P4544 Buying Feed G

dp &单调队列优化

 

这个题 ： k<=i, 决策点k 可以等于i ，所以在 i 入队后递推

#include<iostream>
#include<algorithm>
#include<cstring>
using namespace std;
const int N =503,M =1e4+2;
#define int long long
 int n,m,E,X[N],F[N],C[N],f[N][M];
 int q[N],hh,tt; 
 
 struct T{
 	int C,F,x;
 }a[N];
 int cmp(T &a,T &b){ return a.x<b.x; }
 int func(int i,int k){
   return f[i - 1][k]-C[i]*k + k*k*(X[i]-X[i-1]); 
 }
 signed main(){
 	cin>>m>>E>>n;
 	int i,j;
 	for(i=1;i<=n;i++) cin>>a[i].x>>a[i].F>>a[i].C;
 	sort(a+1,a+1+n,cmp);
 	for(i=1;i<=n;i++) X[i]=a[i].x,F[i]=a[i].F,C[i]=a[i].C;
 	memset(f,0x3f,sizeof f);
 	for(i=0;i<=n;i++) f[i][0]=0;
 	
 	for(i=1;i<=n;i++){
 		hh=1,tt=0; q[++tt]=0;
 	 for(j=1;j<=m;j++){
 	 	while(hh<=tt&&q[hh]<j-min(F[i],j)) hh++;
 	 	
 	    while(hh<=tt&&func(i,j)<=func(i,q[tt])) tt--;
 	    q[++tt]=j ;
 	    
 	    int k=q[hh];
 	    f[i][j]= func(i,k)+C[i]*j;
 	 } 
 	} 
 	int ans=f[n][m]+ m*m*(E-X[n]); 
 	cout<<ans;
 }