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P1501 [国家集训队] Tree II

P1501 [国家集训队] Tree II

题面

题目链接

解法

一道LCT的模版题。

但是我竟然错了$2$次!!!

$4$种操作容易进行不多说,考虑维护addmul操作,需要维护子树$size$,修改的时候要记得修改val而不是只修改sum,其他就和线段树没啥区别了。

相比LCT的模版,只是修改了pushdowngetdown

AC代码

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/**
* @file: P1501.cpp
* @author: yaoxi-std
* @url: https://www.luogu.com.cn/problem/P1501
*/
// #pragma GCC optimize ("O2")
// #pragma GCC optimize ("Ofast", "inline", "-ffast-math")
// #pragma GCC target ("avx,sse2,sse3,sse4,mmx")
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define resetIO(x) \
freopen(#x ".in", "r", stdin), freopen(#x ".out", "w", stdout)
#define debug(fmt, ...) \
fprintf(stderr, "[%s:%d] " fmt "\n", __FILE__, __LINE__, ##__VA_ARGS__)
template <class _Tp>
inline _Tp& read(_Tp& x) {
bool sign = false;
char ch = getchar();
long double tmp = 1;
for (; !isdigit(ch); ch = getchar())
sign |= (ch == '-');
for (x = 0; isdigit(ch); ch = getchar())
x = x * 10 + (ch ^ 48);
if (ch == '.')
for (ch = getchar(); isdigit(ch); ch = getchar())
tmp /= 10.0, x += tmp * (ch ^ 48);
return sign ? (x = -x) : x;
}
template <class _Tp>
inline void write(_Tp x) {
if (x < 0)
putchar('-'), x = -x;
if (x > 9)
write(x / 10);
putchar((x % 10) ^ 48);
}
const int MAXN = 1e5 + 10;
const int INF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 51061;
struct LCT {
int fa[MAXN], ch[MAXN][2];
int val[MAXN], sum[MAXN], siz[MAXN];
int tag[MAXN], add[MAXN], mul[MAXN];
void connect(int x, int f, int w) { fa[x] = f, (~w) && (ch[f][w] = x); }
void clear(int x) {
val[x] = sum[x] = siz[x] = mul[x] = 1;
tag[x] = add[x] = 0;
}
void pushup(int x) {
siz[x] = siz[ch[x][0]] + siz[ch[x][1]] + 1;
sum[x] = (sum[ch[x][0]] + sum[ch[x][1]] + val[x]) % MOD;
}
int get(int x) {
if (ch[fa[x]][0] == x)
return 0;
if (ch[fa[x]][1] == x)
return 1;
return -1;
}
void getdown(int x, int vm, int va) {
mul[x] = mul[x] * vm % MOD;
add[x] = (add[x] * vm + va) % MOD;
val[x] = (val[x] * vm + va) % MOD;
sum[x] = (sum[x] * vm + va * siz[x]) % MOD;
}
void pushdown(int x) {
if (mul[x] != 1 || add[x] != 0 || tag[x]) {
if (tag[x])
swap(ch[x][0], ch[x][1]);
if (ch[x][0])
getdown(ch[x][0], mul[x], add[x]), tag[ch[x][0]] ^= tag[x];
if (ch[x][1])
getdown(ch[x][1], mul[x], add[x]), tag[ch[x][1]] ^= tag[x];
mul[x] = 1, add[x] = tag[x] = 0;
}
}
void pushall(int x) {
if (~get(x))
pushall(fa[x]);
pushdown(x);
}
void rotate(int x) {
int y = fa[x], z = fa[y], w = get(x);
if (~w)
connect(ch[x][w ^ 1], y, w);
connect(x, z, get(y));
connect(y, x, w ^ 1);
pushup(y);
pushup(x);
}
void splay(int x) {
pushall(x);
for (int f = fa[x]; f = fa[x], ~get(x); rotate(x))
if (~get(f))
rotate(get(f) == get(x) ? f : x);
}
void access(int x) {
int pre = 0;
while (x) {
splay(x);
ch[x][1] = pre;
pushup(x);
pre = x;
x = fa[x];
}
}
void makeroot(int x) {
access(x);
splay(x);
tag[x] ^= 1;
}
int findroot(int x) {
access(x);
splay(x);
while (ch[x][0])
pushdown(x), x = ch[x][0];
splay(x);
return x;
}
void split(int x, int y) {
makeroot(x);
access(y);
splay(y);
}
bool link(int x, int y) {
makeroot(x);
if (findroot(y) == x)
return false;
fa[x] = y;
return true;
}
bool cut(int x, int y) {
if (findroot(x) != findroot(y))
return false;
split(x, y);
if (fa[x] != y || ch[x][1])
return false;
fa[x] = ch[y][0] = 0;
return true;
}
};
int n, q;
LCT lct;
signed main() {
read(n), read(q);
for (int i = 1; i <= n; ++i)
lct.clear(i);
for (int i = 1; i < n; ++i) {
int u, v;
read(u), read(v);
lct.link(u, v);
}
while (q--) {
char op = getchar();
if (op == '+') {
int u, v, c;
read(u), read(v), read(c);
lct.split(u, v);
lct.getdown(v, 1, c);
} else if (op == '-') {
int u1, v1, u2, v2;
read(u1), read(v1), read(u2), read(v2);
lct.cut(u1, v1);
lct.link(u2, v2);
} else if (op == '*') {
int u, v, c;
read(u), read(v), read(c);
lct.split(u, v);
lct.getdown(v, c, 0);
} else {
int u, v;
read(u), read(v);
lct.split(u, v);
write(lct.sum[v]), putchar('\n');
}
}
return 0;
}