HDU-2844 Coins (多重背包+完全背包)

Coins

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 16754    Accepted Submission(s): 6664

Problem Description

Whuacmers use coins.They have coins of value A1,A2,A3...An Silverland dollar. One day Hibix opened purse and found there were some coins. He decided to buy a very nice watch in a nearby shop. He wanted to pay the exact price(without change) and he known the price would not more than m.But he didn't know the exact price of the watch.

You are to write a program which reads n,m,A1,A2,A3...An and C1,C2,C3...Cn corresponding to the number of Tony's coins of value A1,A2,A3...An then calculate how many prices(form 1 to m) Tony can pay use these coins.

 

Input

The input contains several test cases. The first line of each test case contains two integers n(1 ≤ n ≤ 100),m(m ≤ 100000).The second line contains 2n integers, denoting A1,A2,A3...An,C1,C2,C3...Cn (1 ≤ Ai ≤ 100000,1 ≤ Ci ≤ 1000). The last test case is followed by two zeros.

 

Output

For each test case output the answer on a single line.

 

Sample Input

3 101 2 4 2 1 12 51 4 2 10 0

 

Sample Output

84

#include <bits/stdc++.h>using namespace std;int a[1001], c[1001], dp[100001];int main(){int n, m;while(scanf("%d %d", &n, &m) != EOF){if(n == 0 && m == 0) return 0;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));for(int i = 1; i <= n; ++i){if(a[i] * c[i] >= m){for(int j = a[i]; j <= m; ++j){dp[j] = max(dp[j], dp[j - a[i]] + a[i]);}}else{for(int j = 1; j <= c[i]; j *= 2){int v = j * a[i];for(int k = m; k >= v; --k){dp[k] = max(dp[k], dp[k - v] + v);}c[i] -= j;}if(c[i]){int v = c[i] * a[i];for(int j = m; j >= v; --j){dp[j] = max(dp[j], dp[j - v] + v);}}}}int ans = 0;for(int i = 1; i <= m; ++i){ans += (dp[i] == i);}printf("%d\n", ans);}}/*题意：给你100种硬币和每种硬币的个数，不超过1000个，硬币价格不超过1e5，问你用这些硬币可以组成多少种不同的价格。价格区间1~1e5。思路：可以有一个想法是，dp[i]表示i的价格背包可以得到多少价值的硬币，如果dp[i]==i说明可以组成用这些硬币组成i的价格。如果每一个都跑多重背包会T，那么优化一下，如果某种硬币的总价格超过m的话，跑完全背包即可。否则跑多重背包。*/