ICPCCamp 2017-Day1 E.Lowest Common Ancestor(树链剖分/lct)

题意：给一棵带权树,问每个点和所有标号小于它的点的带权lca和。

分析：这种lca和可以看成是两段权值不同的链的差，这样我们用lct来维护树上每段链的带权重量和，每次插入一个点。

#include<iostream>
#include<string>
#include<algorithm>
#include<cstdlib>
#include<cstdio>
#include<set>
#include<map>
#include<vector>
#include<cstring>
#include<stack>
#include<queue>
#define INF 2147483640
#define eps 1e-9
#define MAXN 200005
using namespace std;
int n,q,u[MAXN],w[MAXN],s[MAXN],v[MAXN],size[MAXN],spa[MAXN],lazy[MAXN],lazy2[MAXN];
int father[MAXN],ch[MAXN][2],value1[MAXN],value2[MAXN],sum1[MAXN],sum2[MAXN],sum_v1[MAXN],sum_v2[MAXN],fa[MAXN];
vector<int> G[MAXN];
void dfs(int u,int fa,int sp)
{
father[u] = fa;
spa[u] = sp;
for(int i = 0;i < G[u].size();i++)
{
int v = G[u][i];
if(v != fa) dfs(v,u,(u == 1) ? v : sp);
}
}
inline bool isroot(int x)
{
return ch[fa[x]][0] != x && ch[fa[x]][1] != x;
}
void push_up(int x)
{
size[0] = sum1[0] = sum2[0] = sum_v1[0] = sum_v2[0] = 0;
sum1[x] = sum1[ch[x][0]] + sum1[ch[x][1]] + value1[x] * size[x];
sum2[x] = sum2[ch[x][0]] + sum2[ch[x][1]] + value2[x] * size[x];
sum_v1[x] = sum_v1[ch[x][0]] + value1[x] + sum_v1[ch[x][1]];
sum_v2[x] = sum_v2[ch[x][0]] + value2[x] + sum_v2[ch[x][1]];
}
void rotate(int x)
{
int y = fa[x],z = fa[y];
int d = ch[y][0] == x ? 0 : 1;
if(!isroot(y))
{
if(ch[z][0] == y) ch[z][0] = x;
else ch[z][1] = x;
}
fa[y] = x,fa[x] = z,fa[ch[x][d^1]] = y;
ch[y][d] = ch[x][d^1],ch[x][d^1] = y;
push_up(y),push_up(x);
}
void deal(int u,int num)
{
if(!u) return;
lazy2[u] += num;
size[u] += num;
sum1[u] += num*sum_v1[u];
sum2[u] += num*sum_v2[u];
}
inline void push_down(int x)
{
int ls = ch[x][0],rs = ch[x][1];
if(lazy[x])
{
lazy[x]^=1,lazy[ls]^=1;lazy[rs]^=1;
swap(ch[ls][0],ch[ls][1]);
swap(ch[rs][0],ch[rs][1]);
}
if(lazy2[x])
{
deal(ls,lazy2[x]),deal(rs,lazy2[x]);
lazy2[x] = 0;
}
}
void splay(int x)
{
int tot = 0;s[++tot] = x;
for(int i = x;!isroot(i);i = fa[i]) s[++tot] = fa[i];
for(;tot;tot--) push_down(s[tot]);
while(!isroot(x))
{
int y = fa[x],z = fa[y];
if(!isroot(y))
{
if((ch[z][0] == y) ^ (ch[y][0] == x)) rotate(x);
else rotate(y);
}
rotate(x);
}
}
void access(int x)
{
int t = 0;
while(x)
{
splay(x);
ch[x][1] = t;
push_up(x);
t = x,x = fa[x];
}
}
void makeroot(int x)
{
access(x),splay(x);
swap(ch[x][0],ch[x][1]);
lazy[x]^=1;
}
void link(int x,int y)
{
makeroot(x);fa[x] = y;
}
int main()
{
while(~scanf("%d",&n))
{
memset(fa,0,sizeof(int) * (n + 2));
memset(ch,0,sizeof(int) * (n + 2) * 2);
memset(lazy,0,sizeof(int) * (n + 2));
memset(lazy2,0,sizeof(int) * (n + 2));
for(int i = 1;i <= n;i++)
{
scanf("%d",&w[i]);
G[i].clear();
}
for(int i = 2;i <= n;i++)
{
scanf("%d",&u[i-1]);
v[i-1] = i;
G[u[i-1]].push_back(v[i-1]);
G[v[i-1]].push_back(u[i-1]);
}
dfs(1,0,0);
for(int i = 1;i <= n;i++)
{
value1[i] = sum_v1[i] = w[i];
value2[i] = sum_v2[i] = w[father[i]];
sum1[i] = sum2[i] = 0;
size[i] = 0;
}
sum1[1] = sum_v1[1],sum2[1] = sum_v2[1];
size[1] = 1;
for(int i = 1;i < n;i++) link(u[i],v[i]);
for(int i = 2;i <= n;i++)
{
makeroot(1);
access(i);
splay(i);
int temp1 = sum1[i];
makeroot(spa[i]);
access(i);
splay(i);
int temp2 = sum2[i];
printf("%d\n",temp1 - temp2);
makeroot(1);
access(i);
splay(i);
deal(i,1);
}
}
}