HYSBZ - 1036 树的统计

思路：这是经典的树链剖分，有三个操作。

1.两点路径中的最大点权；

2.两点路径中的点权和；

3.更改某个点的权值；

如果不用数据结构维护的话，直接搜带来的就是时间消耗太大，主要是因为搜的过程中做了很多无用功，不够直接的找到目标点和线段。树剖就是先按照儿子节点数的节点多少进行划分险段，线段不会相交，树上两个点的路径必然是通过它们的LCA的。我们可以通过线段往上找，知道两个点在同一个线段中，这样我们就可以成段的更新值了。

/*****************************************Author      :Crazy_AC(JamesQi)Time        :2016File Name   :*****************************************/// #pragma comment(linker, "/STACK:1024000000,1024000000")#include <iostream>#include <algorithm>#include <iomanip>#include <sstream>#include <string>#include <stack>#include <queue>#include <deque>#include <vector>#include <map>#include <set>#include <cstdio>#include <cstring>#include <cmath>#include <cstdlib>#include <climits>using namespace std;#define MEM(x,y) memset(x, y,sizeof x)#define pk push_back#define lson rt << 1#define rson rt << 1 | 1#define bug cout << "BUG HERE\n"typedef long long LL;typedef unsigned long long ULL;typedef pair<int,int> ii;typedef pair<ii,int> iii;const double eps = 1e-10;const int inf = 1 << 30;const int INF = 0x3f3f3f3f;const int MOD = 1e9 + 7;int nCase = 0;const int maxn = 30100;int n, q;int a[maxn];/*************************************************/struct node {int l, r;int maxNum;LL sum;}p[maxn<<2];int tmp[maxn];void up(int rt) {p[rt].maxNum = max(p[lson].maxNum, p[rson].maxNum);p[rt].sum = p[lson].sum + p[rson].sum;}void build(int rt,int L, int R) {p[rt].l = L, p[rt].r = R;if (L == R) {p[rt].maxNum = p[rt].sum = tmp[L];return ;}int mid = (L + R) >> 1;build(lson, L, mid);build(rson, mid + 1, R);up(rt);}void updata(int rt, int pos,int val) {if (p[rt].l == pos && p[rt].r == pos) {p[rt].sum = p[rt].maxNum = val;return ;}int mid = (p[rt].l + p[rt].r) >> 1;if (pos <= mid) updata(lson, pos, val);if (pos > mid) updata(rson, pos, val);up(rt);}LL QuerySum(int rt,int L, int R) {if (L <= p[rt].l && p[rt].r <= R) {return 1LL*p[rt].sum;}LL ret = 0LL;int mid = (p[rt].l + p[rt].r) >> 1;if (L <= mid) ret += QuerySum(lson, L, R);if (R > mid) ret += QuerySum(rson, L, R);return ret;}int QueryMax(int rt,int L, int R) {if (L <= p[rt].l && p[rt].r <= R) {return p[rt].maxNum;}int ans = -inf;int mid = (p[rt].l + p[rt].r) >> 1;if (L <= mid) ans = max(ans, QueryMax(lson, L, R));if (R > mid) ans = max(ans, QueryMax(rson, L, R));return ans;}/*************************************************/vector<int> G[maxn];int Times;int fa[maxn], top[maxn], size[maxn], son[maxn];int SegId[maxn], TreeId[maxn];int dep[maxn];int dfs_first(int u,int pre,int depth) {fa[u] = pre, dep[u] = depth, size[u] = 1;int tmp = 0;for (int i = 0;i < G[u].size();++i) {int v = G[u][i];if (v == pre) continue;int now = dfs_first(v, u, depth + 1);size[u] += now;if (now > tmp) {tmp = now;son[u] = v;}}return size[u];}void dfs_second(int u,int header) {top[u] = header;if (son[u] != -1) {SegId[u] = ++Times;TreeId[Times] = u;dfs_second(son[u], header);}else if (son[u] == -1) {SegId[u] = ++Times;TreeId[Times] = u;return ;}for (int i = 0;i < G[u].size();++i) {int v = G[u][i];if (v == fa[u] || v == son[u]) continue;dfs_second(v, v);}}/*************************************************/int findmax(int u,int v) {int ans = -inf;int p = top[u], q = top[v];while(p != q) {if (dep[p] < dep[q]) {swap(u, v);swap(p, q);}ans = max(ans, QueryMax(1,SegId[p], SegId[u]));u = fa[p];p = top[u];}if (dep[u] < dep[v]) swap(u, v);ans = max(ans, QueryMax(1, SegId[v], SegId[u]));return ans;}LL findsum(int u,int v) {int p = top[u], q = top[v];LL sum = 0LL;while(p != q) {if (dep[p] < dep[q]) {swap(u, v);swap(p, q);}sum += QuerySum(1, SegId[p], SegId[u]);u = fa[p];p = top[u];}if (dep[u] < dep[v]) swap(u, v);sum += QuerySum(1, SegId[v], SegId[u]);return sum;}void change(int u,int val) {updata(1, SegId[u], val);}/*************************************************/int main(int argc, const char * argv[]){// freopen("in.txt","r",stdin);// freopen("out.txt","w",stdout);while(~scanf("%d",&n)) {for (int i = 1;i <= n;++i)G[i].clear();int u, v;for (int i = 1;i < n;++i) {scanf("%d%d",&u,&v);G[u].push_back(v);G[v].push_back(u);}memset(son, -1, sizeof son);Times = 0;for (int i = 1;i <= n;++i)scanf("%d", &a[i]);//链的剖分dfs_first(1, -1, 0);dfs_second(1, 1);for (int i = 1;i <= n;++i) {tmp[ SegId[i] ] = a[i];}//建立线段树build(1, 1, n);scanf("%d",&q);char op[10];while(q--) {scanf("%s", op);if (strcmp(op, "QMAX") == 0) {scanf("%d%d",&u,&v);printf("%d\n", findmax(u, v));}if (strcmp(op, "QSUM") == 0) {scanf("%d%d",&u,&v);printf("%lld\n", findsum(u, v));}if (strcmp(op, "CHANGE") == 0) {scanf("%d%d",&u,&v);change(u, v);}}}return 0;}