HDOJ 3401 Trade

本文介绍了一个股票交易策略问题,通过使用单调队列优化动态规划算法来解决特定条件下的最大收益问题。该问题考虑了买入卖出限制、持有股票数量上限及交易间隔等约束。

单调队列优化DP :
dp[ i ] [ j ] = max{ dp[ i-1 ] [ j ]  ,  dp[ i - w -1 ] [ k ] - ( j - k )*ap[ i ]  ,  dp [ i - w - 1 ] [ k ] + ( k - j )*bp[ i ]  }
后两项 dp [ i - w - 1 ][ k ] + k* xx - j * xx 且 abs( j - x) < yy 可以维护一个单调递减的队列。。。

Trade

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 3156    Accepted Submission(s): 1008


Problem Description
Recently, lxhgww is addicted to stock, he finds some regular patterns after a few days' study.
He forecasts the next T days' stock market. On the i'th day, you can buy one stock with the price APi or sell one stock to get BPi. 
There are some other limits, one can buy at most ASi stocks on the i'th day and at most sell BSi stocks.
Two trading days should have a interval of more than W days. That is to say, suppose you traded (any buy or sell stocks is regarded as a trade)on the i'th day, the next trading day must be on the (i+W+1)th day or later.
What's more, one can own no more than MaxP stocks at any time.

Before the first day, lxhgww already has infinitely money but no stocks, of course he wants to earn as much money as possible from the stock market. So the question comes, how much at most can he earn?
 

Input
The first line is an integer t, the case number.
The first line of each case are three integers T , MaxP , W .
(0 <= W < T <= 2000, 1 <= MaxP <= 2000) .
The next T lines each has four integers APi,BPi,ASi,BSi( 1<=BPi<=APi<=1000,1<=ASi,BSi<=MaxP), which are mentioned above.
 

Output
The most money lxhgww can earn.
 

Sample Input
  
1 5 2 0 2 1 1 1 2 1 1 1 3 2 1 1 4 3 1 1 5 4 1 1
 

Sample Output
  
3
 

Author
lxhgww
 

Source
 

#include <iostream>
#include <cstring>
#include <cstdio>
#include <queue>
#include <algorithm>

using namespace std;

const int maxn=2200;

int N,P,W,dp[maxn][maxn],ap[maxn],bp[maxn],as[maxn],bs[maxn];

struct node
{
    int val,pos;
}que[maxn];

void solve()
{
    int head,tail,pre;

    memset(dp,0xcf,sizeof(dp));

    for(int i=1;i<=N;i++)
    {
        for(int j=0;j<=min(as[i],P);j++)
        {
            dp[i][j]=-ap[i]*j;
        }
    }

    for(int i=2;i<=N;i++)
    {
        for(int j=0;j<=P;j++)
        {
            dp[i][j]=max(dp[i-1][j],dp[i][j]);
        }
    }

    for(int i=W+2;i<=N;i++)
    {
        pre=i-W-1;
        head=0,tail=-1;
        for(int j=0;j<=P;j++)///buy
        {
            dp[i][j]=max(dp[i-1][j],dp[i][j]);

            node temp;
            temp.val=dp[pre][j]+j*ap[i];
            temp.pos=j;

            while(head<=tail&&que[tail].val<temp.val) tail--;
            que[++tail]=temp;
            while(head<=tail&&(j-que[head].pos)>as[i]) head++;

            if(head<=tail)
            {
                dp[i][j]=max(dp[i][j],que[head].val-j*ap[i]);
            }
        }

        head=0;tail=-1;
        for(int j=P;j>=0;j--)///sell
        {
            dp[i][j]=max(dp[i-1][j],dp[i][j]);

            node temp;
            temp.val=dp[pre][j]+bp[i]*j;
            temp.pos=j;

            while(head<=tail&&que[tail].val<temp.val) tail--;
            que[++tail]=temp;
            while(head<=tail&&(que[head].pos-j)>bs[i]) head++;

            if(head<=tail)
            {
                dp[i][j]=max(dp[i][j],que[head].val-bp[i]*j);
            }
        }
    }
}

int main()
{
    int cas;
    scanf("%d",&cas);
while(cas--)
{
    scanf("%d%d%d",&N,&P,&W);
    for(int i=1;i<=N;i++) scanf("%d%d%d%d",ap+i,bp+i,as+i,bs+i);
    solve();
    printf("%d\n",dp[N][0]);
}
    return 0;
}





内容概要:本文系统介绍了算术优化算法(AOA)的基本原理、核心思想及Python实现方法,并通过图像分割的实际案例展示了其应用价值。AOA是一种基于种群的元启发式算法,其核心思想来源于四则运算,利用乘除运算进行全局勘探,减运算进行局部开发,通过数学优化器速函数(MOA)和数学优化概率(MOP)动态控制搜索过程,在全局探索与局部开发之间实现平衡。文章详细解析了算法的初始化、勘探与开发阶段的更新策略,并提供了完整的Python代码实现,结合Rastrigin函数进行测试验证。进一步地,以Flask框架搭建前后端分离系统,将AOA应用于图像分割任务,展示了其在实际工程中的可行性与高效性。最后,通过收敛速度、寻优精度等指标评估算法性能,并提出自适应参数调整、模型优化和并行计算等改进策略。; 适合人群:具备一定Python编程基础和优化算法基础知识的高校学生、科研人员及工程技术人员,尤其适合从事人工智能、图像处理、智能优化等领域的从业者;; 使用场景及目标:①理解元启发式算法的设计思想与实现机制;②掌握AOA在函数优化、图像分割等实际问题中的建模与求解方法;③学习如何将优化算法集成到Web系统中实现工程化应用;④为算法性能评估与改进提供实践参考; 阅读建议:建议读者结合代码逐行调试,深入理解算法流程中MOA与MOP的作用机制,尝试在不同测试函数上运行算法以观察性能差异,并可进一步扩展图像分割模块,引入更复杂的预处理或后处理技术以提升分割效果。
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