HDU-2602 Bone Collector

最新推荐文章于 2022-04-03 11:21:11 发布

原创最新推荐文章于 2022-04-03 11:21:11 发布 · 127 阅读

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#0-1背包

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本文介绍了一种经典的背包问题场景，并提供了两种不同维度的动态规划解决方案。通过具体实例输入输出，展示了如何计算骨骸收集者能获得的最大价值，帮助读者深入理解背包问题及其解决方法。

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背包问题：https://www.cnblogs.com/A-S-KirigiriKyoko/p/6036368.html

Many years ago , in Teddy’s hometown there was a man who was called “Bone Collector”. This man like to collect varies of bones , such as dog’s , cow’s , also he went to the grave …
The bone collector had a big bag with a volume of V ,and along his trip of collecting there are a lot of bones , obviously , different bone has different value and different volume, now given the each bone’s value along his trip , can you calculate out the maximum of the total value the bone collector can get ?

Input

The first line contain a integer T , the number of cases.
Followed by T cases , each case three lines , the first line contain two integer N , V, (N <= 1000 , V <= 1000 )representing the number of bones and the volume of his bag. And the second line contain N integers representing the value of each bone. The third line contain N integers representing the volume of each bone.

Output

One integer per line representing the maximum of the total value (this number will be less than 231).

Sample Input
1
5 10
1 2 3 4 5
5 4 3 2 1

Sample Output
14

注意：对于背包问题，可以使用一维数组和二维数组，二维数组更好理解。

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
int v[1010],w[1010];
int dp[1010][1010];
int main()
{
    int c;
    scanf("%d",&c);
    while(c--)
    {
        memset(dp,0,sizeof(dp));
        memset(v,0,sizeof(v));
        memset(w,0,sizeof(w));
        int n,m;
        scanf("%d%d",&n,&m);
        for(int i=1;i<=n;i++)
        scanf("%d",&v[i]);
        for(int i=1;i<=n;i++)
        scanf("%d",&w[i]);
        for(int i=1;i<=n;i++)
        {
            for(int j=0;j<=m;j++)//**********
                dp[i][j]=dp[i-1][j];
            for(int k=w[i];k<=m;k++)
                dp[i][k]=max(dp[i-1][k],dp[i-1][k-w[i]]+v[i]);
        }
        printf("%d\n",dp[n][m]);
    }
    return 0;
}

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
int v[1010],w[1010];
int dp[1010];
int main()
{
    int c;
    scanf("%d",&c);
    while(c--)
    {
        memset(dp,0,sizeof(dp));
        memset(v,0,sizeof(v));
        memset(w,0,sizeof(w));
        int n,m;
        scanf("%d%d",&n,&m);
        for(int i=1;i<=n;i++)
        scanf("%d",&v[i]);
        for(int i=1;i<=n;i++)
        scanf("%d",&w[i]);
        for(int i=1;i<=n;i++)
        {
            for(int j=m;j>=w[i];j--)
            {
                dp[j]=max(dp[j],dp[j-w[i]]+v[i]);
            }
        }
        printf("%d\n",dp[m]);
    }
    return 0;
}