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Questions and Answers
What is a limitation of in-order traversal?
What is a limitation of in-order traversal?
What is the space complexity of vertical order traversal?
What is the space complexity of vertical order traversal?
Which scenario might require additional techniques to handle during vertical order traversal?
Which scenario might require additional techniques to handle during vertical order traversal?
What does boundary traversal of a binary tree involve?
What does boundary traversal of a binary tree involve?
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Which nodes are included in the boundary traversal of a binary tree?
Which nodes are included in the boundary traversal of a binary tree?
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What is the order in which nodes are visited in boundary traversal?
What is the order in which nodes are visited in boundary traversal?
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Study Notes
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.
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Description
Test your knowledge of binary tree traversal techniques and their time complexities. Check your understanding of pre-order, in-order, post-order, and level-order traversals.