HDU2844(多重部分和)

Coins

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 10961 Accepted Submission(s): 4418


[align=left]Problem Description[/align]
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.

[align=left]Input[/align]
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.

[align=left]Output[/align]
For each test case output the answer on a single line.

[align=left]Sample Input[/align]

3 10
1 2 4 2 1 1
2 5
1 4 2 1
0 0

[align=left]Sample Output[/align]

8
4
该题卡多重背包，数组开的不够大WA，开的太大MLE。
下面是用多重背包做该题的思路。

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int A[105],C[105];
int n,m;
int dp[100005];
int w[100005];
int used[100005];
int main()
{
while(scanf("%d%d",&n,&m)!=EOF)
{
if(!n&&!m)
break;
memset(dp,0,sizeof(dp));
memset(used,0,sizeof(used));
for(int i=0;i<n;i++)    scanf("%d",&A[i]);
for(int i=0;i<n;i++)    scanf("%d",&C[i]);

int cnt=0;
for(int i=0;i<n;i++)
{
int e=1;
while(e<C[i])
{
w[cnt++]=e*A[i];
C[i]-=e;
e<<=1;
}
if(C[i]>0)
w[cnt++]=C[i]*A[i];
}

for(int i=0;i<cnt;i++)
for(int j=m;j>=w[i];j--)
dp[j]=max(dp[j],dp[j-w[i]]+w[i]);

int res=0;
for(int i=m;i>=1;i--)
if(!used[dp[i]])
{
used[dp[i]]=1;
res++;
}
printf("%d\n",res);
}

return 0;
}

下面转化为多重部分和问题求解。

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int A[105],C[105];
int n,m;
int dp[100005];
int main()
{
while(scanf("%d%d",&n,&m)!=EOF)
{
if(!n&&!m)
break;
memset(dp,-1,sizeof(dp));
for(int i=0;i<n;i++)    scanf("%d",&A[i]);
for(int i=0;i<n;i++)    scanf("%d",&C[i]);
dp[0]=0;
for(int i=0;i<n;i++)
for(int j=0;j<=m;j++)
if(dp[j]>=0)
dp[j]=C[i];
else if(j<A[i]||dp[j-A[i]]<0)
dp[j]=-1;
else
dp[j]=dp[j-A[i]]-1;
int res=0;
for(int i=1;i<=m;i++)
if(dp[i]>=0)
res++;
printf("%d\n",res);
}

return 0;
}