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 ivorysifreopen("f1.in","r",stdin);
#endifSolve();
}