洛谷P3038 [USACO11DEC] Grass Planting G 題解 樹鏈剖分

題目鏈接：https://www.luogu.com.cn/problem/P3038

題目大意：

一棵樹維護兩種操作：

1. 一條路徑上每條邊邊權 \(+1\)；
2. 查詢路徑上的邊權和。

解題思路：

樹鏈剖分模板題。

示例程序：

#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
int fa[maxn], dep[maxn], size[maxn], son[maxn], top[maxn], seg[maxn], rev[maxn];
int n, m, seg_cnt;
vector<int> g[maxn];

void dfs1(int u, int p) {
    size[u] = 1;
    for (auto v : g[u]) {
        if (v != p) {
            fa[v] = u;
            dep[v] = dep[u] + 1;
            dfs1(v, u);
            size[u] += size[v];
            if (size[v] > size[son[u]])
                son[u] = v;
        }
    }
}

void dfs2(int u, int tp) {
    seg[u] = ++seg_cnt;
    rev[seg_cnt] = u;
    top[u] = tp;
    if (son[u])
        dfs2(son[u], tp);
    for (auto v : g[u])
        if (v != fa[u] && v != son[u])
            dfs2(v, v);
}

long long tr[maxn<<2];
int lazy[maxn<<2];
#define lson l, mid, rt<<1
#define rson mid+1, r, rt<<1|1
void push_up(int rt) {
    tr[rt] = tr[rt<<1] + tr[rt<<1|1];
}
void push_down(int l, int r, int rt) {
    int mid = (l + r) / 2;
    if (lazy[rt]) {
        tr[rt<<1] += (long long) (mid - l + 1) * lazy[rt];
        lazy[rt<<1] += lazy[rt];
        tr[rt<<1|1] += (long long) (r - mid) * lazy[rt];
        lazy[rt<<1|1] += lazy[rt];
        lazy[rt] = 0;
    }
}
long long query(int L, int R, int l, int r, int rt) {
    if (L <= l && r <= R) return tr[rt];
    int mid = (l + r) / 2;
    push_down(l, r, rt);
    long long res = 0;
    if (L <= mid) res += query(L, R, lson);
    if (R > mid) res += query(L, R, rson);
    return res;
}
void update(int L, int R, int val, int l, int r, int rt) {
    if (L <= l && r <= R) {
        lazy[rt] += val;
        tr[rt] += (long long) val * (r - l + 1);
        return;
    }
    push_down(l, r, rt);
    int mid = (l + r) / 2;
    if (L <= mid) update(L, R, val, lson);
    if (R > mid) update(L, R, val, rson);
    push_up(rt);
}
long long func_query(int u, int v) {
    long long res = 0;
    while (top[u] != top[v]) {
        if (dep[top[u]] < dep[top[v]]) swap(u, v);
        res += query(seg[top[u]], seg[u], 1, n, 1);
        u = fa[top[u]];
    }
    if (dep[u] < dep[v]) swap(u, v);
    if (u != v)
        res += query(seg[v] + 1, seg[u], 1, n, 1);
    return res;
}
void func_update(int u, int v) {
    while (top[u] != top[v]) {
        if (dep[top[u]] < dep[top[v]]) swap(u, v);
        update(seg[top[u]], seg[u], 1, 1, n, 1);
        u = fa[top[u]];
    }
    if (dep[u] < dep[v]) swap(u, v);
    if (u != v)
        update(seg[v] + 1, seg[u], 1, 1, n, 1);
}

int main() {
    scanf("%d%d", &n, &m);
    for (int i = 1; i < n; i++) {
        int u, v;
        scanf("%d%d", &u, &v);
        g[u].push_back(v);
        g[v].push_back(u);
    }
    dfs1(1, -1);
    dfs2(1, 1);
    while (m--) {
        char op[2];
        int u, v;
        scanf("%s%d%d", op, &u, &v);
        if (op[0] == 'P') {
            func_update(u, v);
        }
        else {
            long long ans = func_query(u, v);
            printf("%lld\n", ans);
        }
    }
    return 0;
}