Merge pull request #966 from Frogrey/master

添加 背包问题理论基础多重背包 Java版本

problems/背包问题理论基础多重背包.md

@@ -147,6 +147,51 @@ int main() {
 
 Java：
 
+```Java
+public void testMultiPack1(){
+    // 版本一：改变物品数量为01背包格式
+    List<Integer> weight = new ArrayList<>(Arrays.asList(1, 3, 4));
+    List<Integer> value = new ArrayList<>(Arrays.asList(15, 20, 30));
+    List<Integer> nums = new ArrayList<>(Arrays.asList(2, 3, 2));
+    int bagWeight = 10;
+
+    for (int i = 0; i < nums.size(); i++) {
+        while (nums.get(i) > 1) { // 把物品展开为i
+            weight.add(weight.get(i));
+            value.add(value.get(i));
+            nums.set(i, nums.get(i) - 1);
+        }
+    }
+
+    int[] dp = new int[bagWeight + 1];
+    for(int i = 0; i < weight.size(); i++) { // 遍历物品
+        for(int j = bagWeight; j >= weight.get(i); j--) { // 遍历背包容量
+            dp[j] = Math.max(dp[j], dp[j - weight.get(i)] + value.get(i));
+        }
+        System.out.println(Arrays.toString(dp));
+    }
+}
+
+public void testMultiPack2(){
+    // 版本二：改变遍历个数
+    int[] weight = new int[] {1, 3, 4};
+    int[] value = new int[] {15, 20, 30};
+    int[] nums = new int[] {2, 3, 2};
+    int bagWeight = 10;
+
+    int[] dp = new int[bagWeight + 1];
+    for(int i = 0; i < weight.length; i++) { // 遍历物品
+        for(int j = bagWeight; j >= weight[i]; j--) { // 遍历背包容量
+            // 以上为01背包，然后加一个遍历个数
+            for (int k = 1; k <= nums[i] && (j - k * weight[i]) >= 0; k++) { // 遍历个数
+                dp[j] = Math.max(dp[j], dp[j - k * weight[i]] + k * value[i]);
+            }
+            System.out.println(Arrays.toString(dp));
+        }
+    }
+}
+```
+
 Python：
 
 ```python