题意：[ZJOI2008] 树的统计

一棵树上有 $n$ 个节点，编号分别为 $1$ 到 $n$，每个节点都有一个权值 $w$。

支持操作：

I. CHANGE u t : 把结点 $u$ 的权值改为 $t$。

II. QMAX u v: 询问从点 $u$ 到点 $v$ 的路径上的节点的最大权值。

III. QSUM u v: 询问从点 $u$ 到点 $v$ 的路径上的节点的权值和。

树链剖分，20pts

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>

using namespace std;

typedef long long ll;

const int N = 30010, M = N << 1;

int n, q, a[N], cnt;
int h[N], e[M], ne[M], idx;
int sz[N], son[N], f[N], top[N], dep[N], dfn[N], rnk[N];

template <typename T> inline void read(T &x) {
    int f = 1; x = 0; char s = getchar();
    while (s < '0' || s > '9') { if (s == '-') f = -1; s = getchar(); }
    while (s <= '9' && s >= '0') x = x * 10 + (s ^ 48), s = getchar();
    x *= f;
}

inline void add(int a, int b) {
    e[idx] = b;
    ne[idx] = h[a];
    h[a] = idx ++ ;
}

struct Segtree {
    ll sum[N*4], maxx[N*4];
    inline int lc(int u) { return u << 1; }
    inline int rc(int u) { return u << 1 | 1; }
    void pushUp(int p) {
        sum[p] = sum[lc(p)] + sum[rc(p)];
        maxx[p] = max(maxx[lc(p)], maxx[rc(p)]);
    }
    void build(int u, int l, int r) {
        if (l == r) {
            sum[u] = a[r];
            maxx[u] = a[r];
            return;
        }
        int mid = (l + r) >> 1;
        build(lc(u), l, mid);
        build(rc(u), mid + 1, r);
        pushUp(u);
    }
    void update(int u, int l, int r, int x, ll c) {
        if (l == r) {
            sum[u] = c;
            maxx[u] = c;
            return;
        }
        int mid = (l + r) >> 1;
        if (x <= mid) update(lc(u), l, mid, x, c);
        else update(rc(u), mid + 1, r, x, c);
        pushUp(u);
    }
    ll querySum(int u, int l, int r, int ql, int qr) {
        if (l >= ql && r <= qr) return sum[u];
        int mid = (l + r) >> 1;
        ll ans = 0;
        if (ql <= mid) ans += querySum(lc(u), l, mid, ql, qr);
        if (qr > mid) ans += querySum(rc(u), mid + 1, r, ql, qr);
        return ans;
    }
    ll queryMax(int u, int l, int r, int ql, int qr) {
        if (l >= ql && r <= qr) return maxx[u];
        int mid = (l + r) >> 1;
        ll ans = -1e18;
        if (ql <= mid) ans = queryMax(lc(u), l, mid, ql, qr);
        if (qr > mid) ans = max(ans, queryMax(rc(u), mid + 1, r, ql, qr));
        return ans;
    }
}segtree;

inline void dfs1(int u) {
    sz[u] = 1;
    son[u] = -1;
    for (int i = h[u]; ~i; i = ne[i]) {
        if (dep[e[i]] == 0) {
            dep[e[i]] = dep[u] + 1;
            f[e[i]] = u;
            dfs1(e[i]);
            sz[u] += sz[e[i]];
            if (son[u] == -1 || sz[son[u]] < sz[e[i]]) son[u] = e[i];
        }
    }
}

inline void dfs2(int u, int tp) {
    top[u] = tp;
    cnt ++ ;
    dfn[u] = cnt;
    rnk[cnt] = u;
    if (son[u] == -1) return;
    dfs2(son[u], tp);
    for (int i = h[u]; ~i; i = ne[i]) {
        if (e[i] != son[u] && e[i] != f[u]) dfs2(e[i], e[i]);
    }
}

inline ll querymax(int x, int y) {
    ll ans = -1e18;
    int fx = top[x], fy = top[y];
    while (fx != fy) {
        if (dep[fx] >= dep[fy]) {
            ans = max(ans, segtree.queryMax(1, 1, n, dfn[fx], dfn[x]));
        } else {
            ans = max(ans, segtree.queryMax(1, 1, n, dfn[fy], dfn[y]));
        }
        fx = top[x];
        fy = top[y];
    }
    if (dfn[x] < dfn[y]) {
        ans = max(ans, segtree.queryMax(1, 1, n, dfn[x], dfn[y]));
    } else {
        ans = max(ans, segtree.queryMax(1, 1, n, dfn[y], dfn[x]));
    }
    return ans;
}

inline ll querysum(int x, int y) {
    ll ans = 0;
    int fx = top[x], fy = top[y];
    while (fx != fy) {
        if (dep[fx] >= dep[fy]) {
            ans += segtree.querySum(1, 1, n, dfn[fx], dfn[x]);
        } else {
            ans += segtree.querySum(1, 1, n, dfn[fy], dfn[y]);
        }
        fx = top[x];
        fy = top[y];
    }
    if (dfn[x] < dfn[y]) {
        ans += segtree.querySum(1, 1, n, dfn[x], dfn[y]);
    } else {
        ans += segtree.querySum(1, 1, n, dfn[y], dfn[x]);
    }
    return ans;
}

int main() {
    read(n);
    memset(h, -1, sizeof h);
    for (int i = 1; i < n; i ++ ) {
        int x, y;
        read(x), read(y);
        add(x, y), add(y, x);
    }
    dfs1(1);
    dfs2(1, 1);
    for (int i = 1; i <= n; i ++ ) read(a[i]);
    segtree.build(1, 1, n);
    read(q);
    while (q -- ) {
        string op; cin >> op;
        ll x, y; read(x), read(y);
        if (op[0] == 'C') segtree.update(1, 1, n, dfn[x], y);
        else if (op[1] == 'M') printf("%lld\n", querymax(x, y));
        else printf("%lld\n", querysum(x, y));
    }
    return 0;
}

求助，感谢！