loj10140. 「一本通 4.5 练习 2」软件包管理器 （loj2130. 「NOI2015」软件包管理器 ）

思路：

　　树链剖分+修改版线段树，将所有点后移一位使编号从1到n，先剖分树链维护end[x]为x为根的子树中最后访问的点，再用线段树维护每一区间内已安装的包数。

　　最后回答问题时注意，安装应采用一段一段累加法，卸载应采用整段累加法。

#include<cstdio>
#include<iostream>
#include<vector>
#include<cmath>
#include<string>
using namespace std;
const int maxn = 100010;
inline void qread(int &x){
    x = 0;
    register int ch = getchar(), flag = 0;
    while(ch < '0' || ch > '9')    {
        if(ch == '-')    flag = 1;
        ch = getchar();
    }
    while(ch >= '0' && ch <= '9')
        x = 10 * x + ch - 48, ch = getchar();
    if(flag)    x = -x;    
}
int n, q, rt = 1;
int head[maxn];
int nxt[maxn];

int f[maxn];
int deep[maxn];
int val[maxn];
int size[maxn];
int son[maxn];
int seg[maxn];
int rev[maxn];
int top[maxn];
int end[maxn];
int sum[maxn << 2];
int cov[maxn << 2];
void init(){
    qread(n);
    for(int i=2; i<=n; ++i){
        qread(f[i]);
        nxt[i] = head[++f[i]];
        head[f[i]] = i;
    }
    qread(q);
    deep[1] = top[1] = seg[0] = seg[1] = rev[1] = 1;
}
void dfs1(int x){
    size[x] = 1;
    for(register int i = head[x]; i; i=nxt[i]){
        if(!deep[i]){
            deep[i] = deep[x] + 1;
            dfs1(i);
            size[x] += size[i];
            if(size[i] > size[son[x]])
                son[x] = i;
        }
    }
}
void dfs2(int x){
    end[x] = x;
    if(son[x]){
        top[son[x]] = top[x];
        seg[son[x]] = ++seg[0];
        dfs2(son[x]);
        end[x] = end[son[x]];
    }
    for(register int i = head[x]; i; i=nxt[i])
        if(!top[i]){
            top[i] = i;
            seg[i] = ++seg[0];
            dfs2(i);
            end[x] = end[i];
        }    
}
inline void pushdown(int x, int t){
    cov[x << 1] = cov[x];
    cov[x << 1 | 1] = cov[x];
    sum[x << 1] = (cov[x] - 1) * ((t + 1) >> 1);
    sum[x << 1 | 1] = (cov[x] - 1) * (t >> 1);
    cov[x] = 0;
}
void segcha(int l, int r, int L, int R, int v, int x){
    if(L <= l && R >= r){
        cov[x] = v;
        sum[x] = (v - 1) * (r - l + 1);
        return ;
    }
    if(cov[x])    pushdown(x, r - l + 1);
    int mid = (l + r) >> 1;
    if(mid >= L)    segcha(l, mid, L, R, v, x << 1);
    if(mid < R)        segcha(mid + 1, r, L, R, v, x << 1 | 1);
    sum[x] = sum[x << 1] + sum[x << 1 | 1];
}
int segask(int l, int r, int L, int R, int x){
    if(L <= l && R >= r)
        return sum[x];
    if(cov[x])    pushdown(x, r - l + 1);
    int mid = (l + r) >> 1, ans = 0;
    if(mid >= L)    ans += segask(l, mid, L, R, x << 1);
    if(mid < R)        ans += segask(mid + 1, r, L, R, x << 1 | 1);
    return ans;    
}
void show(int l, int r, int x){
    cout << l << " " << r << " " << sum[x] << endl;
    if(l!=r){
        int mid = (l + r) >> 1;
        show(l, mid, x << 1);
        show(mid + 1, r, x << 1 | 1);
    }
}
void SHOW(){
    cout << "--" << endl;
    show(1, n, 1);
    cout << "--" << endl;
}
int ask(int x, int y, int v){
    int fx = top[x], fy = top[y], ans = 0;
    if(deep[fx] < deep[fy])    swap(x, y), swap(fx, fy);
    while(fx != fy){
        ans += segask(1, n, seg[fx], seg[x], 1);
        segcha(1, n, seg[fx], seg[x], v+1, 1);
        x = f[fx];
        fx = top[x];
    }
    if(deep[x] > deep[y])    swap(x, y);
    ans += segask(1, n, seg[x], seg[y], 1);
    segcha(1, n, seg[x], seg[y], v+1, 1);
    return ans;
}
int main(void){
    init();
    dfs1(1);    
    dfs2(1);
    while(q--){
        string op;
        cin >> op;
        if(op == "install"){
            int x;
            qread(x);
            x++;
            printf("%d\n", deep[x] - ask(1, x, 1));
        }
        else{
            int x;
            qread(x);
            x++;
            printf("%d\n", segask(1, n, seg[x], seg[end[x]], 1));
            segcha(1, n, seg[x], seg[end[x]], 0 + 1, 1);
        }
    }
}