Question

Given a binary tree, return the values of its boundary in anti-clockwise

direction starting from root. Boundary includes left boundary, leaves, and
right boundary in order without duplicate nodes. (The values of the nodes may still be duplicates.)
Left boundary is defined as the path from root to the left-most node. Right
boundary is defined as the path from 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.

Answer 1

The values of the binary tree's boundary in anti-clockwise direction, starting from the root, are returned as follows: left boundary, leaves, and right boundary without duplicate nodes.

Step-by-step explanation:

In the context of a binary tree, the left boundary is the path from the root to the leftmost node, and the right boundary is the path from the root to the rightmost node. The leftmost node is the leaf node that can be reached by always traveling to the left subtree if it exists; otherwise, one travels to the right subtree until a leaf node is reached. The same definition applies to the rightmost node with left and right exchanged. The leaves of the tree are simply the leaf nodes.

To implement this, one can traverse the tree in three steps: left boundary, leaves, and right boundary. In each step, it's crucial to avoid duplicate nodes. The left boundary is traversed top-down, the leaves are traversed left to right, and the right boundary is traversed bottom-up. By combining these three traversals, one can construct the anti-clockwise boundary of the binary tree.

The algorithm involves careful consideration of the left and right boundaries and the leaves to ensure that nodes are not duplicated. The goal is to produce a sequence of nodes that represents the boundary in the required order. This approach adheres to the given definition of the left and right boundaries and efficiently returns the desired result.

Answer 2

The problem asks for the values of the boundary of a binary tree in anti-clockwise direction starting from the root. The left boundary, leaves, and right boundary are included, without duplicate nodes. The solution involves traversing the tree in a specific order to collect the boundary values.

Step-by-step explanation:

Binary Tree Boundary Traversal

The problem asks for the values of the boundary of a binary tree in anti-clockwise direction starting from the root.

The boundary includes the left boundary, leaves, and right boundary, without duplicate nodes.

The left boundary is the path from the root to the left-most node, and the right boundary is the path from the root to the right-most node.

If the root does not have a left subtree or a right subtree, then the root itself is the left boundary or the right boundary.

Traverse the left boundary in a top-down manner:

Check if the root has a left child. If it does, add the root's value to the result.

If the root does not have a left child, but has a right child, set the root to the right child and repeat step 1.

Traverse the leaves in a bottom-up manner:

Recursively traverse the left subtree, adding the leaf nodes to the result.

Recursively traverse the right subtree, adding the leaf nodes to the result.

Traverse the right boundary in a bottom-up manner:

Check if the root has a right child. If it does, add the root's value to the result.

If the root does not have a right child, but has a left child, set the root to the left child and repeat step 1.

Finally, return the result.