E54 斜率优化DP [NOIP2018 普及组] 摆渡车

视频链接：464 斜率优化DP [NOIP2018 普及组] 摆渡车_哔哩哔哩_bilibili

Luogu P5017 [NOIP2018 普及组] 摆渡车

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

const int N=4e6+10;
int n,m,last,q[N];
int c[N],s[N],f[N];

double slope(int i,int j){
  return 1.0*(f[i]+s[i]-f[j]-s[j])
            /(c[i]==c[j]?1e-9:c[i]-c[j]);
}
int main(){
  scanf("%d%d",&n,&m);
  for(int i=1; i<=n; i++){
    int t; scanf("%d",&t);
    c[t]++; s[t]+=t; last=max(last,t);
  }
  for(int i=1; i<last+m; i++) c[i]+=c[i-1],s[i]+=s[i-1];
  for(int i=0;i<m;i++) f[i]=i*c[i]-s[i];
  
  int h=1,t=0; int ans=1e9;
  for(int i=m; i<last+m; i++){
    while(h<t && slope(i-m,q[t])<=slope(q[t],q[t-1])) t--;
    q[++t]=i-m;
    while(h<t && slope(q[h+1],q[h])<=i) h++;
    int j=q[h];
    f[i]=f[j]+i*(c[i]-c[j])-(s[i]-s[j]);
    if(i>=last) ans=min(ans,f[i]);
  }
  printf("%d\n",ans);
}