SPOJ - QTREE Query on a tree

給一棵樹

修改邊權和詢問路徑上的最大邊權

樹鍊剖分

把每條重鍊變成一條線段

然後用線段樹來記錄每條線段

查詢的時候再用lca的方法往上走直到到達同一條重鍊

#include <iostream>
#include <algorithm>
#include <sstream>
#include <string>
#include <queue>
#include <cstdio>
#include <map>
#include <set>
#include <utility>
#include <stack>
#include <cstring>
#include <cmath>
#include <vector>
#include <ctime>
#include <bitset>
using namespace std;
#define pb push_back
#define sd(n) scanf("%d",&n)
#define sdd(n,m) scanf("%d%d",&n,&m)
#define sddd(n,m,k) scanf("%d%d%d",&n,&m,&k)
#define sld(n) scanf("%lld",&n)
#define sldd(n,m) scanf("%lld%lld",&n,&m)
#define slddd(n,m,k) scanf("%lld%lld%lld",&n,&m,&k)
#define sf(n) scanf("%lf",&n)
#define sff(n,m) scanf("%lf%lf",&n,&m)
#define sfff(n,m,k) scanf("%lf%lf%lf",&n,&m,&k)
#define ss(str) scanf("%s",str)
#define ansn() printf("%d\n",ans)
#define lansn() printf("%lld\n",ans)
#define r0(i,n) for(int i=0;i<(n);++i)
#define r1(i,e) for(int i=1;i<=e;++i)
#define rn(i,e) for(int i=e;i>=1;--i)
#define mst(abc,bca) memset(abc,bca,sizeof abc)
#define lowbit(a) (a&(-a))
#define all(a) a.begin(),a.end()
#define pii pair<int,int>
#define mp(aa,bb) make_pair(aa,bb)
#define lrt rt<<1
#define rrt rt<<1|1
#define X first
#define Y second
#define PI (acos(-1.0))
typedef long long ll;
typedef unsigned long long ull;
const ll mod = +;
const double eps=;
const int inf=;
//const ll infl = 10000000000000000;
const int maxn=  +;
const int maxm = +;
//Pretests passed
int in(int &ret)
{
    char c;
    int sgn ;
    if(c=getchar(),c==EOF)return -;
    while(c!='-'&&(c<'0'||c>'9'))c=getchar();
    sgn = (c=='-')?-:;
    ret = (c=='-')?:(c-'0');
    while(c=getchar(),c>='0'&&c<='9')ret = ret*+(c-'0');
    ret *=sgn;
    return ;
}
vector<int>g[maxn];
int son[maxn],sz[maxn],fa[maxn],dep[maxn];
int id[maxn], top[maxn];
int dclock;
void dfs1(int u,int f)
{
    son[u] = ;
    sz[u] = ;
    fa[u] = f;
    dep[u] = dep[f] + ;
    for(int i=  ; i<g[u].size(); ++i)
    {
        int v = g[u][i];
        if(v==f)continue;
        dfs1(v,u);
        if(sz[son[u]]<sz[v])son[u] =v;
        sz[u]+=sz[v];
    }
}
void dfs2(int u,int f)
{
    id[u] = ++dclock;
    top[u] = f;
    if(son[u]!=)dfs2(son[u],top[u]);
    int s = g[u].size();
    for(int i = ; i<s; ++i)
    {
        int v = g[u][i];
        if(v==fa[u]||v==son[u])continue;
        dfs2(v,v);
    }
}
int seg[maxn<<];int n;
void update(int rt,int l,int r,int p,int v)
{
    if(l==r)
    {
        seg[rt] = v;
        return;
    }
    int mid = (l+r)>>;
    if(p<=mid)update(lrt,l,mid,p,v);
    else update(rrt,mid+,r,p,v);
    seg[rt] = max(seg[lrt],seg[rrt]);
}
int query(int rt,int l,int r,int ql,int qr)
{
    if(ql<=l&&qr>=r)return seg[rt];
    int mx = -inf;
    int mid = (l+r)>>;
    if(ql<=mid)mx = max(mx,query(lrt,l,mid,ql,qr));
    if(qr>mid)mx = max(mx,query(rrt,mid+,r,ql,qr));
    return mx;
}
int lca(int a,int b)
{
    int ans = -inf;
    while(top[a]!=top[b])
    {
        if(dep[top[a]]<dep[top[b]])swap(a,b);
        ans = max(ans,query(,,n,id[top[a]],id[a]));
        a = fa[top[a]];
    }
    if(dep[a]>dep[b])swap(a,b);
    if(a!=b)ans = max(ans,query(,,n,id[a]+,id[b]));
    return ans;
}
int u[maxn],v[maxn],w[maxn];
int main()
{
#ifdef LOCAL
    freopen("input.txt","r",stdin);
//    freopen("output.txt","w",stdout);
#endif // LOCAL

    int t;
    sd(t);
    while(t--)
    {
//        int n;
        sd(n);
        r1(i,n)g[i].clear();
        r1(i,n-)
        {
            int a,b,c;
            sddd(a,b,c);
            u[i] = a;
            v[i] = b;
            w[i] = c;
            g[a].pb(b);
            g[b].pb(a);
        }
        dclock  = ;
        dfs1(,);
        fa[] = ;
        dfs2(,);
        mst(seg,);
//        printf("%d",seg[0]);
        r1(i,n-)
        {
            int &a = u[i], &b = v[i];
            if(dep[a]<dep[b])swap(a,b);
            update(,,n,id[a],w[i]);
        }
        while()
        {
            char s[];
            ss(s);
            if(s[]=='D')break;
            if(s[]=='Q')
            {
                int a,b;
                sdd(a,b);
                int ans = lca(a,b);
                ansn();
            }
            else
            {
                int a,b;
                sdd(a,b);
                update(,,n,id[u[a]],b);
            }
        }
    }
    return ;
}