[USACO11DEC] 牧草种植Grass Planting

Posted 2020-10-17 xayata

https://www.luogu.org/problemnew/show/3038

将为边加权转化成为点加权

对于每条边，我们将其深度更大的端点加权，则区间 [l, r] 的加权（或询问）即为去掉深度最小的点，给其余点加权（或询问）。

1）最后一次树剖查询时，当前两点 x,y 必定在同一重链上（y 的深度小于 x）；

2）根据处理前的 dfs 序，我们是优先遍历重儿子，那么重儿子在线段树中的编号一定紧邻其父节点（即为其父节点编号 + 1），则我们要忽略深度最小的那个点 y ，即为处理区间 [ y 在线段树中的编号 + 1， x 在线段树中的编号]（另外还要注意的是，y = x 时在线段树内执行会出错，我们要特判这种情况） 。

#include <bits/stdc++.h>

using namespace std;
const int N = 1e5 + 10;

#define gc getchar()
#define lson jd << 1
#define rson jd << 1 | 1 

struct Node_1{
    int v, nxt;
}G[N << 1];
struct Node_2{
    int fa, son, deep, topp, siz, tree;
}P[N];
struct Node_3{
    int l, r, w, f;
}T[N << 2];
int n, Ti, now = 1, head[N], tim, ans;

inline int read(){
    int x = 0; char c = gc;
    while(c < ‘0‘ || c > ‘9‘) c = gc;
    while(c >= ‘0‘ && c <= ‘9‘) x = x * 10 + c - ‘0‘, c = gc;
    return x;
}

inline void add(int u, int v){
    G[now].v = v;
    G[now].nxt = head[u];
    head[u] = now ++;
}

void dfs_find_son(int u, int fa, int dep){
    P[u].fa = fa;
    P[u].deep = dep;
    P[u].siz = 1;
    for(int i = head[u]; ~ i; i = G[i].nxt){
        int v = G[i].v;
        if(v != fa){
            dfs_find_son(v, u, dep + 1);
            P[u].siz += P[v].siz;
            if(P[v].siz > P[P[u].son].siz) P[u].son = v;
        }
    }
}

void dfs_to_un(int u, int tp){
    P[u].topp = tp;
    P[u].tree = ++ tim;
    if(!P[u].son) return ;
    dfs_to_un(P[u].son, tp);
    for(int i = head[u]; ~ i; i = G[i].nxt){
        int v = G[i].v;
        if(v != P[u].son && v != P[u].fa) dfs_to_un(v, v);
    }
}

void down(int jd){
    int F = T[jd].f;
    T[lson].w += (T[lson].r - T[lson].l + 1) * F; T[lson].f += F;
    T[rson].w += (T[rson].r - T[rson].l + 1) * F; T[rson].f += F;
    T[jd].f = 0; 
}

void Sec_G(int l, int r, int jd, int x, int y){
    if(x <= l && r <= y){
        int yj = r - l + 1;
        T[jd].w += yj;
        T[jd].f ++;
        return ;
    }
    if(T[jd].f) down(jd);
    int mid = (l + r) >> 1;
    if(x <= mid) Sec_G(l, mid, lson, x, y);
    if(y > mid) Sec_G(mid + 1, r, rson, x, y);
}

void Sec_G_imp(int x, int y){
    int tp1 = P[x].topp, tp2 = P[y].topp;
    while(tp1 != tp2){
        if(P[tp1].deep < P[tp2].deep) swap(x, y), swap(tp1, tp2);
        Sec_G(1, n, 1, P[tp1].tree, P[x].tree);
        x = P[tp1].fa;
        tp1 = P[x].topp;
    }
    if(x == y) return ;
    if(P[x].deep > P[y].deep) swap(x, y);
    Sec_G(1, n, 1, P[x].tree + 1, P[y].tree);
}

void build_tree(int l, int r, int jd){
    T[jd].l = l; T[jd].r = r;
    if(l == r) return ;
    int mid = (l + r) >> 1;
    build_tree(l, mid, lson);
    build_tree(mid + 1, r, rson);
}

void Sec_A(int l, int r, int jd, int x, int y){
    if(x <= l && r <= y){
        ans += T[jd].w;
        return ;
    }
    if(T[jd].f) down(jd);
    int mid = (l + r) >> 1;
    if(x <= mid) Sec_A(l, mid, lson, x, y);
    if(y > mid) Sec_A(mid + 1, r, rson, x, y);
}

int Sec_A_imp(int x, int y){
    int ret = 0;
    int tp1 = P[x].topp, tp2 = P[y].topp;
    while(tp1 != tp2){
        if(P[tp1].deep < P[tp2].deep) swap(x, y), swap(tp1, tp2);
        ans = 0;
        Sec_A(1, n, 1, P[tp1].tree, P[x].tree);
        ret += ans;
        x = P[tp1].fa;
        tp1 = P[x].topp;
    }
    if(x == y) return ret;
    ans = 0;
    if(P[x].deep > P[y].deep) swap(x, y);
    Sec_A(1, n, 1, P[x].tree + 1, P[y].tree);
    ret += ans;
    return ret;
}

int main()
{
    n = read(); Ti = read();
    for(int i = 1; i <= n; i ++) head[i] = -1;
    for(int i = 1; i < n; i ++) {
        int u = read(), v = read();
        add(u, v); add(v, u);
    }
    dfs_find_son(1, 0, 1);
    dfs_to_un(1, 1);
    build_tree(1, n, 1);
    while(Ti --){
        string s; cin >> s;
        int x = read(), y = read();
        if(s[0] == ‘P‘) Sec_G_imp(x, y);
        else cout << Sec_A_imp(x, y) << endl;
        
    }
    return 0;
}