HDU 2639 Bone Collector II

最新推荐文章于 2021-01-18 14:47:36 发布

sunnykema

最新推荐文章于 2021-01-18 14:47:36 发布

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本文介绍了一种求解第K大的01背包问题的方法，通过动态规划记录不同体积限制下的最大价值，并进一步找出第K大的价值。示例输入输出展示了算法的有效性。

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Bone Collector II

Time Limit: 5000/2000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)

Problem Description

The title of this problem is familiar,isn't it?yeah,if you had took part in the "Rookie Cup" competition,you must have seem this title.If you haven't seen it before,it doesn't matter,I will give you a link:

Here is the link: http://acm.hdu.edu.cn/showproblem.php?pid=2602

Today we are not desiring the maximum value of bones,but the K-th maximum value of the bones.NOTICE that,we considerate two ways that get the same value of bones are the same.That means,it will be a strictly decreasing sequence from the 1st maximum , 2nd maximum .. to the K-th maximum.

If the total number of different values is less than K,just ouput 0.

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, K(N <= 100 , V <= 1000 , K <= 30)representing the number of bones and the volume of his bag and the K we need. 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 K-th maximum of the total value (this number will be less than 2 ³¹).

Sample Input

Sample Output

求第K大的01背包问题。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <set>
#include <queue>

using namespace std;
#define maxn 105
#define Max_n 1005
#define inf 0x7ffffff
int v[maxn],w[maxn];
int dp[Max_n][35];
int n,t,m,k;
int main()
{
    scanf("%d",&t);
    while(t--){
        scanf("%d%d%d",&n,&m,&k);
        for(int i = 1; i <= n; i++){
            scanf("%d",&v[i]);
        }
        for(int i = 1; i <= n; i++){
            scanf("%d",&w[i]);
        }
        int arr[35],brr[35];
        memset(dp,0,sizeof(dp));
        int j;
        for(int i = 1; i <= n; i++){
            for(j = m; j >= w[i];j--){
                memset(arr, -1, sizeof(arr));
                memset(brr, -1, sizeof(brr));
                for(int t = 1; t <= k; ++t){
                    arr[t] = dp[j][t];
                    brr[t] = dp[j-w[i]][t]+v[i];
                }
                int x = 1, y = 1, z = 1;
                while(z <= k){
                    if(arr[x] == -1 && brr[y] == -1){
                        break;
                    }
                    if(arr[x] > brr[y]){
                        dp[j][z] = arr[x++];
                    }
                    else{
                        dp[j][z] = brr[y++];
                    }
                    if(dp[j][z] != dp[j][z-1]){
                        z++;
                    }
                }
                while(z <= k){
                    dp[j][z++] = 0;
                }


            }
//                for(int t = 1; t <= k; t++){
//                cout <<dp[m][t] << " ";
//            }
//                cout << endl;
        }

        printf("%d\n",dp[m][k]);
    }
    return 0;
}