Tree II

luogu 1501

题目大意

给出一棵树，让你进行若干操作，操作如下：
1.把两个点路径上的所有点权值加k
2.把两个点路径上的所有点权值乘k
3.把一条边断开，连上另一条边
4.查询两个点路径上的权值和

输入样例

3 2
1 2
2 3
* 1 3 4
/ 1 1

输出样例

4

数据范围

$1⩽n,q⩽10^5,1⩽c⩽10^4$

解题思路

LCT模板
多了两个计算的值
在下传lazym的时候把lazya乘上lazym即可（lazya为加值的lazy，lazym为乘值的lazy）

代码

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#define ll long long
#define N 100010
#define wyc 51061
using namespace std;
ll n, q, x, y, z, s[N], v[N], p[N], sz[N], la[N], lm[N], fa[N], son[N][2];
char c;
bool NR(ll x)
{return son[fa[x]][0] == x || son[fa[x]][1] == x;
}
bool IRS(ll x)
{return son[fa[x]][1] == x;
}
void pushr(ll x)
{swap(son[x][0], son[x][1]);p[x] ^= 1;return;
}
void pushm(ll x, ll y)//下传乘
{lm[x] = lm[x] * y % wyc;la[x] = la[x] * y % wyc;//把a的乘上，这样就不会有问题了s[x] = s[x] * y % wyc;v[x] = v[x] * y % wyc;return;
}
void pusha(ll x, ll y)
{la[x] = (la[x] + y) % wyc;s[x] = (s[x] + y * sz[x] % wyc) % wyc;v[x] = (v[x] + y) % wyc;return;
}
void push_down(ll x)
{if (lm[x] != 1) pushm(son[x][0], lm[x]), pushm(son[x][1], lm[x]), lm[x] = 1;if (la[x]) pusha(son[x][0], la[x]), pusha(son[x][1], la[x]), la[x] = 0;if (p[x]){if (son[x][0]) pushr(son[x][0]);if (son[x][1]) pushr(son[x][1]);p[x] = 0;}return;
}
void push_up(ll x)
{s[x] = (s[son[x][0]] + s[son[x][1]] + v[x]) % wyc;sz[x] = sz[son[x][0]] + sz[son[x][1]] + 1;return;
}
void rotate(ll x)
{ll y = fa[x], z = fa[y], k = IRS(x), g = son[x][!k];if (NR(y)) son[z][IRS(y)] = x;if (g) fa[g] = y;son[x][!k] = y;son[y][k] = g;fa[x] = z;fa[y] = x;push_up(y);return;
}
void push_hall(ll x)
{if (NR(x)) push_hall(fa[x]);push_down(x);return;
}
void Splay(ll x)
{push_hall(x);while(NR(x)){if (NR(fa[x]))rotate(IRS(x) == IRS(y) ? fa[x] : x);rotate(x);}push_up(x);return;
}
void access(ll x)
{for (ll y = 0; x; y = x, x = fa[x])Splay(x), son[x][1] = y, push_up(x);return;
}
void make_root(ll x)
{access(x);Splay(x);pushr(x);return;
}
ll find_root(ll x)
{access(x);Splay(x);while(son[x][0]) push_down(x), x = son[x][0];Splay(x);return x;
}
void Split(ll x, ll y)
{make_root(x);access(y);Splay(y);return;
}
void link(ll x, ll y)
{make_root(x);if (find_root(y) != x) fa[x] = y;return;
}
void cut(ll x, ll y)
{make_root(x);if (find_root(y) == x && fa[y] == x && !son[y][0]){fa[y] = son[x][1] = 0;push_up(x);}return;
}
int main()
{scanf("%lld%lld", &n, &q);for (ll i = 1; i <= n; ++i)sz[i] = lm[i] = v[i] = 1;for (ll i = 1; i < n; ++i){scanf("%lld%lld", &x, &y);link(x, y);}while(q--){cin>>c;if (c == '+'){scanf("%lld%lld%lld", &x, &y, &z);Split(x, y);pusha(y, z);}else if (c == '-'){scanf("%lld%lld", &x, &y);cut(x, y);scanf("%lld%lld", &x, &y);link(x, y);}else if (c == '*'){scanf("%lld%lld%lld", &x, &y, &z);Split(x, y);pushm(y, z);}else if (c == '/'){scanf("%lld%lld", &x, &y);Split(x, y);printf("%lld\n", s[y]);}}return 0;
}