dp优化

单调队列优化DP 优化方法大杂烩 I. - qAlex_Weiq - 博客园 (cnblogs.com)

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

typedef long long LL;
const int N=1e5+10;
int n,k,q[N];
LL w[N],f[N],sum;

int main(){
  cin>>n>>k; k++; //
  for(int i=1;i<=n;i++) cin>>w[i],sum+=w[i];
  
  int h=1,t=0; LL s=1e18;
  for(int i=1;i<=n;i++){
    while(h<=t && f[q[t]]>=f[i-1]) t--;
    q[++t]=i-1;
    if(q[h]<i-k) h++;
    f[i]=f[q[h]]+w[i];
    if(i>n-k) s=min(s,f[i]);
  }
  cout<<sum-s;
}

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

typedef long long LL;
const int N = 500010;
int n,m,q[N];
LL s[N],f[N];

double slope(int i,int j){ 
  return (double)(f[i]+s[i]*s[i]-f[j]-s[j]*s[j])
                /(s[i]==s[j]?1e-9:s[i]-s[j]);
}
int main(){
  while(~scanf("%d%d",&n,&m)){
    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]) h++;
      int j=q[h];
      f[i]=f[j]+(s[i]-s[j])*(s[i]-s[j])+m;
    }
    printf("%lld\n",f[n]);
  }
}