hdu 2191 悼念512汶川大地震遇难同胞——珍惜现在，感恩生活（多重背包+dp）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=2191

思路分析：该问题为多重背包问题；假设状态dp[i][v]表示在前i件物品中选择物品放入大小为v的背包的最大的重量，则可以第i件物品可以选择0~n[i]件，所以可以得出状态方程 dp[i][v] = Max{dp[i-1][v – k * c[i]] + k * w[i]}, 0 <= k <= n[i]；

代码如下：

import java.util.*;

public class Main {
    static int MAX_N = 100 + 10;
    static int[] c = new int[MAX_N];
    static int[] w = new int[MAX_N];
    static int[] n = new int[MAX_N];
    static int[][] dp = new int[MAX_N][MAX_N];
    
    public static int Max(int a, int b) {
        return a > b ? a : b;
    }
    public static void main(String[] args) {
        int case_times;
        Scanner in = new Scanner(System.in);
        
        case_times = in.nextInt();
        while (case_times-- != 0) {
            int V, M;
            
            V = in.nextInt();
            M = in.nextInt();
            for (int i = 1; i <= M; ++ i) {
                c[i] = in.nextInt();
                w[i] = in.nextInt();
                n[i] = in.nextInt();
            }
            for (int i = 0; i < MAX_N; ++ i)
                for (int j = 0; j < MAX_N; ++ j)
                    dp[i][j] = 0;
            for (int i = 1; i <= M; ++ i) {
                for (int v = 0; v <= V; ++ v) {
                    for (int k = 0; k <= n[i]; ++ k)
                        if (v - k * c[i] >= 0)
                            dp[i][v] = Max(dp[i][v], dp[i-1][v - k * c[i]] + k * w[i]);
                }
            }
            System.out.println(dp[M][V]);
        }
    }
}