CF916E Jamie and Tree

CF916E Jamie and Tree

题意翻译

有一棵n个节点的有根树，标号为1-n，你需要维护以下三种操作

1.给定一个点v，将整颗树的根变为v

2.给定两个点u, v，将lca(u, v)所在的子树都加上x

3.给定一个点v，你需要回答以v所在的子树的权值和

Translated by mangoyang

---

错误日志： 第一次 \(debug\) 是 \(jump\) 数组第二维开小了； 交了一次错了， 第二次没有特判修改/查询节点等于根的情况； 第三次 \(RE\) 又是数组开销了 。。。空间那么大我倒是把数组卡大点啊啊啊

---

Solution

树链剖分， 要求换根修改和查询

\(lca(u,v)\) 等于 \(lca(u, v)\ ,lca(u, root)\ ,lca(v, root)\) 里深度最大的点

修改和查询： 分三种情况考虑：

1. 操作节点为根节点： 直接操作于整棵树
2. 根节点在操作节点子树之外： 直接操作即可
3. 根节点位于操作节点子树内： 利用容斥（最好画图看看）。设点 \(son\) 为从根节点到操作节点路径上的倒数第二个点，先整棵树更新， 再将 \(son\) 的子树减去更新值即可
   
   （又或者常数较大的先更新整棵树， 反过来减去操作节点的子树， 再更新操作节点这一个点）

Code

#include<iostream>
#include<cstdio>
#include<queue>
#include<cstring>
#include<algorithm>
typedef long long LL;
using namespace std;
LL RD(){
    LL out = 0,flag = 1;char c = getchar();
    while(c < '0' || c >'9'){if(c == '-')flag = -1;c = getchar();}
    while(c >= '0' && c <= '9'){out = out * 10 + c - '0';c = getchar();}
    return flag * out;
    }
const LL maxn = 200019,INF = 1e9 + 19;
LL head[maxn],nume = 1;
struct Node{
    LL v,dis,nxt;
    }E[maxn << 2];
void add(LL u,LL v,LL dis){
    E[++nume].nxt = head[u];
    E[nume].v = v;
    E[nume].dis = dis;
    head[u] = nume;
    }
LL num, na;
LL dep[maxn], size[maxn], fa[maxn], wson[maxn], top[maxn], pos[maxn], ori[maxn], cnt;
LL v[maxn];
void dfs1(LL id, LL F){
	size[id] = 1;
	for(LL i = head[id];i;i = E[i].nxt){
		LL v = E[i].v;
		if(v == F)continue;
		dep[v] = dep[id] + 1;
		fa[v] = id;
		dfs1(v, id);
		size[id] += size[v];
		if(size[v] > size[wson[id]])wson[id] = v;
		}
	}
void dfs2(LL id, LL TP){
	pos[id] = ++cnt;
	ori[cnt] = id;
	top[id] = TP;
	if(!wson[id])return ;
	dfs2(wson[id], TP);
	for(LL i = head[id];i;i = E[i].nxt){
		LL v = E[i].v;
		if(v == fa[id] || v == wson[id])continue;
		dfs2(v, v);
		}
	}
#define lid (id << 1)
#define rid (id << 1) | 1
struct seg_tree{
	LL l, r;
	LL lazy, sum;
	}tree[maxn << 2];
void pushup(LL id){tree[id].sum = tree[lid].sum + tree[rid].sum;}
void pushdown(LL id){
	if(tree[id].lazy){
		LL val = tree[id].lazy;
		tree[lid].lazy += val;
		tree[rid].lazy += val;
		tree[lid].sum += (tree[lid].r - tree[lid].l + 1) * val;
		tree[rid].sum += (tree[rid].r - tree[rid].l + 1) * val;
		tree[id].lazy = 0;
		}
	}
void build(LL id, LL l, LL r){
	tree[id].l = l, tree[id].r = r;
	if(l == r){
		tree[id].sum = v[ori[l]];
		return ;
		}
	LL mid = (l + r) >> 1;
	build(lid, l, mid), build(rid, mid + 1, r);
	pushup(id);
	}
void update(LL id, LL val, LL l, LL r){
	pushdown(id);
	if(tree[id].l == l && tree[id].r == r){
		tree[id].sum += (tree[id].r - tree[id].l + 1) * val;
		tree[id].lazy += val;
		return ;
		}
	LL mid = (tree[id].l + tree[id].r) >> 1;
	if(mid < l)update(rid, val, l, r);
	else if(mid >= r)update(lid, val, l, r);
	else update(lid, val, l, mid), update(rid, val, mid + 1, r);
	pushup(id);
	}
LL query(LL id, LL l ,LL r){
	pushdown(id);
	if(tree[id].l == l && tree[id].r == r){
		return tree[id].sum;
		}
	LL mid = (tree[id].l + tree[id].r) >> 1;
	if(mid < l)return query(rid, l, r);
	else if(mid >= r)return query(lid, l, r);
	else return query(lid, l, mid) + query(rid, mid + 1, r);
	}
LL root = 1, jump[maxn][25];
void get_jump(){
	for(LL i = 1;i <= num;i++)jump[i][0] = fa[i];
	for(LL i = 1;i <= 19;i++){
		for(LL j = 1;j <= num;j++){
			jump[j][i] = jump[jump[j][i - 1]][i - 1];
			}
		}
	}
LL LCA(LL x, LL y){
	if(dep[x] < dep[y])swap(x, y);
	for(LL i = 19;i >= 0;i--)if(dep[jump[x][i]] >= dep[y])x = jump[x][i];
	if(x == y)return x;
	for(LL i = 19;i >= 0;i--)if(jump[x][i] != jump[y][i])x = jump[x][i], y = jump[y][i];
	return jump[x][0];
	}
LL real_LCA(LL x, LL y){
	LL lca1 = LCA(x, y), lca2 = LCA(x, root), lca3 = LCA(y, root);
	LL lca = dep[lca1] > dep[lca2] ? lca1 : lca2;
	return dep[lca] > dep[lca3] ? lca : lca3;
	}
LL son_LCA(LL x, LL y = root){
	if(dep[x] >= dep[y])return -1;
	for(LL i = 19;i >= 0;i--)if(dep[jump[y][i]] >= dep[x] + 1)y = jump[y][i];
	if(fa[y] == x)return y;
	return -1;
	}
void change_root(){root = RD();}
void uprange(){
	LL x = RD(), y = RD(), val = RD();
	LL lca = real_LCA(x, y);
	if(lca == root){update(1, val, pos[1], pos[1] + size[1] - 1);return ;}
	LL son = son_LCA(lca);
	if(son == -1){update(1, val, pos[lca], pos[lca] + size[lca] - 1);return ;}
	update(1, val, pos[1], pos[1] + size[1] - 1);
	update(1,-val, pos[son], pos[son] + size[son] - 1);
	}
void get_sum(){
	LL x = RD();
	if(x == root){printf("%lld\n", query(1, pos[1], pos[1] + size[1] - 1));return ;}
	LL son = son_LCA(x);
	if(son == -1){printf("%lld\n", query(1, pos[x], pos[x] + size[x] - 1));return ;}
	printf("%lld\n", query(1, pos[1], pos[1] + size[1] - 1) - query(1, pos[son], pos[son] + size[son] - 1));
	}
int main(){
	num = RD();na = RD();
	for(LL i = 1;i <= num;i++)v[i] = RD();
	for(LL i = 1;i <= num - 1;i++){
		LL u = RD(), v = RD();
		add(u, v, 1), add(v, u, 1);
		}
	dep[1] = 1;
	dfs1(1, -1), dfs2(1, 1);
	build(1, 1, num);
	get_jump();
	for(LL i = 1;i <= na;i++){
		LL cmd = RD();
		if(cmd == 1)change_root();
		else if(cmd == 2)uprange();
		else get_sum();
		}
	return 0;
	}