bzoj1036: [ZJOI2008]树的统计Count - 树链剖分

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题目链接: http://www.lydsy.com/JudgeOnline/problem.php?id=1036

题意: 

给一棵树, 点上有权值, 带单点更新, 询问两点间权值最大值以及路径上所有点权值和。


树链剖分入门题。


#include <bits/stdc++.h>using namespace std;#define lson l,m,rt<<1#define rson m+1,r,rt<<1|1typedef long long ll;const int maxn = 30000 + 10;const int inf = 1 << 30;struct Edge{    int to, next;}e[maxn*2];int n;int cnt, head[maxn], w[maxn];//int fa[maxn], size[maxn], dep[maxn];int top[maxn];int son[maxn];int idx[maxn];int pos;//int Max[maxn<<2], Sum[maxn<<2];void init(){    cnt = pos = 0;    memset(head, -1, sizeof(head));    memset(son, -1, sizeof(son));}void add(int u, int v){    e[cnt].to = v;    e[cnt].next = head[u];    head[u] = cnt++;}void dfs1(int u, int pre, int deep){    fa[u] = pre; size[u] = 1; dep[u] = deep;    for(int i=head[u]; i!=-1; i=e[i].next)    {        int v = e[i].to;        if(v == pre) continue;        dfs1(v, u, deep+1);        size[u] += size[v];        if(son[u] == -1 || size[v] > size[son[u]]) son[u] = v;    }}void dfs2(int u, int anc){    top[u] = anc;    if(son[u] != -1)    {        idx[u] = pos++;        dfs2(son[u], anc);    }    else    {        idx[u] = pos++;        return;    }    for(int i=head[u]; i!=-1; i=e[i].next)    {        int v = e[i].to;        if(v != fa[u] && v!= son[u]) dfs2(v, v);    }}void build(int l, int r, int rt){    Max[rt] = -inf;    Sum[rt] = 0;    if(l == r) return;    int m = (l+r) >> 1;    build(lson);    build(rson);}void pushUp(int rt){    Max[rt] = max(Max[rt<<1], Max[rt<<1|1]);    Sum[rt] = Sum[rt<<1] + Sum[rt<<1|1];}void update(int p, int v, int l, int r, int rt){    if(l == r)    {        Max[rt] = v;        Sum[rt] = v;        return;    }    int m = (l+r) >> 1;    if( p <= m) update(p, v, lson);    else update(p, v, rson);    pushUp(rt);}int query_sum(int L, int R, int l, int r, int rt){    if( L<= l && r <= R) return Sum[rt];    int ret = 0;    int m = (l + r) >> 1;    if(L <= m) ret += query_sum(L, R, lson);    if(R > m) ret += query_sum(L, R, rson);    return ret;}int query_max(int L, int R, int l, int r, int rt){    if( L<= l && r <= R) return Max[rt];    int ret = -inf;    int m = (l + r) >> 1;    if(L <= m) ret = max(ret, query_max(L, R, lson) );    if(R > m) ret = max(ret, query_max(L, R, rson) );    return ret;}int find_sum(int u, int v){    int f1 = top[u], f2 = top[v];    int ret = 0;    while(f1 != f2)    {        if(dep[f1] < dep[f2])        {            swap(f1, f2);            swap(u , v);        }        ret += query_sum(idx[f1], idx[u], 0, pos-1, 1);        u = fa[f1]; f1 = top[u];    }    if(dep[u] < dep[v]) swap(u, v);    ret += query_sum(idx[v], idx[u], 0, pos-1, 1);    return ret;}int find_max(int u, int v){    int f1 = top[u], f2 = top[v];    int ret = -inf;    while(f1 != f2)    {        if(dep[f1] < dep[f2])        {            swap(f1, f2);            swap(u , v);        }        ret = max(ret, query_max(idx[f1], idx[u], 0, pos-1, 1) );        u = fa[f1]; f1 = top[u];    }    if(dep[u] < dep[v]) swap(u, v);    ret = max(ret, query_max(idx[v], idx[u], 0, pos-1, 1) );    return ret;}int main(){    init();    scanf("%d", &n);    int u, v;    for(int i=0; i<n-1; i++)    {        scanf("%d%d", &u, &v);        add(u, v);        add(v, u);    }    for(int i=1; i<=n; i++) scanf("%d", &w[i]);    dfs1(1, -1, 0); dfs2(1, 1);//    for(int i=1; i<=n; i++)//    {//        printf("son:%d size:%d dep:%d id:%d top:%d\n", son[i], size[i], dep[i], idx[i], top[i]);//    }    build(0, pos-1, 1);    for(int i=1; i<=n; i++)    {        update(idx[i], w[i], 0, pos-1, 1);    }    int Q, a, b;    char buf[10];    cin >> Q;    while(Q--)    {        scanf("%s%d%d", buf, &a, &b);        if(buf[0] == 'C') update(idx[a], b, 0, pos-1, 1);        else if(buf[1] == 'S') printf("%d\n", find_sum(a, b));        else printf("%d\n", find_max(a, b));    }    return 0;}


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