HDU-2844-Coins

链接：https://vjudge.net/problem/HDU-2844#author=CCOA

题意：

给定几种不同面额的硬币若干枚，需要求的用这些硬币可以组成多少种范围在1~m的不同面额的组合。

思路：

多重背包，二进制优化。

代码：

#include <iostream>
#include <memory.h>
#include <vector>
#include <map>
#include <algorithm>
#include <cstdio>
#include <math.h>

using namespace std;

typedef long long LL;

const int MAXN = 1e2 + 10;
const int MAXM = 1e5 + 10;
const int INF = 1e9;

int dp[MAXM];
int a[MAXN], b[MAXN];

int main()
{
    int n, m;
    while (scanf("%d %d", &n, &m), n|m)
    {
        memset(dp, 0, sizeof(dp));
        for (int i = 1;i <= n;i++)
            scanf("%d", &a[i]);
        for (int i = 1;i <= n;i++)
            scanf("%d", &b[i]);
        for (int i = 1;i <= n;i++)
        {
            int k = 1;
            int v;
            while (k <= b[i])
            {
                v = k * a[i];
                b[i] -= k;
                for (int j = m;j >= v;j--)
                    dp[j] = max(dp[j], dp[j - v] + v);
                k = k << 1;
            }
            if (b[i] > 0)
            {
                k = b[i];
                v = k * a[i];
                for (int j = m;j >= v;j--)
                    dp[j] = max(dp[j], dp[j - v] + v);
            }
        }
        int res = 0;
        for (int i = 1;i <= m;i++)
            if (dp[i] == i)
                res++;
        printf("%d\n", res);
    }


    return 0;
}