（背包三）多重背包

public class BeiBaoMulti {

    public static void main(String[] args) {

         int[] value = {10,40,30,50};
         int[] weight = {5,4,6,3};
         int[] num = {2,3,2,2};
         int capacity =12;

        int result = packageMulti(value, weight,num, capacity);
        System.out.println(result);

    }
    /**
     * @param value      物体价值数组
     * @param weight     对应物体价值的重量数组
     * @param num        对应物体的每个物体的个数
     * @param capacity   背包的容量
     * @return           可以背的最大价值
     */
    public static int packageMulti(int[] value, int[] weight, int[] num,int capacity) {
        int length = value.length;
        int[][] dp = new int[length + 1][capacity + 1];
        for (int column = 0; column <= capacity; column++) {
            dp[0][column] = 0;
        }
        for (int row = 0; row <= length; row++) {
            dp[row][0] = 0;
        }
        int maxVal = 0;
        for (int row = 1; row <= length; row++) {
            for (int column = 0; column <= capacity; column++) {
                for (int k = 0; k<=num[row-1]&&k * weight[row-1] <= column; k++) {
                    dp[row][column] = Math.max(dp[row][column], dp[row - 1][column - k * weight[row-1]] + k * value[row-1]);
                }
            }
        }
        return dp[length][capacity];
    }
}

//结果：
140