[CF321E]Ciel and Gondolas&&[BZOJ5311]貞魚
阿新 • • 發佈:2018-08-13
namespace 復雜度 con || .com and clu spa php
codeforces
bzoj
description
有\(n\)個人要坐\(k\)輛車。如果第\(i\)個人和第\(j\)個人同坐一輛車,就會產生\(w_{i,j}\)的代價。
求最小化代價。\(n\le4000\)
sol
凸優化+決策單調性優化
這麽一講其實這題就已經做完了,復雜度\(O(n\log n\log w)\)
code
\(bzoj\)上需要卡常。上網蒯個讀入優化模板就行了。
#include<cstdio> #include<algorithm> #include<cstring> using namespace std; int gi(){ int x=0,w=1;char ch=getchar(); while ((ch<'0'||ch>'9')&&ch!='-') ch=getchar(); if (ch=='-') w=0,ch=getchar(); while (ch>='0'&&ch<='9') x=(x<<3)+(x<<1)+ch-'0',ch=getchar(); return w?x:-x; } const int N = 4005; struct node{int j,l,r;}q[N]; int n,k,s[N][N],f[N],g[N],hd,tl; int cal(int j,int i){ return f[j]+(s[i][i]-s[i][j]-s[j][i]+s[j][j]>>1); } bool better(int i,int j,int k){ int si=cal(i,k),sj=cal(j,k); return si<sj||(si==sj&&g[i]<g[j]); } int binary(int i,int j){ int l=q[tl].l,r=n,res=0; while (l<=r){ int mid=l+r>>1; if (better(i,j,mid)) res=mid,r=mid-1; else l=mid+1; } return res; } void solve(int c){ q[hd=tl=1]=(node){0,0,n}; for (int i=1;i<=n;++i){ ++q[hd].l;if (q[hd].l>q[hd].r) ++hd; f[i]=cal(q[hd].j,i)+c;g[i]=g[q[hd].j]+1; if (hd>tl||better(i,q[tl].j,n)){ while (hd<=tl&&better(i,q[tl].j,q[tl].l)) --tl; if (hd>tl) q[++tl]=(node){i,i,n}; else{ int x=binary(i,q[tl].j); q[tl].r=x-1;q[++tl]=(node){i,x,n}; } } } } int main(){ n=gi();k=gi(); for (int i=1;i<=n;++i) for (int j=1;j<=n;++j) s[i][j]=s[i-1][j]+s[i][j-1]-s[i-1][j-1]+gi(); int l=0,r=s[n][n],res=0; while (l<=r){ int mid=l+r>>1;solve(mid); if (g[n]<=k) res=mid,r=mid-1;else l=mid+1; } solve(res);printf("%d\n",f[n]-k*res);return 0; }
[CF321E]Ciel and Gondolas&&[BZOJ5311]貞魚