Binary Tree Traversal
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Questions and Answers

What is a limitation of in-order traversal?

  • It preserves the original tree structure
  • It only works for balanced binary trees
  • It doesn't guarantee the nodes will be visited in sorted order (correct)
  • It cannot handle binary trees with more than two children per node

    • What is the space complexity of vertical order traversal?

  • O(1)
  • O(log n)
  • O(n) (correct)
  • O(n^2)

    • Which scenario might require additional techniques to handle during vertical order traversal?

  • Binary tree with unbalanced branches
  • Binary tree with only one child per node
  • Binary tree with a height less than two
  • Binary tree with multiple nodes at the same horizontal distance (correct)

    • What does boundary traversal of a binary tree involve?

    <p>Traversing only the nodes on the boundary of the tree</p> Signup and view all the answers

    Which nodes are included in the boundary traversal of a binary tree?

    <p>Both leaf and internal nodes</p> Signup and view all the answers

    What is the order in which nodes are visited in boundary traversal?

    <p>The order depends on the tree structure</p> Signup and view all the answers

    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.

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