hdu-3966 Aragorn's Story 树链剖分

Posted 2020-10-04 Luke_Ye

将一棵树剖分成log条树链，用数据结构维护每一段树链，操作复杂度从n降为log(n)*log(n).

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<string>
#include<algorithm>
#include<iostream>
#include<queue>
#include<map>
#include<cmath>
#include<set>
#include<stack>
#define LL int
using namespace std;
const int N = 50000+15;
LL n, m, p;
LL ene[N];


vector<int> g[N];

LL tim = 1;
LL siz[N];//子树大小
LL top[N];//当前top节点
LL son[N];//重儿子
LL dep[N];//深度
LL fa[N];//父亲
LL tid[N];//节点->新编号
LL rnk[N];//编号->节点
void dfs1(LL now, LL p,LL deep)
{
    siz[now] = 1;
    dep[now] = deep;
    fa[now] = p;
    son[now] = -1;
    for (int i = 0; i < g[now].size(); i++)
    {
        int e = g[now][i];
        if (e == p) continue;
        dfs1(e, now, deep + 1);
        siz[now] += siz[e];
        if (son[now] == -1 || siz[son[now]] < siz[e])
            son[now] = e;
    }
}
void dfs2(int now,int tp)
{
    //这两者需要根据dfs2顺序而设置
    tid[now] = tim++;
    rnk[tid[now]] = now;
    top[now] = tp;
    if (son[now] == -1)return;
    dfs2(son[now], tp);
    for (int i = 0; i < g[now].size(); i++)
    {
        LL e = g[now][i];
        if (e == fa[now]||e==son[now]) continue;
        dfs2(e, e);
    }
}
struct SegTree
{
    struct node
    {
        LL l, r;
        LL v;
    };
    node tre[N << 2];
    void build(LL l, LL r, LL rt)
    {
        tre[rt].l = l;
        tre[rt].r = r;
        tre[rt].v = 0;
        if (l == r)
        {
            tre[rt].v = ene[rnk[l]];
            return;
        }
        LL mid = (l + r) >> 1;
        build(l, mid, rt << 1);
        build(mid + 1, r, rt << 1 | 1);
    }
    void pushDown(LL rt)
    {
        tre[rt << 1].v += tre[rt].v;
        tre[rt << 1 | 1].v += tre[rt].v;
        tre[rt].v = 0;
    }
    int query(LL p, LL rt)
    {
        if (tre[rt].l == tre[rt].r)return tre[rt].v;
        //if (tre[rt].v)pushDown(rt);
        int mid = (tre[rt].l + tre[rt].r) >> 1;
        if (p <= mid)
            return tre[rt].v+query(p, rt << 1);
        return tre[rt].v+query(p, rt << 1 | 1);
    }
    void update(LL rt, LL l, LL r, LL v)
    {
        if (l <= tre[rt].l&&tre[rt].r <= r)
        {
            tre[rt].v += v;
            return;
        }
        //if (tre[rt].v)pushDown(rt);
        LL mid = (tre[rt].l + tre[rt].r) >> 1;
        if (l <= mid)
            update(rt << 1, l, r, v);
        if (r > mid)
            update(rt << 1 | 1, l, r, v);
    }
}t;
void change(LL u, LL v, LL k)
{
    while (top[u] != top[v])//深点向浅点靠近，直到在同一条链上
    {
        if (dep[top[v]] < dep[top[u]]) swap(u, v);
        t.update(1, tid[top[v]], tid[v], k);
        v = fa[top[v]];
    }
    if (dep[u] > dep[v])swap(u, v);
    t.update(1, tid[u], tid[v], k);
}

int main()
{
    cin.sync_with_stdio(false);
    while (scanf("%d%d%d",&n,&m,&p)!=EOF)
    {
        for (int i = 0; i <= n; i++) g[i].clear();
        for (int i = 1; i <= n; i++)scanf("%d", &ene[i]);
        for (int i = 0; i < m; i++)
        {
            int uu, vv;
            scanf("%d%d", &uu, &vv);
            g[uu].push_back(vv);
            g[vv].push_back(uu);
        }
        tim = 1;
        dfs1(1,0,0);//第一遍构造重边
        dfs2(1,1);//第二遍构造重链
        t.build(1, n, 1);
        while (p--)
        {
            char c[2];
            LL c1, c2, value;
            scanf("%s",c);
            if (c[0] == ‘I‘)
            {
                scanf("%d%d%d", &c1, &c2, &value);
                change(c1, c2, value);
            }
            if (c[0] == ‘D‘)
            {
                scanf("%d%d%d", &c1, &c2, &value);
                change(c1, c2, -value);
            }
            if (c[0] == ‘Q‘)
            {
                scanf("%d", &c1);
                cout << t.query(tid[c1],1) << endl;
            }
        }
    }
    return 0;
}