HDU-2844：Coins（多重背包+二进制优化）

链接：HDU-2844：Coins

题意：给你n个种类的钱和对应的数量，同统计一下从1到m能够凑成的钱有多少个。

题解：C[i] = 1 + 2 + 4 + ··· + 2^k + a (0 <= a < 2^(k+1))。

#include <bits/stdc++.h>
using namespace std;

const double EPS = 1e-6;
const int INF = 0x3f3f3f3f;
const int mod = 1e9 + 7;
const int maxn = 1e5 + 10;
int n, m;
int a[maxn], c[maxn];
int dp[maxn];

int main()
{
    while(scanf("%d%d", &n, &m) && (n || m)){
        for(int i = 1; i <= n; i++) scanf("%d", &a[i]);
        for(int i = 1; i <= n; i++) scanf("%d", &c[i]);
        
        memset(dp, 0, sizeof(dp));

        dp[0] = 1;
        for(int i = 1; i <= n; i++){
            int num = c[i];
            for(int k = 1; num > 0; k <<= 1){
                int mul = min(k, num);
                for(int j = m; j >= a[i] * mul; j--){
                    if(dp[j - a[i] * mul])dp[j] = 1;
                }
                num -= mul;
            }
        }

        int ans = 0;
        for(int i = 1; i <= m; i++) if(dp[i]) ans++;

        printf("%d\n", ans);
    }

    return 0;
}