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Decode the Coding Interview in Rust: Real-World Examples

Boundary of Binary Tree

Explore how to identify and return the boundary of a binary tree by decomposing the problem into handling the root, left boundary, leaves, and right boundary separately. Understand recursive approaches to traverse these parts efficiently and learn the time and space complexities involved.

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Description

Let’s start by defining what a boundary of a binary tree is. We can define it as:

The boundary of a binary tree is the concatenation of the root, the left boundary, the leaves ordered from left-to-right, and the reverse order of the right boundary. Take a look at the example given below:

Take a look at the example given below:

As mentioned above, the boundary can be divided into four categories; the following explains these categories:

  • Root node

  • Left boundary

    • The root node’s left child is in the left boundary. If the root does not have a left child, the left boundary is empty.
    • If a node in the left boundary has a left child, the left child is in the left boundary.
    • If a node in the left boundary has a right child but no left child, the right child is in the left boundary.
    • The leftmost leaf is not in the left boundary.

  • Right boundary

    • The right boundary is similar to the left boundary, except it is on the right side of the root's right subtree.
    • The leaf is not part of the right boundary.
    • The right boundary is empty if the root does not have a right child.

  • Leaves

    • The leaves are nodes that do not have any children. For this problem, we can assume that the root is not a leaf.

Considering the definition of the boundary ...