈入栈序,所以+1-1不一定是序列中下一个节点,所以我们要查询前继后继,也就是提取pre(in[x])和nxt(out[x])

然后还卡时间,我用fread卡过去了

#include<bits/stdc++.h>
using namespace std;
const int N = 400010, Maxlen = 100 * N;
int n, m, dfs_clock = 1, root;
int in[N], out[N];
long long w[N];
vector<int> G[N];
char buf[Maxlen], *C = buf;
int Len;
inline int read() 
{
     int x = 0;
     while (*C < '0' || '9' < *C) ++C;
     while ('0' <= *C && *C <= '9') x = x * 10 + *C - '0', ++C;
     return x;
}
namespace Splay_tree
{
    int cnt;
    int child[N][2], fa[N], st[N];
    long long sum[N], key[N], tag[N], tim[N], sum_tim[N];
    inline bool wh(int x)
    {
        return child[fa[x]][1] == x;
    }
    inline void update(int x)
    {
        sum[x] = sum[child[x][0]] + sum[child[x][1]] + key[x];
        sum_tim[x] = sum_tim[child[x][0]] + sum_tim[child[x][1]] + tim[x];
    }
    inline void pushdown(int x)
    {
        if(tag[x] == 0) return;
        tag[child[x][0]] += tag[x];
        tag[child[x][1]] += tag[x]; 
        key[child[x][0]] += tag[x] * tim[child[x][0]];
        key[child[x][1]] += tag[x] * tim[child[x][1]];
        sum[child[x][0]] += tag[x] * sum_tim[child[x][0]];
        sum[child[x][1]] += tag[x] * sum_tim[child[x][1]]; 
        tag[x] = 0;
    }
    inline void rotate(int x)
    {
        int y = fa[x], z = fa[y], t = wh(x);
        fa[x] = z;
        child[z][wh(y)] = x;
        child[y][t] = child[x][t ^ 1];
        fa[child[x][t ^ 1]] = y;
        child[x][t ^ 1] = y;
        fa[y] = x;
        update(y);
        update(x);
    }
    inline void up(int x)
    {
        int top = 0, now = x;
        while(now != root) 
        {
            st[++top] = now;
            now = fa[now];
        }
        st[++top] = root;
        for(int i = top; i; --i) pushdown(st[i]);
    }
    inline void splay(int x, int t)
    {
        up(x);
        for(int f; (f = fa[x]) != t; rotate(x))
            if(fa[f] != t) rotate(wh(x) == wh(f) ? f : x);
        if(!t) root = x;    
    }
    inline void build(int l, int r, int &x, int last)
    {
        if(l > r) return;
        int mid = (l + r) >> 1;
        x = mid;
        fa[x] = last;
        build(l, mid - 1, child[x][0], x); 
        build(mid + 1, r, child[x][1], x);
        update(x);  
    }
    inline int pre(int x)
    {
        splay(x, 0);
        x = child[x][0];
        while(child[x][1]) x = child[x][1];
        return x;
    }
    inline int nxt(int x)
    {
        splay(x, 0);
        x = child[x][1];
        while(child[x][0]) x = child[x][0];
        return x;
    }
    inline void change(int x, int y)
    {
        int a = pre(in[x]), b = nxt(out[x]);
        splay(a, 0);
        splay(b, root);
        int t = child[child[root][1]][0];
        fa[t] = child[child[root][1]][0] = 0;
        update(child[root][1]);
        update(root);
        a = nxt(in[y]);
        splay(in[y], 0);
        splay(a, root);
        fa[t] = child[root][1];
        child[child[root][1]][0] = t;
        update(child[root][1]);
        update(root);
    }
    inline void ask(int x)
    {
        x = nxt(in[x]);
        splay(1, 0);
        splay(x, root); 
        int t = child[child[root][1]][0];
        printf("%lld\n", sum[t]);   
    }
    inline void add(int x, int delta)
    {
        int a = pre(in[x]), b = nxt(out[x]);
        splay(a, 0);
        splay(b, root);
        int t = child[child[root][1]][0];
        tag[t] += delta;
        sum[t] += delta * sum_tim[t];
        key[t] += delta * tim[t];
    }
} using namespace Splay_tree;
void dfs(int u)
{
    in[u] = ++dfs_clock;
    tim[in[u]] = 1;
    key[in[u]] = w[u];
    for(int i = 0; i < G[u].size(); ++i)
    {
        int v = G[u][i];
        dfs(v);
    }
    out[u] = ++dfs_clock;
    key[out[u]] = -w[u];
    tim[out[u]] = -1;
}
int main()
{
//    freopen("galaxy20.in", "r", stdin);
//    freopen("output.txt", "w", stdout);
    Len = fread(C, 1, Maxlen, stdin);
    buf[Len] = '\0';    
    n = read();
    for(int i = 2; i <= n; ++i) 
    {
        int u = read();
        G[u].push_back(i);
    }
    for(int i = 1; i <= n; ++i) w[i] = read();
    dfs(1);
    ++dfs_clock;
    build(1, dfs_clock, root, 0);
    m = read();
    while(m--)
    {
        char c;
        int x, y;
        for(c = *C; c < 'A' || c > 'Z'; ++C, c = *C);
        if(c == 'Q')
        {
            x = read();
            ask(x);
        }
        if(c == 'C')
        {
            x = read();
            y = read();
            change(x, y);
        }
        if(c == 'F')
        {
            x = read();
            y = read();
            add(x, y);
        }
    }
//    fclose(stdin);
//    fclose(stdout);
    return 0;
}
View Code

 

posted @ 2017-08-15 22:43  19992147  阅读(171)  评论(0编辑  收藏  举报