题意
给定一棵树和 \(3\) 个操作。
- 如果点 \(x\) 是白色，将她染红，否则对她地儿子做这个操作。
- 将点 \(x\) 子树内所有点染白。
- 询问 \(x\) 的颜色。
Sol
考虑对询问分块。
不难想到将当前块内的点建一棵虚树，然后再重构。
暴力建虚树即可。
Code
#include <iostream>
#include <algorithm>
#include <cstdio>
#include <array>
#include <vector>
#include <bitset>
#include <cassert>
#define pii pair <int, int>
using namespace std;
#ifdef ONLINE_JUDGE
#define getchar() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1 << 21, stdin), p1 == p2) ? EOF : *p1++)
char buf[1 << 23], *p1 = buf, *p2 = buf, ubuf[1 << 23], *u = ubuf;
#endif
int read() {
int p = 0, flg = 1;
char c = getchar();
while (c < '0' || c > '9') {
if (c == '-') flg = -1;
c = getchar();
}
while (c >= '0' && c <= '9') {
p = p * 10 + c - '0';
c = getchar();
}
return p * flg;
}
void write(int x) {
if (x < 0) {
x = -x;
putchar('-');
}
if (x > 9) {
write(x / 10);
}
putchar(x % 10 + '0');
}
#define fi first
#define se second
const int N = 2e5 + 5, M = 4e5 + 5, bsk = 317;
namespace G {
array <int, N> fir;
array <int, M> nex, to;
int cnt = 1;
void add(int x, int y) {
cnt++;
nex[cnt] = fir[x];
to[cnt] = y;
fir[x] = cnt;
}
}
namespace T {
array <int, N> fir;
array <int, M> nex, to, len;
int cnt = 1;
void add(int x, int y, int z) {
assert(x != y);
cnt++;
nex[cnt] = fir[x];
to[cnt] = y;
len[cnt] = z;
fir[x] = cnt;
}
}
namespace Hpt {
array <int, N> fa, dep, siz, son;
void dfs1(int x) {
siz[x] = 1;
for (int i = G::fir[x]; i; i = G::nex[i]) {
if (G::to[i] == fa[x]) continue;
fa[G::to[i]] = x;
dep[G::to[i]] = dep[x] + 1;
dfs1(G::to[i]);
siz[x] += siz[G::to[i]];
if (siz[G::to[i]] > siz[son[x]]) son[x] = G::to[i];
}
}
array <int, N> dfn, top, idx;
int cnt;
void dfs2(int x, int Mgn) {
cnt++;
dfn[x] = cnt;
idx[cnt] = x;
top[x] = Mgn;
if (son[x]) dfs2(son[x], Mgn);
for (int i = G::fir[x]; i; i = G::nex[i]) {
if (G::to[i] == fa[x] || G::to[i] == son[x]) continue;
dfs2(G::to[i], G::to[i]);
}
}
int lca(int x, int y) {
while (top[x] != top[y]) {
if (dep[top[x]] < dep[top[y]]) swap(x, y);
x = fa[top[x]];
}
if (dep[x] > dep[y]) swap(x, y);
return x;
}
}
namespace Vit {
array <int, N> stk;
bitset <N> vis;
int top;
array <int, N> isl, agc;
int getdep(int x, int y) {
int ans = 0;
y = Hpt::fa[y];
while (y != x)
ans += !agc[y], y = Hpt::fa[y];
return ans;
}
void build(vector <int> &isl) {
sort(isl.begin(), isl.end(), [](int x, int y) {
return Hpt::dfn[x] < Hpt::dfn[y];
});
isl.erase(unique(isl.begin(), isl.end()), isl.end());
T::cnt = 1;
top = 1, stk[top] = isl.front(), T::fir[isl.front()] = 0;
vis[isl.front()] = 1;
for (int i = 1; i < (int)isl.size(); i++) {
int lcA = Hpt::lca(stk[top], isl[i]);
if (lcA != stk[top]) {
while (Hpt::dfn[stk[top - 1]] > Hpt::dfn[lcA])
T::add(stk[top - 1], stk[top], getdep(stk[top - 1], stk[top])), top--;
if (stk[top - 1] != lcA)
T::fir[lcA] = 0, T::add(lcA, stk[top], getdep(lcA, stk[top])), stk[top] = lcA, vis[lcA] = 1;
else
T::add(stk[top - 1], stk[top], getdep(stk[top - 1], stk[top])), top--;
}
T::fir[isl[i]] = 0, top++, stk[top] = isl[i], vis[isl[i]] = 1;
}
for (int i = 1; i < top; i++)
T::add(stk[i], stk[i + 1], getdep(stk[i], stk[i + 1]));
}
bitset <N> cur;
void rever(int x) {
if (!agc[x]) {
agc[x] = 1;
return;
}
isl[x]++;
for (int i = T::fir[x]; i; i = T::nex[i]) {
if (T::len[i] > isl[x]) continue;
rever(T::to[i]);
}
}
void cover(int x) {
agc[x] = isl[x] = 0;
cur[x] = 1;
for (int i = T::fir[x]; i; i = T::nex[i])
T::len[i] = Hpt::dep[G::to[i]] - Hpt::dep[x], cover(T::to[i]);
}
void dfs(int x, int tp1, int tp2) {
if (vis[x]) tp1 = isl[x], tp2 |= cur[x];
if (!vis[x] && tp2) agc[x] = 0;
if (!vis[x] && !agc[x] && tp1) tp1--, agc[x] = 1;
for (int i = G::fir[x]; i; i = G::nex[i]) {
if (G::to[i] == Hpt::fa[x]) continue;
dfs(G::to[i], tp1, tp2);
}
}
}
vector <pii> qrl;
vector <int> tp;
int main() {
int n = read(), m = read();
for (int i = 2; i <= n; i++) {
int x = read();
G::add(x, i), G::add(i, x);
}
Hpt::dfs1(1), Hpt::dfs2(1, 0);
for (int i = 1; i <= m; i++) {
int op = read(), x = read();
qrl.push_back(make_pair(op, x));
tp.push_back(x), Vit::vis[x] = 1;
/* puts("@"); */
if (i % bsk && i != m) continue;
Vit::build(tp);
for (auto [op, x] : qrl) {
if (op == 1) Vit::rever(x);
if (op == 2) Vit::cover(x);
if (op == 3) puts(Vit::agc[x] ? "black" : "white");
}
Vit::dfs(Vit::stk[1], 0, 0);
Vit::vis = 0, Vit::cur = 0;
Vit::isl.fill(0);
tp.clear(), qrl.clear();
}
return 0;
}