POJ 1276 Cash Machine

最新推荐文章于 2022-05-13 16:43:56 发布

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本文介绍了一种用于自动取款机(ATM)的现金分配算法，该算法通过使用动态规划来确定最大可分配现金金额，确保能根据ATM中不同面额钞票的数量有效地响应用户的取款请求。

Description
A Bank plans to install a machine for cash withdrawal. The machine is able to deliver appropriate @ bills for a requested cash amount. The machine uses exactly N distinct bill denominations, say Dk, k=1,N, and for each denomination Dk the machine has a supply of nk bills. For example,
N=3, n1=10, D1=100, n2=4, D2=50, n3=5, D3=10
means the machine has a supply of 10 bills of @100 each, 4 bills of @50 each, and 5 bills of @10 each.
Call cash the requested amount of cash the machine should deliver and write a program that computes the maximum amount of cash less than or equal to cash that can be effectively delivered according to the available bill supply of the machine.
Notes:
@ is the symbol of the currency delivered by the machine. For instance, @ may stand for dollar, euro, pound etc.

【题目分析】
单调队列优化动态规划，无需记录单调队列，只需要记录一下最近的解就可以了。

【代码】

#include <cstdio>
#include <iostream>
#include <cstring>
bool dp[11][100001];
using namespace std;
int main()
{
    int n,m,t,v,p;
    while (cin>>m>>n)
    {
        memset(dp,0,sizeof dp);
        dp[0][0]=true;
        for (int i=1;i<=n;++i)
        {
            cin>>t>>v;
            for (int j=0;j<v;++j)
            {
                p=-0x3f3f3f3f;
                for (int k=0;k*v+j<=m;++k)
                {
                    if (k-p<=t) dp[i][k*v+j]|=dp[i-1][p*v+j];
                    dp[i][k*v+j]|=dp[i-1][k*v+j];
                    if (dp[i-1][k*v+j]) p=k;
                }
            }
        }
        for (int i=m;;--i)
        if (dp[n][i])
        {
            cout<<i<<endl;
            break;
        }
    }
}