2631: tree

2631: tree

Time Limit: 30 Sec  Memory Limit: 128 MB
Submit: 3561  Solved: 1189

[Submit][Status][Discuss]

Description

　一棵n个点的树，每个点的初始权值为1。对于这棵树有q个操作，每个操作为以下四种操作之一：

+ u v c：将u到v的路径上的点的权值都加上自然数c；

- u1 v1 u2 v2：将树中原有的边(u1,v1)删除，加入一条新边(u2,v2)，保证操作完之后仍然是一棵树；

* u v c：将u到v的路径上的点的权值都乘上自然数c；

/ u v：询问u到v的路径上的点的权值和，求出答案对于51061的余数。

Input

　　第一行两个整数n，q

接下来n-1行每行两个正整数u，v，描述这棵树

接下来q行，每行描述一个操作

Output

　　对于每个/对应的答案输出一行

Sample Input

3 2

1 2

2 3

* 1 3 4

/ 1 1

Sample Output

4

HINT

数据规模和约定

10%的数据保证，1<=n，q<=2000

另外15%的数据保证，1<=n，q<=5*10^4，没有-操作，并且初始树为一条链

另外35%的数据保证，1<=n，q<=5*10^4，没有-操作

100%的数据保证，1<=n，q<=10^5，0<=c<=10^4

Source

[Submit][Status][Discuss]

一看就是LCT?
标记的转移记得用矩阵乘法，，自己先推一下
(WA惨了)
然后这题丧心病狂卡常数啊。。。
maintain可以少打一些(如rotate操作只需要一个maintain)
最后，，本题请使用unsigned int
long long计算更慢些(日。。。)

#include<iostream>
#include<cstdio>
#include<queue>
#include<vector>
#include<bitset>
#include<algorithm>
#include<cstring>
#include<map>
#include<stack>
#include<set>
#include<cmath>
#include<ext/pb_ds/priority_queue.hpp>
using namespace std;

const int maxn = 1E5 + 10;
typedef unsigned int LL;
const LL mo = 51061;

int n,m,ch[maxn][2],rev[maxn],fa[maxn],pfa[maxn],vis[maxn];
LL va[maxn],sum[maxn],Add[maxn],siz[maxn],Multi[maxn];
char com[10];

vector <int> v[maxn];
queue <int> Q;

void pushdown(int x)
{
if (rev[x]) {
swap(ch[x][0],ch[x][1]); rev[x] ^= 1;
if (ch[x][0]) rev[ch[x][0]] ^= 1;
if (ch[x][1]) rev[ch[x][1]] ^= 1;
}
if (Add[x] || Multi[x] != 1) {
va[x] *= Multi[x]; va[x] %= mo;
sum[x] *= Multi[x]; sum[x] %= mo;
va[x] += Add[x]; va[x] %= mo;
sum[x] += Add[x]*siz[x]; sum[x] %= mo;
for (int i = 0; i < 2; i++)
if (ch[x][i]) {
Add[ch[x][i]] = Multi[x]*Add[ch[x][i]] + Add[x],Add[ch[x][i]] %= mo;
Multi[ch[x][i]] *= Multi[x],Multi[ch[x][i]] %= mo;
}
Add[x] = 0; Multi[x] = 1;
}
}

void maintain(int x)
{
siz[x] = 1; sum[x] = va[x];
for (int i = 0; i < 2; i++)
if (ch[x][i]) {
siz[x] += siz[ch[x][i]];
sum[x] += sum[ch[x][i]];
sum[x] %= mo;
}
}

void rotate(int x)
{
int y = fa[x],z = fa[y];
pfa[x] = pfa[y]; pfa[y] = 0;
int d = ch[y][0] == x?0:1;
ch[y][d] = ch[x][d^1];
if (ch[x][d^1]) fa[ch[x][d^1]] = y;
ch[x][d^1] = y; fa[y] = x; fa[x] = z;
if (z) ch[z][ch[z][1] == y] = x;
if (ch[y][0]) pushdown(ch[y][0]);
if (ch[y][1]) pushdown(ch[y][1]);
maintain(y);
}

int s[maxn],top;
void splay(int x)
{
top = 0;
for (int now = x; now; now = fa[now]) s[++top] = now;
while (top) {pushdown(s[top--]);}
for (int y; y = fa[x]; rotate(x))
if (fa[y])
rotate((ch[fa[y]][0] == y)^(ch[y][0] == x)?x:y);
if (ch[x][0]) pushdown(ch[x][0]);
if (ch[x][1]) pushdown(ch[x][1]);
maintain(x);
}

void Access(int x)
{
for (int u = x,v = 0; u; v = u,u = pfa[u]) {
splay(u);
if (ch[u][1]) fa[ch[u][1]] = 0,pfa[ch[u][1]] = u;
ch[u][1] = v;
if (v) pfa[v] = 0,fa[v] = u;
}
}

void ChangeRoot(int x) {Access(x); splay(x); rev[x] ^= 1;}
void Join(int x,int y) {ChangeRoot(x); pfa[x] = y; splay(y);}
void Cut(int x,int y) {ChangeRoot(x); Access(y); splay(y); ch[y][0] = fa[x] = 0;}
int Query(int x,int y) {ChangeRoot(x); Access(y); splay(y); return sum[y];}

void add(int x,int y,int c)
{
ChangeRoot(x); Access(y); splay(y);
Add[y] += 1LL*c; Add[y] %= mo;
}

void multi(int x,int y,int c)
{
ChangeRoot(x); Access(y); splay(y);
//Add[y] *= 1LL*c; Add[y] %= mo;
Multi[y] *= 1LL*c; Multi[y] %= mo;
}

int getint()
{
char ch = getchar();
int ret = 0;
while (ch < '0' ||  '9' < ch) ch = getchar();
while ('0' <= ch && ch <= '9') ret = ret*10 + ch - '0',ch = getchar();
return ret;
}

char c[20];

void print( int k )
{
if (!k) {puts("0"); return;}
int num = 0;
while( k > 0 ) c[++num] = k % 10, k /= 10;
while( num )
putchar( c[num--]+48 );
putchar( 10 );
}

int main()
{
freopen("a.in","r",stdin);
freopen("a.out","w",stdout);
n = getint(); m = getint();
for (int i = 1; i <= n; i++) sum[i] = siz[i] = Multi[i] = va[i] = 1;
for (int i = 1; i < n; i++) Join(getint(),getint());
while (m--) {
scanf("%s",com);
int x = getint(),y = getint();
if (com[0] == '+') {
int c = getint();
add(x,y,c);
}
else if (com[0] == '-') {
Cut(x,y);
x = getint(); y = getint();
Join(x,y);
}
else if (com[0] == '*') {
int c = getint();
multi(x,y,c);
}
else print(Query(x,y));
}
return 0;
}