USACO Section 3.1 Stamps (stamps)

Stamps

Given a set of N stamp values (e.g., {1 cent, 3 cents}) and an upper limit K to the number of stamps that can fit on an envelope, calculate the largest unbroken list of postages from 1 cent to M cents that can be created.

For example, consider stamps whose values are limited to 1 cent and 3 cents; you can use at most 5 stamps. It's easy to see how to assemble postage of 1 through 5 cents (just use that many 1 cent stamps), and successive values aren't much harder:

• 6 = 3 + 3
• 7 = 3 + 3 + 1
• 8 = 3 + 3 + 1 + 1
• 9 = 3 + 3 + 3
• 10 = 3 + 3 + 3 + 1
• 11 = 3 + 3 + 3 + 1 + 1
• 12 = 3 + 3 + 3 + 3
• 13 = 3 + 3 + 3 + 3 + 1.

However, there is no way to make 14 cents of postage with 5 or fewer stamps of value 1 and 3 cents. Thus, for this set of two stamp values and a limit of K=5, the answer is M=13.

The most difficult test case for this problem has a time limit of 3 seconds.

PROGRAM NAME: stamps

INPUT FORMAT

Line 1:	Two integers K and N. K (1 <= K <= 200) is the total number of stamps that can be used. N (1 <= N <= 50) is the number of stamp values.
Lines 2..end:	N integers, 15 per line, listing all of the N stamp values, each of which will be at most 10000.

SAMPLE INPUT (file stamps.in)

5 2
1 3

OUTPUT FORMAT

Line 1:

One integer, the number of contiguous postage values starting at 1 cent that can be formed using no more than K stamps from the set.

SAMPLE OUTPUT (file stamps.out)

13

思路：尝试过很多方法，虽然知道是DP，发现其他方法都有漏洞。没啥可说的。

Executing...
   Test 1: TEST OK [0.000 secs, 11040 KB]
   Test 2: TEST OK [0.000 secs, 11040 KB]
   Test 3: TEST OK [0.000 secs, 11040 KB]
   Test 4: TEST OK [0.000 secs, 11040 KB]
   Test 5: TEST OK [0.000 secs, 11040 KB]
   Test 6: TEST OK [0.000 secs, 11040 KB]
   Test 7: TEST OK [0.000 secs, 11040 KB]
   Test 8: TEST OK [0.000 secs, 11040 KB]
   Test 9: TEST OK [0.000 secs, 11040 KB]
   Test 10: TEST OK [0.054 secs, 11040 KB]
   Test 11: TEST OK [0.518 secs, 11040 KB]
   Test 12: TEST OK [0.119 secs, 11040 KB]
   Test 13: TEST OK [0.000 secs, 11040 KB]

All tests OK.

/*
ID:wuhuaju2
PROG:stamps
LANG:C++
*/
#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <algorithm>
#include <cstring>
#include <string>
using namespace std;

const int maxn=2000100;
int f[maxn];
int a[52];
int n,k,maxx;

void close()
{
    fclose(stdin);
    fclose(stdout);
    exit(0);
}

void work()
{
}

void init ()
{
freopen("stamps.in","r",stdin);
freopen("stamps.out","w",stdout);
   scanf("%d %d",&k,&n);
    for (int i=0;i<n;i++)
        scanf("%d",&a[i]);
    sort(a,a+n);
    maxx=a[n-1]*k;
    for (int i=1;i<=maxx;i++)
    {
        f[i]=100000000;
        for (int j=0;j<n;j++)
        {
            if (i-a[j]>=0) //注意：此时是排好序了的！
                f[i]=min(f[i],f[i-a[j]]+1);
            else break; //所以可以break了！
        }
    }
    for (int i=1;i<=maxx;i++)
        if (f[i]>k)
        {
            cout<<i-1<<endl;
            close();
        }
    cout<<maxx<<endl;//这句话比较关键
}

int main ()
{
    init();
    work();
    close();
    return 0;
}