【无标题】2024.6.6

2024.6.6 【一天高考！！！ “夏天周而复始、该相逢的人会再相逢”】

Thursday 五月初一

来学习一下DP的优化

~~其实考试时我应该很难用到优化的~~

P2569 [SCOI2010] 股票交易

DP柿子比较好推，

T，Maxp都比较小，

作为f数组的两维还是挺合理的。

那么设f[i][j]为第i天，有j张票的最大价值

$没票时买\\ f[i][j]\ = \ -ap[i] * j\\ (0 \le j \le as[i])\\ 不参与买卖\\ f[i][j]\ = \ max(f[i][j],f[i-1][j])\\ (0 \le j \le Maxp)\\ 买\\ f[i][j]\ = \ max(f[i][j],f[i-w-1][k]-(j-k)*ap[i])\\ (j-as[i] \le k < j)\\ 卖\\ f[i][j]\ = \ max(f[i][j],f[i−w−1][k]+(k−j)*bp[i])\\ (j < k \le j+bs[i])\\$

然后就可以利用单调队列优化了

单调队列

//2024.6.6
//by white_ice
//[SCOI2010] 股票交易 | P2569
#include<bits/stdc++.h>
//#include"fopen.cpp"
using namespace std;
#define itn int
constexpr int oo = 2003;int jntm(itn a,int b){return a>b?a:b;}
int ngm (itn a,int b){return a<b?a:b;}int t,p,w;
int ap[oo],bp[oo],as[oo],bs[oo];
int f[oo][oo];itn stk[oo];int main(){//fre();ios::sync_with_stdio(0);cin.tie(0),cout.tie(0);cin >> t >> p >> w;memset(f,128,sizeof(f));for (itn i=1;i<=t;i++)cin >> ap[i] >> bp[i] >> as[i] >>bs[i];// for (int i=1;i<=t;i++){//     for (itn j=0;j<=as[i];j++)//         f[i][j] = -1*j*ap[i];//     for (itn j=0;j<=p;j++)//         f[i][j] = jntm(f[i][j],f[i-1][j]);//     if (i<=w)//         continue;//     int l,r;//     l = 1;r = 0;//     for (itn j=0;j<=p;j++){//         while (l<=r&&stk[l]<j-as[i])//             l++;//         while (l<=r&&f[i-w-1][stk[r]]+stk[r]*ap[i]<=f[i-w-1][j]+j*ap[i]);//                   //f[i-w-1][stk[r]]+stk[r]*ap[i]<=f[i-w-1][j]+j*ap[i]//             r--;//         stk[++r] = j;//         if (l<=r)//             f[i][j] = jntm(f[i][j],f[i-w-1][stk[l]]+stk[l]*ap[i]-j*ap[i]);//     }                            //f[i-w-1][stk[l]]+stk[l]*ap[i]-j*ap[i]//     l = 1,r = 0;//     for (itn j=p;j>=0;j--){//         while (l<=r&&stk[l]>j+bs[i])//             l++;//         while (l<=r&&f[i-w-1][stk[r]]+stk[r]*bp[i]<=f[i-w-1][j]+j*bp[i])//                    //f[i-w-1][stk[r]]+stk[r]*bp[i]<=f[i-w-1][j]+j*bp[i]//             r--;//         stk[++r] = j;//         if (l<=r)//             f[i][j] = jntm(f[i][j],f[i-w-1][stk[l]]+stk[l]*bp[i]-j*bp[i]);//                                  //f[i-w-1][stk[l]]+stk[l]*bp[i]-j*bp[i]//     }// }for(int i=1;i<=t;i++){cin >> ap[i] >> bp[i] >> as[i] >> bs[i];for(int j=0;j<=as[i];j++)f[i][j] = -1*j*ap[i]; for(int j=0;j<=p;j++)f[i][j] = jntm(f[i][j],f[i-1][j]); if(i<=w)continue;    int l,r;l = 1 , r = 0;for(int j=0;j<=p;j++){while(l<=r&&stk[l]<j-as[i])l++; while(l<=r&&f[i-w-1][stk[r]]+stk[r]*ap[i]<=f[i-w-1][j]+j*ap[i])r--; stk[++r] = j; if (l<=r)f[i][j] = jntm(f[i][j],f[i-w-1][stk[l]]+stk[l]*ap[i]-j*ap[i]); }l = 1 , r = 0;for(int j=p;j>=0;j--){while(l<=r&&stk[l]>j+bs[i])l++;while(l<=r&&f[i-w-1][stk[r]]+stk[r]*bp[i]<=f[i-w-1][j]+j*bp[i])r--;stk[++r] = j;if(l <= r)f[i][j] = jntm(f[i][j],f[i-w-1][stk[l]]+stk[l]*bp[i]-j*bp[i]); }}int out =  -0x3f3f3f3f;for (itn i=0;i<=p;i++)out = jntm (out,f[t][i]);cout << out;return 0;
}