Binary Tree Traversal

Boundary Traversal

• Boundary traversal of a binary tree involves traversing only the nodes on the boundary of the tree.
• It includes both leaf and internal nodes.
• Nodes are visited in a specific order: root node first, then nodes at every level, from left to right.

Time and Space Complexity

• The time complexity of boundary traversal in a binary tree with n nodes is O(n).
• The space complexity of boundary traversal is O(n).

Depth-First Traversal

• Boundary traversal typically uses depth-first traversal.
• It starts from the root node and explores as far as possible along each branch before backtracking.

Traversal Techniques

• Pre-order traversal visits nodes in a top-down manner (root node first).
• In-order traversal visits nodes in a left-root-right manner.
• Post-order traversal visits nodes in a left-right-root manner.
• Level-order traversal visits nodes level by level, from left to right.

Tree Views

• Pre-order view is also known as the depth-first traversal.
• Level-order view is also known as the breadth-first traversal.
• In-order view is used in expression tree evaluation.
• Pre-order view is used to create a copy of the tree.

Important Notes

• Boundary traversal does not guarantee nodes will be visited in sorted order.
• Boundary traversal may require additional techniques to handle binary trees with multiple nodes at the same horizontal distance.
• Vertical order traversal has a space complexity of O(n) and may require additional techniques to handle binary trees with multiple nodes at the same horizontal distance.