給定一個不含重複元素的整數陣列。一個以此陣列構建的最大二叉樹定義如下：

二叉樹的根是陣列中的最大元素。
左子樹是通過陣列中最大值左邊部分構造出的最大二叉樹。
右子樹是通過陣列中最大值右邊部分構造出的最大二叉樹。
通過給定的陣列構建最大二叉樹，並且輸出這個樹的根節點。

Example 1:
輸入: [3,2,1,6,0,5]
輸出: 返回下面這棵樹的根節點：

  6
/   \
3     5
\    / 
 2  0   
   \
    1

注意:

給定的陣列的大小在 [1, 1000] 之間。

public class constructMaximumBinaryTree
 
 {

    @Test
    public void constructMaximumBinaryTreeTest() {
        int[] nums = new int[]{3,2,1,6,0,5};
        TreeNode treeNode = constructMaximumBinaryTree(nums);
        Assert.assertEquals(6 , treeNode.val);
        Assert.assertEquals(3, treeNode.left.val);
        Assert.assertEquals(5, treeNode.right.val);
        Assert.assertEquals(null
 
, treeNode.left.left);
        Assert.assertEquals(2, treeNode.left.right.val);
        Assert.assertEquals(null, treeNode.left.right.left);
        Assert.assertEquals(1, treeNode.left.right.right.val);
        Assert.assertEquals(0, treeNode.right.left.val);
        Assert.assertEquals(null, treeNode.right.right);
    }

    public
 
 class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;
        TreeNode(int x) { val = x; }
    }

    public TreeNode constructMaximumBinaryTree(int[] nums) {
        if (nums == null || nums.length == 0) return null;
        int maxInt = Arrays.stream(nums).max().getAsInt();
        TreeNode root = new TreeNode(maxInt);
        int[] left = getLeftArray(nums, getIndexInArray(nums, maxInt));
        int[] rigt = getRightArray(nums, getIndexInArray(nums, maxInt));
        root.left = constructMaximumBinaryTree(left);
        root.right = constructMaximumBinaryTree(rigt);
        return root;
    }

    @Test
    public void getLeftArrayTest() {
        int[] nums = new int[]{3,2,1,6,0,5};
        Assert.assertArrayEquals(new int[]{3,2,1}, getLeftArray(nums, 3));
    }

    private int[] getLeftArray(int[] nums, int index) {
        if (index == -1) {
            return null;
        }
        int[] left = new int[index];
        Arrays.setAll(left, i -> nums[i]);
        return left;
    }

    @Test
    public void getRightArrayTest() {
        int[] nums = new int[]{3,2,1,6,0,5};
        Assert.assertArrayEquals(new int[]{0,5}, getRightArray(nums, 3));
    }

    private int[] getRightArray(int[] nums, int index) {
        if (index == -1) {
            return null;
        }
        int[] right = new int[nums.length - index - 1];
        Arrays.setAll(right, i -> nums[index + i + 1]);
        return right;
    }

    @Test
    public void getIndexInArrayTest() {
        int[] nums = new int[]{3,2,1,6,0,5};
        Assert.assertEquals(3, getIndexInArray(nums, 6));
    }

    private int getIndexInArray(int[] nums, int maxInt) {
        for (int i = 0; i < nums.length; i++) {
            if (maxInt == nums[i]) {
                return i;
            }
        }
        return -1;
    }

}