E55 斜率优化DP Cats Transport

视频链接：465 斜率优化DP Cats Transport_哔哩哔哩_bilibili

CF311B Cats Transport

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

typedef long long LL;
const int N=100010,M=100010,P=110;
int n,m,p,H,q[M];
LL d[N],t[N],a[N],s[N],f[P][M];

double slope(int i,int j,int k){
  return 1.0*(f[i-1][j]+s[j]-f[i-1][k]-s[k])
            /(j==k?1e-9:j-k);
}
int main(){
  scanf("%d%d%d",&n,&m,&p);
  for(int i=2;i<=n;i++)scanf("%lld",&d[i]), d[i]+=d[i-1];
  for(int i=1;i<=m;i++)scanf("%d%lld",&H,&t[i]), a[i]=t[i]-d[H];
  sort(a+1,a+m+1);
  for(int i=1; i<=m; i++) s[i]=s[i-1]+a[i];
  for(int i=1; i<=m; i++) f[0][i]=1e18; //非法状态的初值
  
  for(int i=1; i<=p; i++){    //枚举人
    int h=1,t=0;
    for(int j=1; j<=m; j++){  //枚举猫
      while(h<t && slope(i,j-1,q[t])<=slope(i,q[t],q[t-1])) t--;
      q[++t]=j-1;    
      while(h<t && slope(i,q[h+1],q[h])<=a[j]) h++;
      int k=q[h];
      f[i][j]=f[i-1][k]+a[j]*(j-k)-(s[j]-s[k]);
      // printf("f[%d %d]=f[%d %d]+%d=%d\n",i,j,i-1,k,a[j]*(j-k)-(s[j]-s[k]),f[i][j]);
    }
  }
  printf("%lld\n",f[p][m]);
}

 

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

typedef long long LL;
const int N=100010,M=100010,P=110;
int n,m,p,H,q[M];
LL d[N],t[N],a[N],s[N];
LL f[P][M];

LL dy(int i,int j,int k){return f[i-1][j]+s[j]-(f[i-1][k]+s[k]);}
LL dx(int j,int k){return j-k;}
int main(){
  scanf("%d%d%d",&n,&m,&p);
  for(int i=2;i<=n;i++)scanf("%lld",&d[i]), d[i]+=d[i-1];
  for(int i=1;i<=m;i++)scanf("%d%lld",&H,&t[i]), a[i]=t[i]-d[H];
  sort(a+1,a+m+1);
  for(int i=1; i<=m; i++) s[i]=s[i-1]+a[i];
  memset(f,0x3f,sizeof f); for(int i=0;i<=p;i++) f[i][0]=0;
  
  for(int i=1; i<=p; i++){    //枚举人
    int h=1,t=0;
    for(int j=1; j<=m; j++){  //枚举猫
      while(h<t && dy(i,j-1,q[t])*dx(q[t],q[t-1])
                 <=dx(j-1,q[t])*dy(i,q[t],q[t-1])) t--;
      q[++t]=j-1;
      while(h<t && dy(i,q[h+1],q[h])
                 <=dx(q[h+1],q[h])*a[j]) h++;
      int k=q[h];
      f[i][j]=f[i-1][k]+a[j]*(j-k)-(s[j]-s[k]);      
    }
  }
  printf("%lld\n",f[p][m]);
}

 

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