Description
给出一个n个节点的有根树(编号为0到n-1,根节点为0)。一个点的深度定义为这个节点到根的距离+1。
设dep[i]表示点i的深度,LCA(i,j)表示i与j的最近公共祖先。
有q次询问,每次询问给出l r z,求sigma_{l<=i<=r}dep[LCA(i,z)]。
(即,求在[l,r]区间内的每个节点i与z的最近公共祖先的深度之和)
Input
第一行2个整数n q。
接下来n-1行,分别表示点1到点n-1的父节点编号。
接下来q行,每行3个整数l r z。
Output
输出q行,每行表示一个询问的答案。每个答案对201314取模输出
Sample Input
5 2
0
0
1
1
1 4 3
1 4 2
0
0
1
1
1 4 3
1 4 2
Sample Output
8
5
5
HINT
共5组数据,n与q的规模分别为10000,20000,30000,40000,50000。
题解
[HNOI 2015]开店的简化版。
//It is made by Awson on 2018.1.8
#include <set>
#include <map>
#include <cmath>
#include <ctime>
#include <queue>
#include <stack>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
#define LL long long
#define RE register
#define lowbit(x) ((x)&(-(x)))
#define Max(a, b) ((a) > (b) ? (a) : (b))
#define Min(a, b) ((a) < (b) ? (a) : (b))
#define Swap(a, b) ((a) ^= (b), (b) ^= (a), (a) ^= (b))
using namespace std;
const int N = ;
const int MOD = ;
const int INF = ~0u>>; int n, q, f, u, v, c, fa[N+], dep[N+], top[N+], cnt, size[N+], son[N+], pos[N+];
struct tt {
int to, next;
}edge[N+];
int path[N+], tot;
void add(int u, int v) {
edge[++tot].to = v;
edge[tot].next = path[u];
path[u] = tot;
}
struct Segment_tree {
int root[N+], sum[N*+], lazy[N*+], ch[N*][], pos;
int newnode(int r) {
int o = ++pos; sum[o] = sum[r], lazy[o] = lazy[r], ch[o][] = ch[r][], ch[o][] = ch[r][];
return o;
}
void update(int &o, int l, int r, int a, int b, int last) {
if (o <= last) o = newnode(o);
if (a <= l && r <= b) {
sum[o] += r-l+, sum[o] %= MOD, lazy[o]++; return;
}
int mid = (l+r)>>;
if (mid >= a) update(ch[o][], l, mid, a, b, last);
if (mid < b) update(ch[o][], mid+, r, a, b, last);
sum[o] = (sum[ch[o][]]+sum[ch[o][]]+(LL)lazy[o]*(r-l+)%MOD)%MOD;
}
int query(int o, int l, int r, int a, int b) {
if (!o) return ;
if (a <= l && r <= b) return sum[o];
int mid = (l+r)>>, c1 = , c2 = ;
if (mid >= a) c1 = query(ch[o][], l, mid, a, b);
if (mid < b) c2 = query(ch[o][], mid+, r, a, b);
return (c1+c2+(LL)lazy[o]*(Min(r, b)-Max(l, a)+)%MOD)%MOD;
}
}T;
void dfs1(int o, int father, int depth) {
fa[o] = father, dep[o] = depth+, size[o] = ;
for (int i = path[o]; i; i = edge[i].next) {
dfs1(edge[i].to, o, depth+);
size[o] += size[edge[i].to];
if (size[edge[i].to] > size[son[o]]) son[o] = edge[i].to;
}
}
void dfs2(int o, int tp) {
top[o] = tp, pos[o] = ++cnt;
if (son[o]) dfs2(son[o], tp);
for (int i = path[o]; i; i = edge[i].next)
if (edge[i].to != son[o]) dfs2(edge[i].to, edge[i].to);
}
void lca_update(int id, int o, int last) {while (top[o]) T.update(T.root[id], , n, pos[top[o]], pos[o], last), o = fa[top[o]]; }
int lca_query(int id, int o) {
int ans = ;
while (top[o]) ans += T.query(T.root[id], , n, pos[top[o]], pos[o]), ans %= MOD, o = fa[top[o]];
return ans;
}
void work() {
scanf("%d%d", &n, &q);
for (int i = ; i <= n; i++) scanf("%d", &f), add(f+, i);
dfs1(, , ), dfs2(, );
for (int i = ; i <= n; i++) {
T.root[i] = T.root[i-]; lca_update(i, i, T.pos);
}
while (q--) {
scanf("%d%d%d", &u, &v, &c);
printf("%d\n", (lca_query(v+, c+)-lca_query(u, c+)+MOD)%MOD);
}
}
int main() {
work();
return ;
}