[codeforces366C]Dima and Salad

最新推荐文章于 2020-04-26 01:11:06 发布

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背包型动态规划

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在一场关于制作水果沙拉的烹饪难题中，Inna必须从具有特定口味和热量的水果中选择，以达到预设的口味与热量比。本篇探讨如何运用01背包问题的算法解决这一挑战，确保情侣的幸福。

time limit per test : 1 second
memory limit per test : 256 megabytes

Dima, Inna and Seryozha have gathered in a room. That’s right, someone’s got to go. To cheer Seryozha up and inspire him to have a walk, Inna decided to cook something.

Dima and Seryozha have n fruits in the fridge. Each fruit has two parameters: the taste and the number of calories. Inna decided to make a fruit salad, so she wants to take some fruits from the fridge for it. Inna follows a certain principle as she chooses the fruits: the total taste to the total calories ratio of the chosen fruits must equal k. In other words, 在这里插入图片描述 , where aj is the taste of the j-th chosen fruit and bj is its calories.

Inna hasn’t chosen the fruits yet, she is thinking: what is the maximum taste of the chosen fruits if she strictly follows her principle? Help Inna solve this culinary problem — now the happiness of a young couple is in your hands!

Inna loves Dima very much so she wants to make the salad from at least one fruit.

Input

The first line of the input contains two integers $n, k (1 \leq n \leq 100, 1 \leq k \leq 10)$ . The second line of the input contains n integers $a_1, a_2, ..., a_n (1 ≤ a_i ≤ 100)$ — the fruits’ tastes. The third line of the input contains n integers $b_1, b_2, ..., b_n (1 ≤ b_i ≤ 100)$ — the fruits’ calories. Fruit number i has taste ai and calories $b_i$ .

Output

If there is no way Inna can choose the fruits for the salad, print in the single line number $- 1$ . Otherwise, print a single integer — the maximum possible sum of the taste values of the chosen fruits.

Input

3 2
10 8 1
2 7 1

Output

Input

5 3
4 4 4 4 4
2 2 2 2 2

Output

-1

Note

In the first test sample we can get the total taste of the fruits equal to 18 if we choose fruit number 1 and fruit number 2, then the total calories will equal 9. The condition fulfills, that’s exactly what Inna wants.

In the second test sample we cannot choose the fruits so as to follow Inna’s principle.

题意：
给 $n$ 个元素，第 $j$ 个元素有两个性质 $a_j$ 和 $b_j$ ，从中选出 $m$ 个元素，使得在这里插入图片描述若不存在方案符合，则输出-1，否则输出最大的sigma( $a_i$ )。

题解：
将 $b_j$ 设为 $a_j-k*b_j$
然后就是裸的01背包问题了
物品大小可能为负数，要用到map

#include<bits/stdc++.h>
#define LiangJiaJun main
#define POS(a,b) (a*10001+b)
using namespace std;
int n,k;
int a[104],b[104];
map<int,int>mert,val;
int w33ha(){
    map<int,int>::iterator it;
    mert.clear();
    val.clear();
    for(int i=1;i<=n;i++)scanf("%d",&a[i]);
    for(int i=1;i<=n;i++){
        scanf("%d",&b[i]);
        b[i]=a[i]-k*b[i];
    }
    val[0]=0;
    for(int i=1;i<=n;i++){
        mert=val;
        for(it=mert.begin();it!=mert.end();it++){
            val[(it->first)+b[i]]=max(val[(it->first)+b[i]],(it->second)+a[i]);
        }
    }
    if(val[0]==0)puts("-1");
    else printf("%d\n",val[0]);
    return 0;
}
int LiangJiaJun(){
    while(scanf("%d%d",&n,&k)!=EOF)w33ha();
    return 0;
}