BZOJ 3672 购票

Description

Input

Output

Sample Input

Sample Output

Hint

#include<iostream>
#include<cmath>
#include<vector>
#include<cstdio>
#include<cstdlib>
using namespace std;

typedef long long ll;
#define eps (1e-6)
#define maxn (400010)
int N,side[maxn],toit[maxn],next[maxn],cnt,size[maxn],id[maxn],father[maxn];
int top[maxn]; ll len[maxn],d[maxn],f[maxn],Map[maxn],P[maxn],Q[maxn],L[maxn];
struct node
{
ll x,y;
friend inline int operator /(const node &a,const node &b)
{
double res = 1.0*a.x*b.y-1.0*b.x*a.y;
if (fabs(res-0) <= eps) return 0;
else if (res > 0) return 1; else return -1;
}
friend inline node operator -(const node &a,const node &b) { return (node){a.x-b.x,a.y-b.y}; }
inline double angle() { return 1.0*y/x; }
};
vector <node> convex[maxn*2]; vector <double> slop[maxn*2];

inline void add(int a,int b,ll c) { next[++cnt] = side[a]; side[a] = cnt; toit[cnt] = b; len[cnt] = c; }
inline void ins(int a,int b,ll c) { add(a,b,c); add(b,a,c); }

inline ll read()
{
char ch; ll ret = 0,f = 1;
do ch = getchar(); while (!(ch >= '0'&&ch <= '9')&&ch != '-');
if (ch == '-') ch = getchar(),f = -1;
do ret = ret*10+(ll)(ch-'0'),ch = getchar(); while (ch >= '0'&&ch <= '9');
return f*ret;
}

inline void dfs(int now)
{
size[now] = 1;
for (int i = side[now];i;i = next[i])
{
if (toit[i] == father[now]) continue;
father[toit[i]] = now; d[toit[i]] = d[now]+len[i];
dfs(toit[i]); size[now] += size[toit[i]];
}
}

inline void Div(int now,int Top)
{
top[now] = Top; id[now] = ++cnt; Map[cnt] = now;
int heavy = 0;
for (int i = side[now];i;i = next[i])
if (toit[i] != father[now]&&size[toit[i]] > size[heavy]) heavy = toit[i];
if (!heavy) return; Div(heavy,Top);
for (int i = side[now];i;i = next[i]) if (toit[i] != father[now]&&toit[i] != heavy) Div(toit[i],toit[i]);
}

inline ll br(int now,ll key)
{
int l = 0,r = slop[now].size()-1,mid;
while (l <= r)
{
mid = (l+r) >> 1;
if (slop[now][mid] < key) l = mid+1;
else r = mid-1;
}
return convex[now][l].y-key*convex[now][l].x;
}

inline ll query(int now,int l,int r,int ql,int qr,ll key)
{
if (ql <= l&&r <= qr) return br(now,key);
int mid = (l+r)>>1;
if (qr <= mid) return query(now<<1,l,mid,ql,qr,key);
else if (ql > mid) return query(now<<1|1,mid+1,r,ql,qr,key);
else return min(query(now<<1,l,mid,ql,mid,key),query(now<<1|1,mid+1,r,mid+1,qr,key));
}
inline void insert(int now,int l,int r,int pos,const node &pp)
{
int nn = convex[now].size();
while (nn>1&&(pp-convex[now][nn-1])/(convex[now][nn-1]-convex[now][nn-2]) >= 0)
--nn,convex[now].pop_back(),slop[now].pop_back();
++nn; convex[now].push_back(pp);
if (nn > 1) slop[now].push_back((convex[now][nn-1]-convex[now][nn-2]).angle());
if (l == r) return; int mid = (l+r) >> 1;
if (pos <= mid) insert(now<<1,l,mid,pos,pp);
else insert(now<<1|1,mid+1,r,pos,pp);
}

inline void work(int now)
{
int Top = now,i; f[now] = 1LL<<60;
while (true)
{
if (L[now] >= d[Top]-d[father[top[Top]]]) L[now] -= d[Top]-d[father[top[Top]]],Top = father[top[Top]];
else
{
int l = id[top[Top]],r = id[Top],mid;
while (l <= r)
{
mid = (l+r)>>1;
if (d[Top]-d[Map[mid]] > L[now]) l = mid+1;
else r = mid-1;
}
Top = Map[l]; break;
}
}
if (Top == now) return;
for (i = father[now];top[i] != top[Top];i = father[top[i]])
f[now] = min(query(1,1,N,id[top[i]],id[i],P[now]),f[now]);
f[now] = min(query(1,1,N,id[Top],id[i],P[now]),f[now]);
f[now] += P[now]*d[now]+Q[now];
}

inline void Dfs(int now)
{
work(now);
insert(1,1,N,id[now],(node){d[now],f[now]});
for (int i = side[now];i;i = next[i])
if (toit[i] != father[now]) Dfs(toit[i]);
}

int main()
{
freopen("3672.in","r",stdin);
freopen("3672.out","w",stdout);
N = read(); read();
for (int i = 2,a,b;i <= N;++i)
{
a = read(),b = read(),ins(i,a,b);
P[i] = read(),Q[i] = read(),L[i] = read();
}
d[cnt = 0] = -1LL << 60; dfs(1); Div(1,1); insert(1,1,N,id[1],(node){0,0});
for (int i = side[1];i;i = next[i]) Dfs(toit[i]);
for (int i = 2;i <= N;++i) printf("%lld\n",f[i]);
fclose(stdin); fclose(stdout);
return 0;
}