bzoj 3672 利用点分治将CDQ分治推广到树型结构上

  1 #include <cstdio>
  2 #include <cassert>
  3 #include <cstring>
  4 #include <algorithm>
  5 #define N 200010
  6 #define M N<<1
  7 #define fill(arr,lf,rg,v) memset(arr+lf,v,sizeof(arr[0])*(rg-lf+1))
  8 using namespace std;
  9 
 10 typedef long long dnt;
 11 struct Vector {
 12     dnt x, y;
 13     Vector(){}
 14     Vector( dnt x, dnt y ):x(x),y(y){}
 15     Vector operator+( const Vector &o ) const { return Vector(x+o.x,y+o.y); }
 16     Vector operator-( const Vector &o ) const { return Vector(x-o.x,y-o.y); }
 17     double operator^( const Vector &o ) const { return (double)x*o.y-(double)y*o.x; }
 18 };
 19 typedef Vector Point;
 20 bool onleft( const Point &a, const Point &b, const Point &c ) {
 21     return ((b-a)^(c-a)) >= 0.0;
 22 }
 23 struct Convex {
 24     Point stk[N];
 25     int top;
 26     void init() {
 27         top=-1;
 28     }
 29     inline void append( const Point &p ) {
 30         while( top>0 && onleft(stk[top-1],stk[top],p) ) top--;
 31         stk[++top] = p;
 32     }
 33     const Point& query( dnt k ) {
 34         int lf=0;
 35         int rg=top;
 36         if( lf==rg ) return stk[top];
 37         assert(k*(stk[lf].x-stk[lf+1].x)>=0);
 38         if( k*(stk[lf].x-stk[lf+1].x) >= (stk[lf].y-stk[lf+1].y) )
 39             return stk[lf];
 40         assert(k*(stk[rg-1].x-stk[rg].x)>=0);
 41         if( k*(stk[rg-1].x-stk[rg].x) <= (stk[rg-1].y-stk[rg].y) ) 
 42             return stk[rg];
 43         lf++;
 44         rg--;
 45         while( lf<rg ) {
 46             int mid=(lf+rg)>>1;
 47             assert(k*(stk[mid].x-stk[mid+1].x)>=0);
 48             if( k*(stk[mid].x-stk[mid+1].x) > (stk[mid].y-stk[mid+1].y) )
 49                 rg=mid;
 50             else
 51                 lf=mid+1;
 52         }
 53         return stk[lf];
 54     }
 55 };
 56 
 57 int n, case_type;
 58 int head[N], next[M], dest[M], etot;
 59 dnt wp[N], wq[N], lim[N], ws[M];
 60 int anc[N], fat[N], vis[N], siz[N], bac[N];
 61 dnt dep[N], dp[N];
 62 int qu[N], bg, ed;
 63 Convex convex;
 64 
 65 void adde( int u, int v, dnt s ) {
 66     etot++;
 67     dest[etot] = v;
 68     next[etot] = head[u];
 69     ws[etot] = s;
 70     head[u] = etot;
 71 }
 72 void bfs( int s ) {
 73     qu[bg=ed=1] = s;
 74     anc[s] = 0;
 75     dep[s] = 0;
 76     while( bg<=ed ) {
 77         int u=qu[bg++];
 78         for( register int t=head[u]; t; t=next[t] ) {
 79             int v=dest[t];
 80             if( v==anc[u] ) continue;
 81             qu[++ed] = v;
 82             anc[v] = u;
 83             dep[v] = dep[u]+ws[t];
 84         }
 85     }
 86 }
 87 int getc( int s ) {
 88     qu[bg=ed=1] = s;
 89     fat[s] = 0;
 90     bac[s] = 0;
 91     siz[s] = 0;
 92     while( bg<=ed ) {
 93         int u=qu[bg++];
 94         for( register int t=head[u]; t; t=next[t] ) {
 95             int v=dest[t];
 96             if( vis[v] || v==fat[u] ) continue;
 97             qu[++ed] = v;
 98             fat[v] = u;
 99             bac[v] = 0;
100             siz[v] = 0;
101         }
102     }
103     int c = 0;
104     for( register int i=ed; i>=1; i-- ) {
105         int u=qu[i];
106         siz[u]++;
107         if( fat[u] ) {
108             int f=fat[u];
109             siz[f]+=siz[u];
110             if( siz[u]>bac[f] ) bac[f]=siz[u];
111         }
112     }
113     for( register int i=1; i<=ed; i++ ) {
114         int u=qu[i];
115         if( bac[u]<siz[s]-siz[u] ) bac[u]=siz[s]-siz[u];
116         if( !c || bac[u]<bac[c] ) c=u;
117     }
118     //fprintf( stderr, "%d\n", c );
119     return c;
120 }
121 void flood( int s ) {
122     qu[bg=ed=1] = s;
123     fat[s] = 0;
124     while( bg<=ed ) {
125         int u=qu[bg++];
126         for( register int t=head[u]; t; t=next[t] ) {
127             int v=dest[t];
128             if( vis[v] || v==fat[u] ) continue;
129             qu[++ed] = v;
130             fat[v] = u;
131         }
132     }
133 }
134 inline void update( const Point &p, int u ) {
135     dnt v = p.y + wp[u]*(dep[u]-p.x) + wq[u];
136     if( dp[u]>v ) dp[u]=v;
137 }
138 bool cmp( int a, int b ) {
139     return dep[a]-lim[a]>dep[b]-lim[b];
140 }
141 void vdcp( int s ) {
142     int c=getc(s);
143     vis[c] = true;
144     if( c==s ) {
145         Point pc = Point(dep[c],dp[c]);
146         flood(s);
147         for( int i=1; i<=ed; i++ ) {
148             int u=qu[i];
149             if( u!=s && dep[u]-lim[u]<=pc.x ) update(pc,u);
150         }
151     } else {
152         vdcp(s);
153         flood(c);
154         sort( qu+1, qu+1+ed, cmp );
155         convex.init();
156         int cur = c;
157         for( register int i=1; i<=ed; i++ ) {
158             int u=qu[i];
159             while( cur!=s && dep[anc[cur]]>=dep[u]-lim[u] ) {
160                 cur=anc[cur];
161                 convex.append( Point(dep[cur],dp[cur]) );
162             }
163             if( convex.top>=0 ) 
164                 update( convex.query(wp[u]), u );
165         }
166         Point cp = Point(dep[c],dp[c]);
167         for( register int i=ed; i>=1; i-- ) {
168             int u=qu[i];
169             if( u==c ) continue;
170             if( dep[u]-lim[u]>dep[c] ) break;
171             update( cp, u );
172         }
173     }
174     for( int t=head[c]; t; t=next[t] ) {
175         int v=dest[t];
176         if( vis[v] ) continue;
177         vdcp(v);
178     }
179 }
180 int main() {
181     scanf( "%d%d", &n, &case_type );
182     for( int i=2; i<=n; i++ ) {
183         int f;
184         dnt s;
185         scanf( "%d%lld%lld%lld%lld", &f, &s, wp+i, wq+i, lim+i );
186         adde( f, i, s );
187         adde( i, f, s );
188     }
189     fill( dp, 0, n, 0x3f );
190     dp[1] = 0;
191     bfs(1);
192     vdcp(1);
193     for( int i=2; i<=n; i++ ) 
194         printf( "%lld\n", dp[i] );
195 }