【LOJ】#3088. 「GXOI / GZOI2019」旧词

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();
}