Given a binary tree. Given a binary tree, return the values of its boundary in anti-clockwise direction starting from the root.

Boundary includes left boundary, leaves, and right boundary in order without duplicate nodes.

**Left boundary** is defined as the path from the root to the **left-most** node.

**Right boundary** is defined as the path from the root to the **right-most** node.

If the root doesn’t have left subtree or right subtree, then the root itself is left boundary or right boundary.

Note this definition only applies to the input binary tree, and not applies to any subtrees.

The **left-most** node is defined as a leaf node you could reach when you always firstly travel to the left subtree if exists. If not, travel to the right subtree. Repeat until you reach a leaf node.

The **right-most** node is also defined by the same way with left and right exchanged.

Return an array of integers denoting the boundary values of tree in anti-clockwise order.

**For Example**

```
Input 1:
_____1_____
/ \
2 3
/ \ /
4 5 6
/ \ / \
7 8 9 10
Output 1:
[1, 2, 4, 7, 8, 9, 10, 6, 3]
Explanation 1:
The left boundary are node 1,2,4. (4 is the left-most node according to definition)
The leaves are node 4,7,8,9,10.
The right boundary are node 1,3,6,10. (10 is the right-most node).
So order them in anti-clockwise without duplicate nodes we have [1,2,4,7,8,9,10,6,3].
Input 2:
1
/ \
2 3
/ \ / \
4 5 6 7
Output 2:
[1, 2, 4, 5, 6, 7, 3]
```

NOTE:You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.

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