Bzoj 3675 [Apio2014] Sequence segmentation (slope dp)

"Topic link"

http://www.lydsy.com/JudgeOnline/problem.php?id=3675

Test instructions

The sequence of n number is divided k times, the benefit of each time is divided into two parts of the value and the product, to seek maximum benefit.

Ideas

F[I][J] indicates that the maximum benefit of the first I-Partition J is transferred:

f[i][j]=max{f[k][j-1]+ (S (i)-S (k)) *s (k)}

A<b, if B is better than a decision-making:

(S[b]^2-s[a]^2+f[a][j-1]-f[b][j-1])/(S[b]-s[a]) <s[i]

The monotonic queue maintains the upper convex hull.

Code

1#include <Set>2#include <cmath>3#include <queue>4#include <vector>5#include <cstdio>6#include <cstring>7#include <iostream>8#include <algorithm>9 #defineTrav (u,i) for (int i=front[u];i;i=e[i].nxt)Ten #definefor (A,B,C) for (int a= (b); a<= (c); a++) One using namespacestd; A  -typedefLong Longll; - Const intN = 2e5+Ten; the  - ll Read () { -     CharC=GetChar (); -ll f=1, x=0; +      while(!IsDigit (c)) { -         if(c=='-') f=-1; C=GetChar (); +     } A      while(IsDigit (c)) atx=x*Ten+c-'0', c=GetChar (); -     returnx*F; - } -  - intN,k,tot; -ll f[n][2],cur,q[n],qh,qt,a[n],s[n]; in /* - Double Slop (ll A,ll b) { to return (double) (s[b]*s[b]-s[a]*s[a]+f[a][cur^1]-f[b][cur^1])/(double) (S[b]-s[a]); + } - */ the ll up (ll A,ll b) * { $     return(s[b]*s[b]-s[a]*s[a]+f[a][cur^1]-f[b][cur^1]);Panax Notoginseng } - ll Down (ll A,ll b) the { +     return(s[b]-S[a]); A } the  + intMain () - { $N=read (), k=read (); $for (I,1, N) { -a[++tot]=read (); -         if(!a[tot])--tot; the     } -n=tot;Wuyifor (I,1, N) s[i]=s[i-1]+A[i]; theFor (round,1, K) { -cur^=1; WuQh=1; qt=0; - For (i,round,n) { About              while(Qh<qt&&up (q[qt-1],Q[QT]) *down (q[qt-1],i-1) >up (q[qt-1],i-1) *down (q[qt-1],Q[QT]) qt--; $q[++qt]=i-1; -              while(Qh<qt&up (q[qh],q[qh+1]) <s[i]*down (q[qh],q[qh+1])) qh++; -             intt=Q[QH]; -f[i][cur]=f[t][cur^1]+ (S[i]-s[t]) *S[t]; A         } +     } theprintf"%lld\n", F[n][cur]); -     return 0; $}

Bzoj 3675 [Apio2014] Sequence segmentation (slope dp)