多重背包java的两种写法

一、把物品拆开成为多个单物品，比如三个a拆成aaa

public static int pack(int[] weight, int[] value, int up) {
		int size = weight.length;
		int[] dp = new int[up+1];
		for (int i = 0; i <= up; i++) {
			dp[i] = 0;
		}
		for (int i = 0; i <size; i++) {
			for (int j = up; j >= weight[i]; j--) {
				dp[j] = Math.max(dp[j], dp[j-weight[i]]+value[i]);
			}
			Print(dp);
			System.out.println();
		}
		return dp[up];
	}
	public static int mulPack(int[] weight, int[] value, int[] nums, int up) {
		int sum = 0;
		for (int i = 0; i < nums.length; i++) {
			sum += nums[i];
		}
		int[] wg = new int[sum];
		int[] vl = new int[sum];
		int left = 0;
		for (int i = 0; i < weight.length; i++) {
			for (int j = 1; j <= nums[i]; j++) {
				wg[left] = weight[i];
				vl[left] = value[i];
				left++;
			}
		}
		return pack(wg, vl, up);
	}
	public static void main(String[] args) {
		int[] weight = {1,2,2};
        int[] value = {6,10,20};
        int[] nums = {10, 5, 2};
		int up = 8;
		mulPack(weight, value, nums, up);
		
	}
	public static void Print(int[] a) {
		for (int i = 0; i < a.length; i++) {
			System.out.print(a[i] + " ");
		}
	}

二、每次计算一个k，即在a物品数量限制下当前背包剩余的重量能最多放多少个a，加层循环

public static int getk(int up, int weight, int maxnum) {
		int start = 0;
		while (start<=maxnum && start*weight<=up) {
			start++;
		}
		return start-1;
	}
	public static int mulPack(int[] weight, int[] value, int[] nums, int up) {
		int size = weight.length;
		int[] dp = new int[up+1];
		for (int i = 0; i <= up; i++) {
			dp[i] = 0;
		}
		for (int i = 0; i <size; i++) {
			for (int j = up; j >= weight[i]; j--) {
				for(int k=0; k<=getk(j, weight[i], nums[i]); k++) {
					dp[j] = Math.max(dp[j], dp[j-k*weight[i]]+k*value[i]);
				}
			}
			Print(dp);
			System.out.println();
		}
		return dp[up];
	}
	public static void main(String[] args) {
		int[] weight = {5,4,7,2,6};
        int[] value = {12,3,10,3,6};
        int[] nums = {2,4,1,5,3};
		int up = 15;
		mulPack(weight, value, nums, up);
		
	}
	public static void Print(int[] a) {
		for (int i = 0; i < a.length; i++) {
			System.out.print(a[i] + " ");
		}
	}