题目链接：hdu 3966 Aragorn‘s Story

题目大意：给定一个棵树，然后三种操作

• Q x：查询节点x的值
• I x y w：节点x到y这条路径上所有节点的值增加w
• D x y w：节点x到y这条路径上所有节点的值减少w

解题思路：树链剖分，用树状数组维护每个节点的值。

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstdio>
#include <cstring>
#include <vector>
#include <algorithm>

using namespace std;

#define lowbit(x) ((x)&(-x))
const int maxn = 50000;

int N, M, Q, val[maxn+5], fenw[maxn+5];
vector<int> g[maxn+5];

inline void add (int x, int v) {
    while (x <= N) {
        fenw[x] += v;
        x += lowbit(x);
    }
}

inline void add (int l, int r, int v) {
    add(l, v);
    add(r+1, -v);
}

inline int query (int x) {
    int ret = 0;
    while (x) {
        ret += fenw[x];
        x -= lowbit(x);
    }
    return ret;
}

int id, far[maxn+5], son[maxn+5], dep[maxn+5], cnt[maxn+5], top[maxn+5], idx[maxn+5];

void dfs_fir(int u, int pre, int d) {
    dep[u] = d;
    cnt[u] = 1;
    son[u] = 0;
    far[u] = pre;

    for (int i = 0; i < g[u].size(); i++) {
        int v = g[u][i];
        if (v == pre)
            continue;

        dfs_fir(v, u, d + 1);
        cnt[u] += cnt[v];
        if (cnt[son[u]] < cnt[v])
            son[u] = v;
    }
}

void dfs_sec(int u, int rot) {
    idx[u] = id++;
    top[u] = rot;

    if (son[u])
        dfs_sec(son[u], rot);

    for (int i = 0; i < g[u].size(); i++) {
        int v = g[u][i];
        if (v == son[u] || v == far[u])
            continue;
        dfs_sec(v, v);
    }
}

void change (int u, int v, int c) {
    int p = top[u], q = top[v];
    while (p != q) {
        if (dep[p] < dep[q]) {
            swap(p, q);
            swap(u, v);
        }
        add(idx[p], idx[u], c);
        u = far[p];
        p = top[u];
    }

    /*
    if (dep[u] > dep[v]) swap(u, v);
    add(idx[u], idx[v], c);
    */
    if (dep[u] < dep[v]) swap(u, v);
    add(idx[v], idx[u], c);
}

int main () {
    while (scanf("%d%d%d", &N, &M, &Q) == 3) {
        id = 1;
        memset(fenw, 0, sizeof(fenw));
        for (int i = 1; i <= N; i++) {
            scanf("%d", &val[i]);
            g[i].clear();
        }

        int u, v, c;
        for (int i = 0; i < M; i++) {
            scanf("%d%d", &u, &v);
            g[u].push_back(v);
            g[v].push_back(u);
        }

        dfs_fir(1, -1, 0);
        dfs_sec(1, 1);

        for (int i = 1; i <= N; i++) add(idx[i], idx[i], val[i]);

        char op[5];
        while (Q--) {
            scanf("%s%d", op, &u);
            if (op[0] == ‘Q‘)
                printf("%d\n", query(idx[u]));
            else {
                scanf("%d%d", &v, &c);
                if (op[0] == ‘D‘) c = -c;
                change(u, v, c);
            }
        }
    }
    return 0;
}

hdu 3966 Aragorn's Story(树链剖分+树状数组)