Problem B
Tree of Almost Clean Money
Input File: B.in
Output File: standard output
Time Limit: 4 seconds (C/C++)
Memory Limit: 256 megabytes
The tree of Almost Clean Money (or ACM Tree, for short) consists of N (1≤N≤500000) vertices in
which, well, (almost clean) money is growing (contrary to the old saying that money doesn’t grow
on trees). The vertices are numbered from 0 to N-1, with vertex 0 being the root of the tree. Every
vertex i except vertex 0 has a parent p(i) in the tree, such that p(i)<i. Initially, every vertex
contains v(i) (0≤v(i)<1000000007) monetary units. Due to its special properties, the tree has
attracted the attention of a large money laundering organization, who wants to use the tree for its
money “cleansing” business. This organization wants to execute Q (1≤Q≤50000) operations on
the tree. Each operation consists of two steps:
1) In step 1, K (1≤K≤1000) vertices from the tree are chosen: x(1), …, x(K) (0≤x(i)≤N-1) –
the same vertex may be selected multiple times here. In each of these vertices, an
amount of monetary units is added (thus increasing the amount of monetary units in
them). More exactly, y(i) (0≤y(i)<1000000007) monetary units are added to the selected
vertex x(i) (1≤i≤K).
2) In step 2, two vertices u and v (0≤u,v≤N-1) are chosen and the organization wants to
know the total amount of money found in the vertices located on the unique path in the
tree between the vertices u and v (with u and v inclusive).
The organization hired you to find the answer for step 2 of each of the Q operations and promised
you a hefty amount of money if you succeed.
Input
The first line of input contains the number of tree vertices N. The next N-1 lines contain two
space-separated integers, p(i) and i, each describing an edge of the tree. The next line contains
N space-separated values: the initial amount of monetary units in each vertex, v(0), …, v(N-1).
The next line contains the number of operations Q. Each of the next Q lines describes an
operation. Each operation is described by 9 space-separated integers, in this order: K, x(1), y(1),
A, B, C, D, u, v (0≤A,B,C,D<1000000007). The values x(2≤i≤K) and y(2≤i≤K) are generated as
follows:
x(i) = (A*x(i-1) + B) modulo N
y(i) = (C*y(i-1) + D) modulo 1000000007
Output
For each of the Q operations print a line containing the answer to step 2 of the operation. When
computing the answer for an operation, the effects of steps 1 from previous operations need to be
considered, too (i.e. after adding y(i) monetary units to a vertex x(i), these units remain added to
the vertex when executing subsequent operations, too).
acm
Sample input Sample output Explanation
4
0 1
0 3
1 2
1 2 3 4
3
1000 1 1 1 0 1 0 0 2
2 0 5 1 1 2 2 2 3
1 3 7 999 999 999 999 1 3
1006
1027
1031
In the first operation the value 1 is added
1000 times to vertex 1 (note A=C=1,
B=D=0). The path between 0 and 2
contains the vertices 0, 1 and 2. The total
amount of monetary units in them is 1006.
In operation 2: x(1)=0, y(1)=5, x(2)=1,
y(2)=12. The path between 2 and 3 contains
all the vertices of the tree.
In operation 3: K=1, so A, B, C, D are
irrelevant.
题意：给你一棵n个节点的树（n<=5e5），现在可以进行至多Q次操作（Q<=5e4），每次至多可以给k个节点（k<=1000）增加一个数值，然后每个操作都有一个询问（u,v），问从u到v的简单路径上的节点权值和。
#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <iostream>
#include <cmath>
#include <vector>
#define MM(a,b) memset(a,b,sizeof(a));
using namespace std;
typedef long long ll;
#define CT continue
#define SC scanf
const int N=5*1e5+10;
const double pi=acos(-1);
int n,siz[N],dep[N],son[N],treepos[N],
top[N],par[N],x[1005],y[1005];
ll tree[N];
vector<int> G[N];
void add_edge(int u,int v)
{
G[u].push_back(v);
G[v].push_back(u);
}
int dfs_clock;
void dfs1(int u,int father,int depth)
{
siz[u]=1;
dep[u]=depth;
son[u]=-1;
par[u]=father;
for(int i=0;i<G[u].size();i++){
int v=G[u][i];
if(v==father) CT;
dfs1(v,u,depth+1);
siz[u]+=siz[v];
if(son[u]==-1||siz[v]>siz[son[u]])
son[u]=v;
}
}
void dfs2(int u,int tp)
{
top[u]=tp;
treepos[u]=++dfs_clock;
if(son[u]==-1) return;
dfs2(son[u],tp);
for(int i=0;i<G[u].size();i++) {
int v=G[u][i];
if(v==par[u]||v==son[u]) CT;
dfs2(v,v);
}
}
int lowbit(int i)
{
return (i&(-i));
}
void add(int pos,int val)
{
while(pos<=n) {
tree[pos]+=val;
pos+=lowbit(pos);
}
}
ll tfind(int x)
{
ll res=0;
while(x>=1){
res+=tree[x];
x-=lowbit(x);
}
return res;
}
ll query(int a,int b)
{
if(a>b) swap(a,b);
return tfind(b)-tfind(a-1);
}
ll ans(int u,int v)
{
ll res=0,tu=top[u],tv=top[v];
while(tu!=tv) {
if(dep[tu]<dep[tv]){
swap(tu,tv);
swap(u,v);
}
int l=treepos[tu],r=treepos[u];
res+=query(l,r);
u=par[tu];
tu=top[u];
}
if(dep[u]<dep[v]) swap(u,v);
res+=query(treepos[v],treepos[u]);
return res;
}
int main()
{
while(~SC("%d",&n))
{
for(int i=1;i<=n;i++) G[i].clear();
for(int i=1;i<n;i++) {
int u,v;
SC("%d%d",&u,&v);
add_edge(u+1,v+1);
}
MM(tree,0);
dfs_clock=0;
dfs1(1,0,1);
dfs2(1,1);
for(int i=1;i<=n;i++) {
int x;SC("%d",&x);
add(treepos[i],x);
}
int q;
SC("%d",&q);
while(q--){
int k,u,v;ll A,B,C,D;
SC("%d%d%d%lld%lld%lld%lld%d%d",&k,&x[1],&y[1],&A,&B,&C,&D,&u,&v);
add(treepos[x[1]+1],y[1]);
for(int i=2;i<=k;i++){
x[i]=(A*x[i-1]+B)%n;
y[i]=(C*y[i-1]+D)%1000000007;
add(treepos[x[i]+1],y[i]);
}
printf("%lld
",ans(u+1,v+1));
}
}
return 0;
}
分析：学了下树链剖分，树连剖分主要是用于对树进行路径求和统计以及去最大值最小值之类的，第一次dfs，找到重儿子，并给
节点深度表好号，记录下每个节点额父节点，，第二次dfs，构建树链，同时建好BIT或线段树，，最后然后路径求和的时候，先要统计链顶节点深度大的。