【BZOJ 1036】 [ZJOI2008]树的统计

题目来源：BZOJ 1036

思路：

练习树链剖分的例题，注意修改操作，所给的信息是树上的点的编号，不是线段树里的编号。

代码：

#include <cstdio>#include <iostream>#include <algorithm>#define mid ((l+r)>>1)#define lch (now<<1)#define rch ((now<<1)+1)const int maxn = 30010;const int inf = 2e9;int n, m, ct;int val[maxn], v[maxn];int head[maxn], next[maxn<<1], to[maxn<<1], cnt;int fa[maxn], dep[maxn], size[maxn], son[maxn];int pos[maxn], top[maxn];int t_max[maxn<<2], t_sum[maxn<<2];void add(int a, int b){    next[++cnt] = head[a];    head[a] = cnt, to[cnt] = b;}void dfs1(int now){    int mx1 = 0, mx2 = 0;    size[now] = 1;    for(int i = head[now]; i; i = next[i]){        if(to[i] == fa[now]) continue;        fa[to[i]] = now, dep[to[i]] = dep[now] + 1;        dfs1(to[i]);        size[now] += size[to[i]];        if(mx1 < size[to[i]]) mx1 = size[to[i]], mx2 = to[i];    }    son[now] = mx2;}void dfs2(int now){    pos[now] = ++ ct;    if(son[now] != 0) top[son[now]] = top[now], dfs2(son[now]);    for(int i = head[now]; i; i = next[i]){        if(to[i] == son[now] || to[i] == fa[now]) continue;        top[to[i]] = to[i], dfs2(to[i]);    }}void build(int now, int l, int r){    if(l == r){t_max[now] = v[l], t_sum[now] = v[l]; return;}    build(lch, l, mid);    build(rch, mid+1, r);    t_max[now] = std::max(t_max[lch], t_max[rch]);    t_sum[now] = t_sum[lch] + t_sum[rch];}int que_max(int now, int l, int r, int pos1, int pos2){    if(l == pos1 && r == pos2) return t_max[now];    if(pos2 <= mid) return que_max(lch, l, mid, pos1, pos2);    else if(pos1 >= mid+1) return que_max(rch, mid+1, r, pos1, pos2);    else return std::max(que_max(lch, l, mid, pos1, mid), que_max(rch, mid+1, r, mid+1, pos2));}int que_sum(int now, int l, int r, int pos1, int pos2){    if(l == pos1 && r == pos2) return t_sum[now];    if(pos2 <= mid) return que_sum(lch, l, mid, pos1, pos2);    else if(pos1 >= mid+1) return que_sum(rch, mid+1, r, pos1, pos2);    else return que_sum(lch, l, mid, pos1, mid) + que_sum(rch, mid+1, r, mid+1, pos2);}void modify(int now, int l, int r, int pos, int k){    if(l == r){t_max[now] = k, t_sum[now] = k; return;}    if(pos <= mid) modify(lch, l, mid, pos, k);    else modify(rch, mid+1, r, pos, k);    t_max[now] = std::max(t_max[lch], t_max[rch]);    t_sum[now] = t_sum[lch] + t_sum[rch];}int que_max(int x, int y){    int res = -inf;    while(top[x] != top[y]){        if(dep[top[x]] < dep[top[y]]) std::swap(x, y);        res = std::max(res, que_max(1, 1, n, pos[top[x]], pos[x]));        x = fa[top[x]];    }    if(pos[x] > pos[y]) std::swap(x, y);    res = std::max(res, que_max(1, 1, n, pos[x], pos[y]));    return res;}int que_sum(int x, int y){    int res = 0;    while(top[x] != top[y]){        if(dep[top[x]] < dep[top[y]]) std::swap(x, y);        res += que_sum(1, 1, n, pos[top[x]], pos[x]);        x = fa[top[x]];    }    if(pos[x] > pos[y]) std::swap(x, y);    res += que_sum(1, 1, n, pos[x], pos[y]);    return res;}int main(){    scanf("%d", &n);    for(int i = 1, a, b; i < n; i ++){scanf("%d%d", &a, &b), add(a, b), add(b, a);}    for(int i = 1; i <= n; i ++) scanf("%d", &val[i]);    scanf("%d", &m);    dep[1] = 1, dfs1(1);    top[1] = 1, dfs2(1);    for(int i = 1; i <= n; i ++) v[pos[i]] = val[i];    build(1, 1, n);    for(int i = 1, a, b; i <= m; i ++){        char ch[20];        scanf("%s%d%d", ch, &a, &b);        if(ch[1] == 'M') printf("%d\n", que_max(a, b));        if(ch[1] == 'S') printf("%d\n", que_sum(a, b));        if(ch[1] == 'H') modify(1, 1, n, pos[a], b);    }    return 0;}