P2146 [NOI2015] 软件包管理器

思路分析

树链剖分板子，每次安装时，将 \(1\) 到 \(x\) 的链变为 \(1\)，卸载时，将 \(x\) 的子树变为 \(0\)。

代码

#include<iostream>

using namespace std;

inline int read(){register int x = 0, f = 1;register char c = getchar();while (c < '0' || c > '9'){if (c == '-') f = -1;c = getchar();}while (c >= '0' && c <= '9'){x = (x << 1) + (x << 3) + (c ^ 48);c = getchar();}return x * f;}
inline void write(int x){if (x < 0) putchar('-'), x = -x;if (x > 9) write(x / 10);putchar(x % 10 + '0');}

const int N = 1e5 + 10;
int n, q;
struct edge{
	int v, nxt;
}e[N << 1];
int head[N], cnt;
int sz[N], dep[N], son[N], f[N], id[N], top[N], tot;
void add(int u, int v){
	e[++cnt] = (edge){v, head[u]};
	head[u] = cnt;
}
void dfs1(int u, int fa){
	sz[u] = 1, f[u] = fa, dep[u] = dep[fa] + 1;
	for (int i = head[u]; i; i = e[i].nxt){
		int v = e[i].v;
		if (v == fa) continue;
		dfs1(v, u);
		sz[u] += sz[v];
		if (sz[v] > sz[son[u]]) son[u] = v;
	}
}
void dfs2(int u, int t){
	id[u] = ++tot;
	top[u] = t;
	if (son[u]) dfs2(son[u], t);
	for (int i = head[u]; i; i = e[i].nxt){
		int v = e[i].v;
		if (v == f[u] || v == son[u]) continue;
		dfs2(v, v);
	}
}
struct tree{
	int sum, tag;
}t[N << 2];
void pushup(int now){
	t[now].sum = t[now << 1].sum + t[now << 1 | 1].sum;
}
void pushdown(int now, int l, int r){
	if (t[now].tag != -1){
		int mid = (l + r) >> 1;
		t[now << 1].sum = t[now].tag * (mid - l + 1);
		t[now << 1 | 1].sum = t[now].tag * (r - mid);
		t[now << 1].tag = t[now].tag;
		t[now << 1 | 1].tag = t[now].tag;
		t[now].tag = -1;
	}
}
void build(int now, int l, int r){
	t[now].tag = -1, t[now].sum = 0;
	if (l == r) return;
	int mid = (l + r) >> 1;
	build(now << 1, l, mid);
	build(now << 1 | 1, mid + 1, r);
}
void modify(int now, int l, int r, int x, int y, int k){
	if (x <= l && r <= y){
		t[now].sum = k * (r - l + 1), t[now].tag = k;
		return;
	}
	pushdown(now, l, r);
	int mid = (l + r) >> 1;
	if (x <= mid) modify(now << 1, l, mid, x, y, k);
	if (mid + 1 <= y) modify(now << 1 | 1, mid + 1, r, x, y, k);
	pushup(now);
}
void modify_chain(int x, int y, int k){
	int fx = top[x], fy = top[y];
	while (fx != fy){
		if (dep[fx] < dep[fy]) swap(x, y), swap(fx, fy);
		modify(1, 1, n, id[fx], id[x], k);
		x = f[fx], fx = top[x];
	}
	if (id[x] > id[y]) swap(x, y);
	modify(1, 1, n, id[x], id[y], k);
}

int main(){
	n = read();
	for (int i = 1; i < n; i++){
		int x = read() + 1;
		add(x, i + 1);
	}
	dfs1(1, 0);
	dfs2(1, 1);
	build(1, 1, n);
	q = read();
	for (int i = 1; i <= q; i++){
		char c[10];
		cin >> c;
		int OP = t[1].sum, x = read() + 1;
		if (c[0] == 'i'){
			modify_chain(1, x, 1);
			cout << t[1].sum - OP << '\n';
		}else{
			modify(1, 1, n, id[x], id[x] + sz[x] - 1, 0);
			cout << OP - t[1].sum << '\n';
		}
	}
	return 0;
}