LOJ#3088. 「GXOI / GZOI2019」旧词
不懂啊5e4感觉有点小
就是离线询问，在每个x上挂上y的询问
然后树剖，每个节点维护轻儿子中已经被加入的点的个数个数乘上\(dep[u]^{k}\)
新加一个点进去只会经过\(\log n\)条轻边只会更新\(\log n\)个节点
然后再维护一下每个子树里被加入点的个数，每次查询一段重链的链尾要加上重儿子个数减去从y来的那个轻儿子的子树个数乘上\(dep[u]^k\)
#include <bits/stdc++.h>
#define fi first
#define se second
#define pii pair<int,int>
#define mp make_pair
#define pb push_back
#define space putchar(' ')
#define enter putchar('\n')
#define eps 1e-10
#define MAXN 50005
#define ba 47
//#define ivorysi
using namespace std;
typedef long long int64;
typedef unsigned int u32;
typedef double db;
template<class T>
void read(T &res) {
res = 0;T f = 1;char c = getchar();
while(c < '0' || c > '9') {
if(c == '-') f = -1;
c = getchar();
}
while(c >= '0' && c <= '9') {
res = res * 10 +c - '0';
c = getchar();
}
res *= f;
}
template<class T>
void out(T x) {
if(x < 0) {x = -x;putchar('-');}
if(x >= 10) {
out(x / 10);
}
putchar('0' + x % 10);
}
const int MOD = 998244353;
int inc(int a,int b) {
return a + b >= MOD ? a + b - MOD : a + b;
}
int mul(int a,int b) {
return 1LL * a * b % MOD;
}
void update(int &x,int y) {
x = inc(x,y);
}
int fpow(int x,int c) {
int res = 1,t = x;
while(c) {
if(c & 1) res = mul(res,t);
t = mul(t,t);
c >>= 1;
}
return res;
}
struct node {
int to,next;
}E[MAXN * 2];
int N,Q,K;
int fa[MAXN],head[MAXN],sumE,x[MAXN],y[MAXN];
int son[MAXN],top[MAXN],dfn[MAXN],siz[MAXN],idx,dep[MAXN],line[MAXN],ans[MAXN];
vector<int> qry[MAXN];
void add(int u,int v) {
E[++sumE].to = v;
E[sumE].next = head[u];
head[u] = sumE;
}
void dfs1(int u) {
siz[u] = 1;dep[u] = dep[fa[u]] + 1;
for(int i = head[u] ; i; i = E[i].next) {
int v = E[i].to;
dfs1(v);
siz[u] += siz[v];
if(siz[v] > siz[son[u]]) son[u] = v;
}
}
void dfs2(int u) {
if(!top[u]) top[u] = u;
dfn[u] = ++idx;
line[idx] = u;
if(!son[u]) return;
top[son[u]] = top[u];
dfs2(son[u]);
for(int i = head[u] ; i ; i = E[i].next) {
int v = E[i].to;
if(v != son[u]) dfs2(v);
}
}
struct tr_node {
int l,r,sum,cnt;
}tr[MAXN * 4];
void update(int u) {
tr[u].cnt = inc(tr[u << 1].cnt,tr[u << 1 | 1].cnt);
tr[u].sum = inc(tr[u << 1].sum,tr[u << 1 | 1].sum);
}
void Add(int u,int pos,int ty) {
if(tr[u].l == tr[u].r) {
if(ty == 0) update(tr[u].cnt,1);
else update(tr[u].sum,fpow(dep[line[pos]],K));
return;
}
int mid = (tr[u].l + tr[u].r) >> 1;
if(pos <= mid) Add(u << 1,pos,ty);
else Add(u << 1 | 1,pos,ty);
update(u);
}
int Query(int u,int l,int r,int ty) {
if(tr[u].l == l &&tr[u].r == r) {
if(ty == 0) return tr[u].cnt;
else return tr[u].sum;
}
int mid = (tr[u].l + tr[u].r) >> 1;
if(r <= mid) return Query(u << 1,l,r,ty);
else if(l > mid) return Query(u << 1 | 1,l,r,ty);
else return inc(Query(u << 1,l,mid,ty),Query(u << 1 | 1,mid + 1,r,ty));
}
void build(int u,int l,int r) {
tr[u].l = l;tr[u].r = r;
if(l == r) {
tr[u].sum = 0;
return;
}
int mid = (l + r) >> 1;
build(u << 1,l,mid);
build(u << 1 | 1,mid + 1,r);
}
void Add_pos(int u) {
Add(1,dfn[u],0);
while(u) {
Add(1,dfn[u],1);
u = fa[top[u]];
}
}
int Process(int y) {
int pre = 0,res = 0;
while(y) {
int d = fpow(dep[y],K);
update(res,Query(1,dfn[top[y]],dfn[y],1));
if(pre) update(res,MOD - mul(d,Query(1,dfn[pre],dfn[pre] + siz[pre] - 1,0)));
if(son[y]) update(res,mul(d,Query(1,dfn[son[y]],dfn[son[y]] + siz[son[y]] - 1,0)));
pre = top[y];y = fa[pre];
}
return res;
}
void Solve() {
read(N);read(Q);read(K);
for(int i = 2 ; i <= N ; ++i) {
read(fa[i]);
add(fa[i],i);
}
for(int i = 1 ; i <= Q ; ++i) {
read(x[i]);read(y[i]);
qry[x[i]].pb(i);
}
dfs1(1);dfs2(1);
build(1,1,N);
for(int i = 1 ; i <= N ; ++i) {
Add_pos(i);
for(auto id : qry[i]) {
ans[id] = Process(y[id]);
}
}
for(int i = 1 ; i <= Q ; ++i) {
out(ans[i]);enter;
}
}
int main() {
#ifdef ivorysi
freopen("f1.in","r",stdin);
#endif
Solve();
}