学步园

题目链接：Light OJ 1348 - Aladdin and the Return Journey

题目大意：给定一棵树，两种操作

• 0 i j：ij路径上的权值和
• 1 i v：将第i个节点的权值修改为v

解题思路：树链剖分的裸题。

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

using namespace std;

const int maxn = 30005;

int N, Q, ne, first[maxn], jump[maxn * 2], link[maxn * 2], val[maxn];
int id, idx[maxn], dep[maxn], far[maxn], son[maxn], top[maxn], cnt[maxn];

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

    for (int i = first[u]; i + 1; i = jump[i]) {
        int v = link[i];
        if (v == pre)
            continue;
        dfs(v, u, d + 1);
        cnt[u] += cnt[v];
        if (cnt[son[u]] < cnt[v])
            son[u] = v;
    }
}

void dfs(int u, int rot) {
    top[u] = rot;
    idx[u] = ++id;
    if (son[u])
        dfs(son[u], rot);
    for (int i = first[u]; i + 1; i = jump[i]) {
        int v = link[i];
        if (v == far[u] || v == son[u])
            continue;
        dfs(v, v);
    }
}

inline void add_Edge(int u, int v) {
    link[ne] = v;
    jump[ne] = first[u];
    first[u] = ne++;
}

#define lson(x) ((x)<<1)
#define rson(x) (((x)<<1)|1)
int lc[maxn << 2], rc[maxn << 2], s[maxn << 2];

inline void pushup(int u) {
    s[u] = s[lson(u)] + s[rson(u)];
}

void build (int u, int l, int r) {
    lc[u] = l;
    rc[u] = r;
    s[u] = 0;

    if (l == r)
        return;
    int mid = (l + r) / 2;
    build(lson(u), l, mid);
    build(rson(u), mid + 1, r);
    pushup(u);
}

int query(int u, int l, int r) {
    if (l <= lc[u] && rc[u] <= r)
        return s[u];
    int mid = (lc[u] + rc[u]) / 2, ret = 0;
    if (l <= mid)
        ret += query(lson(u), l, r);
    if (r > mid)
        ret += query(rson(u), l, r);
    pushup(u);
    return ret;
}

void modify(int u, int x, int v) {
    if (x == lc[u] && x == rc[u]) {
        s[u] = v;
        return;
    }

    int mid = (lc[u] + rc[u]) / 2;
    if (x <= mid)
        modify(lson(u), x, v);
    else
        modify(rson(u), x, v);
    pushup(u);
}

void init () {
    scanf("%d", &N);
    for (int i = 1; i <= N; i++)
        scanf("%d", &val[i]);

    int u, v;
    ne = id = 0;
    memset(first, -1, sizeof(first));
    for (int i = 1; i < N; i++) {
        scanf("%d%d", &u, &v);
        u++, v++;
        add_Edge(u, v);
        add_Edge(v, u);
    }

    dfs(1, 0, 0);
    dfs(1, 1);
    build(1, 1, N);
    for (int i = 1; i <= N; i++)
        modify(1, idx[i], val[i]);
}

int query (int u, int v) {
    int p = top[u], q = top[v], ret = 0;
    while (p != q) {
        if (dep[p] < dep[q]) {
            swap(p, q);
            swap(u, v);
        }
        ret += query(1, idx[p], idx[u]);
        u = far[p];
        p = top[u];
    }
    if (dep[u] > dep[v])
        swap(u, v);
    ret += query(1, idx[u], idx[v]);
    return ret;
}

int main () {
    int cas;
    scanf("%d", &cas);
    for (int kcas = 1; kcas <= cas; kcas++) {
        init();

        scanf("%d", &Q);
        printf("Case %d:\n", kcas);
        int k, u, v;
        while (Q--) {
            scanf("%d%d%d", &k, &u, &v);
            if (k)
                modify(1, idx[u+1], v);
            else
                printf("%d\n", query(u+1, v+1));
        }
    }
    return 0;
}