洛谷P2305 [NOI2014]购票 [DP,树状数组]

传送门

思路

显然是树形DP,显然是斜率优化,唯一的问题就是该怎么维护凸包。

套路1:树上斜率优化,在没有这题的路程的限制的情况下,可以维护一个单调栈,每次加入点的时候二分它会加到哪里,然后替换并记录,等从这个点回溯上来的时候再撤销。

套路2:有路程限制时,不能简单替换,因为你可能会替换掉一个下面有用的点,然后WA掉。解决方法是用树状数组维护后缀单调栈,同样要支持撤销。

听着很简单,但代码不是很好写。

代码

第82行少打一个\(dep\)调了一下午,身败名裂……

#include<bits/stdc++.h>
clock_t t=clock();
namespace my_std{
    using namespace std;
    #define pii pair<int,int>
    #define fir first
    #define sec second
    #define MP make_pair
    #define rep(i,x,y) for (int i=(x);i<=(y);i++)
    #define drep(i,x,y) for (int i=(x);i>=(y);i--)
    #define go(x) for (int i=head[x];i;i=edge[i].nxt)
    #define templ template<typename T>
    #define sz 202200
    typedef long long ll;
    typedef double db;
    mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
    templ inline T rnd(T l,T r) {return uniform_int_distribution<T>(l,r)(rng);}
    templ inline bool chkmax(T &x,T y){return x<y?x=y,1:0;}
    templ inline bool chkmin(T &x,T y){return x>y?x=y,1:0;}
    templ inline void read(T& t)
    {
        t=0;char f=0,ch=getchar();double d=0.1;
        while(ch>'9'||ch<'0') f|=(ch=='-'),ch=getchar();
        while(ch<='9'&&ch>='0') t=t*10+ch-48,ch=getchar();
        if(ch=='.'){ch=getchar();while(ch<='9'&&ch>='0') t+=d*(ch^48),d*=0.1,ch=getchar();}
        t=(f?-t:t);
    }
    template<typename T,typename... Args>inline void read(T& t,Args&... args){read(t); read(args...);}
    char __sr[1<<21],__z[20];int __C=-1,__zz=0;
    inline void Ot(){fwrite(__sr,1,__C+1,stdout),__C=-1;}
    inline void print(register ll x)
    {
        if(__C>1<<20)Ot();if(x<0)__sr[++__C]='-',x=-x;
        while(__z[++__zz]=x%10+48,x/=10);
        while(__sr[++__C]=__z[__zz],--__zz);__sr[++__C]='\n';
    }
    void file()
    {
        #ifdef NTFOrz
        freopen("a.in","r",stdin);
        #endif
    }
    inline void chktime()
    {
        #ifndef ONLINE_JUDGE
        cout<<(clock()-t)/1000.0<<'\n';
        #endif
    }
    #ifdef mod
    ll ksm(ll x,int y){ll ret=1;for (;y;y>>=1,x=x*x%mod) if (y&1) ret=ret*x%mod;return ret;}
    ll inv(ll x){return ksm(x,mod-2);}
    #else
    ll ksm(ll x,int y){ll ret=1;for (;y;y>>=1,x=x*x) if (y&1) ret=ret*x;return ret;}
    #endif
//  inline ll mul(ll a,ll b){ll d=(ll)(a*(double)b/mod+0.5);ll ret=a*b-d*mod;if (ret<0) ret+=mod;return ret;}
}
using namespace my_std;

int n;
#define N (n+10)
struct hh{int t;ll w;int nxt;}edge[sz<<1];
int head[sz],ecnt;
void make_edge(int f,int t,ll w){edge[++ecnt]=(hh){t,w,head[f]};head[f]=ecnt;}

ll dep[sz],dp[sz],P[sz],Q[sz],L[sz];
int a[sz],c;
#define Convex vector<int>
Convex tr[sz];int siz[sz];
ll Calc(int id,ll k)
{
    if (!siz[id]) return 1e18;
    int l=0,r=siz[id]-1;
    while (233)
    {
        if (r-l<=10)
        {
            ll ret=1e18;
            rep(i,l,r) chkmin(ret,dp[tr[id][i]]-k*dep[tr[id][i]]);
            return ret;
        }
        int mid=(l+r)>>1;
        if (dp[tr[id][mid]]-k*dep[tr[id][mid]]<dp[tr[id][mid+1]]-k*dep[tr[id][mid+1]]) r=mid;
        else l=mid+1;
    }
}
ll calc(int x,ll k){ll ret=1e18;while (x) chkmin(ret,Calc(x,k)),x-=(x&(-x));return ret;}
struct hhh{int x,y,siz;};
map<pii,hhh>M;
db K(int x,int y){return 1.0*(dp[y]-dp[x])/(dep[y]-dep[x]);}
void Insert(int id,int x)
{
    int l=1,r=siz[id]-1,pos=(int)tr[id].size();
    while (l<=r)
    {
        int p=(l+r)>>1;
        if (dep[tr[id][p-1]]==dep[x])
        {
            if (dp[tr[id][p-1]]<=dp[x]) return;
            else pos=p-1,r=p-2;
            continue; 
        }
        if (K(tr[id][p-1],x)<K(tr[id][p-1],tr[id][p])) pos=p,r=p-1;
        else l=p+1;
    }
    if (siz[id]&&dep[tr[id][siz[id]-1]]==dep[x]&&dp[tr[id][siz[id]-1]]<=dp[x]) return;
    if (pos==(int)tr[id].size())
    {
        if (pos==siz[id])
		{
			tr[id].push_back(x);
			M[MP(x,id)]=(hhh){pos,-1,siz[id]};++siz[id];
			return;
		}
        pos=siz[id];
    }
    M[MP(x,id)]=(hhh){pos,tr[id][pos],siz[id]};tr[id][pos]=x;siz[id]=pos+1;
}
void insert(int x,int p){while (p<=N) Insert(p,x),p+=(p&(-p));}
void Reset(int id,int x)
{
    hhh s=M[MP(x,id)];
    tr[id][s.x]=s.y;siz[id]=s.siz;
    if (s.y==-1) tr[id].pop_back();
}
void reset(int x,int p){while (p<=N) Reset(p,x),p+=(p&(-p));}
void dfs(int x,int fa)
{
    a[++c]=x;insert(x,N-c);
    #define v edge[i].t
    go(x) if (v!=fa)
    {
        dep[v]=dep[x]+edge[i].w;
        int l=1,r=c,pos;
        while (l<=r)
        {
            int mid=(l+r)>>1;
            if (dep[v]-dep[a[mid]]<=L[v]) pos=mid,r=mid-1;
            else l=mid+1;
        }
        dp[v]=calc(N-pos,P[v])+P[v]*dep[v]+Q[v];
        dfs(v,x);
    }
    reset(x,N-c);--c;
}

int main()
{
    file();
    int _;
    read(n,_);
    int x;ll y;
    rep(i,2,n) read(x,y,P[i],Q[i],L[i]),make_edge(x,i,y);
    dfs(1,0);
    rep(i,2,n) print(dp[i]);Ot();
    return 0;
}
posted @ 2019-07-01 16:41  p_b_p_b  阅读(237)  评论(0编辑  收藏  举报