POJ 1276 Cash Machine 多重背包--二进制优化

Description

Input

Output

Sample Input

735 3  4 125  6 5  3 350
633 4  500 30  6 100  1 5  0 1
735 0
0 3  10 100  10 50  10 10

Sample Output

735
630
0
0

Hint

Source

//600K	79MS
#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
int dp[100007];
int weight[10007],value[10007];
int main()
{
    int sum,n;
    while(scanf("%d%d",&sum,&n)!=EOF)
    {
        int a,b,num=0;
        memset(dp,0,sizeof(dp));
        for(int i=1;i<=n;i++)//进行二分优化
        {
            scanf("%d%d",&a,&b);
            for(int j=1;j<=a;j<<=1)
            {
                value[num]=weight[num]=j*b;
                num++;
                a-=j;
            }
            if(a>0)
            {
                value[num]=weight[num]=a*b;
                num++;
            }
        }
        for(int i=0;i<num;i++)
            for(int j=sum;j>=weight[i];j--)
                dp[j]=max(dp[j-weight[i]]+value[i],dp[j]);
         printf("%d\n",dp[sum]);
    }
    return 0;
}

//524K	63MS
#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
int dp[100007],num[17],weight[17];
int sum;
void ZeroOnePack(int cost)
{
    for(int i=sum;i>=cost;i--)
        dp[i]=max(dp[i],dp[i-cost]+cost);
}
void CompletePack(int cost)
{
    for(int i=cost;i<=sum;i++)
        dp[i]=max(dp[i],dp[i-cost]+cost);
}
void MultiplePack(int count,int cost)
{
    if(count*cost>sum)CompletePack(cost);
    else
    {
        int k=1;
        while(k<count)
        {
            ZeroOnePack(k*cost);
            count-=k;
            k<<=1;
        }
        ZeroOnePack(count*cost);
    }
}
int main()
{
    int n;
    while(scanf("%d%d",&sum,&n)!=EOF)
    {
        for(int i=1;i<=n;i++)
            scanf("%d%d",&num[i],&weight[i]);
        memset(dp,0,sizeof(dp));
        for(int i=1;i<=n;i++)
            MultiplePack(num[i],weight[i]);
        printf("%d\n",dp[sum]);
    }
}