bzoj-4172 Marbles

Test instructions

Whiteboard questions, omitted;

Exercises

First, according to the operation with splay maintenance sequence;

Note that the sequence after maintenance should be guaranteed to be n;

Then there are three arrays of a[i],p[i],q[i];

F[i] Indicates the maximum score for hitting the I-marbles with the front marbles;

Then F[i]=max (0,-a[i]*p[j]+q[j]);

(0<j<i)

Temporarily do not consider 0, deformation can be q[j]=a[i]*p[j]+f[i];

This is obviously a slope optimization form, maintenance of a convex hull, two points on the convex hull is good;

0 of the situation is to add a point to go in, anyway, will not be t out convex shell;

Two points is not very good to write, but seems to be two minutes to l,r answer to take a max to write more (laughter);

Time complexity O (MLOGN+NLOGN);

This problem is clearly two questions!

Code:

#include <stdio.h> #include <string.h> #include <algorithm> #define N 410000#define which (x) (Ch[fa[x] ][1]==x) using namespace Std;typedef long long ll;int fa[n],ch[n][2],size[n],root,tot,cnt;ll val[n],a[n],x[n],y[n];int N,m,i,st[n],top;char str[100];void pushup (int x) {size[x]=size[ch[x][0]]+size[ch[x][1]]+1;} void Rotate (int x) {int f=fa[x];bool k=which (x); Ch[f][k]=ch[x][!k];ch[x][!k]=f;ch[fa[f]][which (f)]=x;fa[ch[f][k]]=f ; fa[x]=fa[f];fa[f]=x;size[x]=size[f]; Pushup (f);} void splay (int x,int g) {while (fa[x]!=g) {int f=fa[x];if (fa[f]==g) {Rotate (x); if (which (x) ^which (f)) Rotate (x); elserotate (f); Rotate (x);} if (!g) root=x;} int rank (int x,int k) {if (k<=size[ch[x][0])) return rank (ch[x][0],k); else if (k==size[ch[x][0]]+1) return x; Elsereturn rank (ch[x][1],k-size[ch[x][0]]-1);} void Insert (int k,ll v) {int X=rank (root,k), Y=rank (root,k+1); Splay (x,0), splay (y,x); fa[++tot]=y;size[tot]=1;ch[y][0]=tot;val[tot]=v; Pushup (y); Pushup (x);} void change (int k,ll v) {int X=rank (root,k); val[x]=v; Pushup (x);} void Print (int x) {if (!x) return; Print (Ch[x][0]); a[++cnt]=val[x]; Print (ch[x][1]);} Double slope (int a,int b) {if (b>=i) return 0;return (double (y[a]-y[b]))/(X[a]-x[b]);} int main () {int j,k,l,r,mid;ll v;scanf ("%d%d", &n,&m); Tot=2;ch[1][1]=2,fa[2]=1;root=1;for (i=1;i<=m;i++) { scanf ("%s%d%lld", Str,&k,&v), if (str[0]== ' I ') Insert (k+1,v); Elsechange (k+2,v);} Cnt=-1; Print (Root), for (i=1;i<=n;i++) scanf ("%lld%lld", X+i,y+i), St[top=2]=1;for (i=2;i<=n;i++) {l=1,r=top;while (l <=r) {mid=l+r>>1;if (slope (st[mid],st[mid+1]) >a[i]) l=mid+1;elser=mid-1;} printf ("%lld\n", Max (Y[st[l]]-a[i]*x[st[l]],y[st[r]]-a[i]*x[st[r])); while (top>1&& (y[st[top]]-y[st[ TOP-1]]) * (X[i]-x[st[top]]) <= (Y[i]-y[st[top]]) * (X[st[top]]-x[st[top-1]])) top--;st[++top]=i;} return 0;}

bzoj-4172 Marbles