NOI2014 购票

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<vector>
using namespace std;
typedef long long LL;
inline LL read()
{
    LL x=0;bool f=0;char c=getchar();
    for (;c<'0'||c>'9';c=getchar()) f=c=='-'?1:0;
    for (;c>='0'&&c<='9';c=getchar()) x=x*10+c-'0';
    return f?-x:x;
}
const int N=200010;
int n,ll=1,to[N],next[N],head[N],fa[N];
LL p[N],q[N],lv[N],fl[N],dis[N],dp[N],_ans,_k;
int ct,id[N],ln[N<<2],rn[N<<2],_l,_r;
 
struct na
{
    LL x,y;
    na (LL a,LL b) {x=a;y=b;}
};
 
inline bool cmp(const na &a,const na &b,const na &c)
{
    return ((double)b.y-a.y)/(b.x-a.x)<((double)c.y-a.y)/(c.x-a.x);
}
 
struct pch
{
    na *h,*dh;
    int *pos,*tp,top;
    void init(int len)
    {
        top=0;
        h=(na*)malloc(sizeof(na)*(len+1));
        dh=(na*)malloc(sizeof(na)*(len+1));
        pos=(int*)malloc(sizeof(int)*(len+1));
        tp=(int*)malloc(sizeof(int)*(len+1));
    }
    void ins(const na &a)
    {
        if (top<2||cmp(h[top-2],h[top-1],a))
            *(dh++)=h[top],*(pos++)=*(tp++)=top,h[top++]=a;
        else if (!cmp(h[0],h[1],a)) 
            *(dh++)=h[1],*(pos++)=1,*(tp++)=top,h[1]=a,top=2;
        else
        {
            int l=0,r=top-2,mid;
            while (l+1<r)
            {
                mid=l+r>>1;
                if (cmp(h[mid],h[mid+1],a)) l=mid;
                else r=mid;
            }
            *(dh++)=h[r+1],*(pos++)=r+1,h[r+1]=a;
            *(tp++)=top,top=r+2;
        }
    }
    void del()
    {
        int p=*(--pos);
        h[p]=*(--dh);top=*(--tp);
    }
    inline double calk(int i)
    {
        if (!i) return -1e18;
        if (i==top) return 1e18;
        return ((double)(h+i)->y-(h+i-1)->y)/((double)(h+i)->x-(h+i-1)->x);
    }
    LL cal(LL k)
    {
        int l=0,r=top,mid;
        while (l+1<r)
        {
            if (calk(mid=l+r>>1)<=k) l=mid;
            else r=mid;
        }
        return (h+l)->y-k*(h+l)->x;
    }
}e[N<<2];
 
inline void adde(int u,int v,LL w)
{
    to[++ll]=v;next[ll]=head[u];head[u]=ll;fl[ll]=w;
}
 
int find(LL x)
{
    int l=0,r=ct-1,mid;
    while (l+1<r)
    {
        if (x<=dis[id[mid=l+r>>1]]) r=mid;
        else l=mid;
    }
    return r;
}
void build(int o,int l,int r)
{
    ln[o]=l;rn[o]=r;
    e[o].init(r-l+1);
    if (l==r) return;
    int mid=l+r>>1;
    build(o<<1,l,mid);
    build(o<<1|1,mid+1,r);
}
 
void query(int o)
{
    if (_l<=ln[o]&&rn[o]<=_r)
    {
        _ans=min(_ans,e[o].cal(_k));
        return;
    }
    int mid=ln[o]+rn[o]>>1;
    if (_l<=mid) query(o<<1);
    if (_r>mid) query(o<<1|1);
}
 
void ins(int p,LL x,LL y)
{
    int o=1,l=1,r=n,mid;
    na pt(x,y);
    e[o].ins(pt);
    while (l!=r)
    {
        if (p<=(mid=l+r>>1)) o=o<<1,r=mid;
        else o=o<<1|1,l=mid+1;
        e[o].ins(pt);
    }
}
 
void del(int x)
{
    int o=1,l=1,r=n,mid;
    e[o].del();
    while (l!=r)
    {
        if (x<=(mid=l+r>>1)) o=o<<1,r=mid;
        else o=o<<1|1,l=mid+1;
        e[o].del();
    }
}
 
void dfs(int u)
{
    id[++ct]=u;
    int lim=find(dis[u]-lv[u]);
    _l=lim;_r=ct-1;_ans=(LL)1e18;_k=p[u];
    query(1);dp[u]=_ans+p[u]*dis[u]+q[u];
    ins(ct,dis[u],dp[u]);
    for (int i=head[u];i;i=next[i]) 
        dis[to[i]]=dis[u]+fl[i],dfs(to[i]);
    del(ct--);
}
 
int main()
{
    n=read();read();
    for (int i=2;i<=n;i++)
    {
        fa[i]=read();
        adde(fa[i],i,read());
        p[i]=read();q[i]=read();lv[i]=read();
    }
    build(1,1,n);
    id[ct=1]=1;ins(1,0,0);
    for (int i=head[1];i;i=next[i])
        dis[to[i]]=fl[i],dfs(to[i]);
    for (int i=2;i<=n;i++) printf("%lld\n",dp[i]);
    return 0;
}