E53 斜率优化DP [HNOI2008]玩具装箱

视频链接：463 斜率优化DP [HNOI2008]玩具装箱_哔哩哔哩_bilibili

Luogu P3195 [HNOI2008]玩具装箱

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

typedef long long LL;
const int N = 50010;
int n,L,q[N];
LL s[N],f[N];

double slope(int i,int j){ 
  return 1.0*(f[i]+(s[i]+i)*(s[i]+i)-f[j]-(s[j]+j)*(s[j]+j))
            /(s[i]+i==s[j]+j?1e-9:s[i]+i-s[j]-j);
}
int main(){
  scanf("%d%d",&n,&L); L++;
  for(int i=1;i<=n;i++) scanf("%lld",&s[i]), s[i]+=s[i-1];

  int h=1,t=0;
  for(int i=1;i<=n;i++){
    while(h<t && slope(i-1,q[t])<=slope(q[t],q[t-1])) t--;
    q[++t]=i-1;    
    while(h<t && slope(q[h+1],q[h])<=2*(s[i]+i-L)) h++;
    int j=q[h];
    f[i]=f[j]+(s[i]+i-s[j]-j-L)*(s[i]+i-s[j]-j-L);
  }
  printf("%lld\n",f[n]);
}

 

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

typedef long long LL;
const int N = 50010;
int n,L,q[N];
LL s[N],f[N];

LL dy(int i,int j){return f[i]+(s[i]+i)*(s[i]+i)-f[j]-(s[j]+j)*(s[j]+j);}
LL dx(int i,int j){return s[i]+i-s[j]-j;}
int main(){
  scanf("%d%d",&n,&L); L++;
  for(int i=1;i<=n;i++)
    scanf("%lld",&s[i]), s[i]+=s[i-1];

  int h=1,t=0;
  for(int i=1;i<=n;i++){
    while(h<t && dy(i-1,q[t])*dx(q[t],q[t-1])<=dx(i-1,q[t])*dy(q[t],q[t-1])) t--;
    q[++t]=i-1;    
    while(h<t && dy(q[h+1],q[h])<=dx(q[h+1],q[h])*2*(s[i]+i-L)) h++;
    int j=q[h];
    f[i]=f[j]+(s[i]+i-s[j]-j-L)*(s[i]+i-s[j]-j-L);
  }
  printf("%lld\n",f[n]);
}