HDU 5527 贪心

Too Rich

Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 1666    Accepted Submission(s): 422

Problem Description

You are a rich person, and you think your wallet is too heavy and full now. So you want to give me some money by buying a lovely pusheen sticker which costs pdollars from me. To make your wallet lighter, you decide to pay exactly p dollars by as many coins and/or banknotes as possible.

For example, if p=17 and you have two $10 coins, four $5 coins, and eight $1 coins, you will pay it by two $5 coins and seven $1 coins. But this task is incredibly hard since you are too rich and the sticker is too expensive and pusheen is too lovely, please write a program to calculate the best solution.

 

Input

The first line contains an integer T indicating the total number of test cases. Each test case is a line with 11 integers p,c1,c5,c10,c20,c50,c100,c200,c500,c1000,c2000, specifying the price of the pusheen sticker, and the number of coins and banknotes in each denomination. The number ci means how many coins/banknotes in denominations of i dollars in your wallet.

1≤T≤20000
0≤p≤109
0≤ci≤100000

 

Output

For each test case, please output the maximum number of coins and/or banknotes he can pay for exactly p dollars in a line. If you cannot pay for exactly p dollars, please simply output '-1'.

 

Sample Input

3
17 8 4 2 0 0 0 0 0 0 0
100 99 0 0 0 0 0 0 0 0 0
2015 9 8 7 6 5 4 3 2 1 0

 

Sample Output

9
-1
36

 

Source

2015ACM/ICPC亚洲区长春站-重现赛（感谢东北师大）

 

听说是一个金牌题，确实很巧妙。

开始的想法是，多重背包，用二进制优化成01背包，d[i] ：钱币为 i 的最多钱币数目，但是开不了这么大的数组，用map映射一下，或者改成记忆化搜索写法，但是是不可能的，记忆化还是得有一个vis数组~~~。

 

 

正解：

先转换思路，凑P求最多硬币，转为求mon - P 的最少硬币数。

然后贪心，但是会像记忆化搜索一样要回溯。直接贪心不太好。但是，硬币问题有一个特点，如果所有的钱币如： 1  ,   5   ,   10  ,   20  , 40   ,   80  ,   800，你已经看出来了，就是这种前面是后面的因子，这样就不可能说要从后往前的过程中要回溯。直接从后往前贪心。

 

怎么转为这种情况呢，发现只要改变两个数  50,500，改成 100,1000来用，就可以了。

#include <bits/stdc++.h>
 
using namespace std;
 
const int inf = 0x3f3f3f3f;
 
int c[];
int v[] = {,,,,,,,,,};
int num[];
int sum,mon,p,ans;
 
int solve(int x) {
    int ret = ,need;
 
    for(int i = ; i >=; i--) {
 
        if(v[i]==) {
            need = x/;
            need = min(need,num[i]/);
            ret +=*need;
            x-=need*;
        }
        else if(v[i]==) {
            need = x/;
            need = min(need,num[i]/);
            ret +=*need;
            x-=need*;
        }
        else {
            need = x/v[i];
            need = min(need,num[i]);
            ret +=need;
            x -=need*v[i];
        }
    }
    if(x) return inf;
    return ret;
 
}
 
int main()
{
    //freopen("in.txt","r",stdin);
    int T;
    scanf("%d",&T);
    while(T--) {
 
        sum = mon = ;
        scanf("%d",&p);
        for(int i = ; i < ; i++) {
            scanf("%d",&num[i]);
            sum +=num[i];
            mon +=num[i]*v[i];
        }
 
        p = mon - p;    //最少的硬币去兑换
 
        if(p<) {
            puts("-1");
            continue;
        }
 
        ans = inf;
        ans = min(ans,solve(p));
 
        if(num[]) {
            p-=;num[]--;
            if(p>=)
                ans = min(ans,solve(p)+);
            p+=;num[]++;
        }
        if(num[]) {
            p-=;num[]--;
            if(p>=)
                ans = min(ans,solve(p)+);
            p+=;
            num[]++;
        }
        if(num[]&&num[]) {
            p-=;num[]--;num[]--;
            if(p>=)
                ans = min(ans,solve(p)+);
        }
        if(ans==inf) puts("-1");
        else printf("%d\n",sum-ans);
    }
 
    return ;
}