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What is the time complexity of deleting an element from a binary search tree (BS

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Question: What is the time complexity of deleting an element from a binary search tree (BST) in the average case?

Options:

  1. O(n)
  2. O(log n)
  3. O(n log n)
  4. O(1)

Correct Answer: O(log n)

Solution: 

In the average case, deleting an element from a balanced binary search tree takes O(log n) time, as it requires finding the element and then restructuring the tree.

What is the time complexity of deleting an element from a binary search tree (BS

Practice Questions

Q1
What is the time complexity of deleting an element from a binary search tree (BST) in the average case?
  1. O(n)
  2. O(log n)
  3. O(n log n)
  4. O(1)

Questions & Step-by-Step Solutions

What is the time complexity of deleting an element from a binary search tree (BST) in the average case?
  • Step 1: Understand what a binary search tree (BST) is. A BST is a data structure where each node has a value, and the left child has a smaller value while the right child has a larger value.
  • Step 2: Know that to delete an element from a BST, you first need to find that element in the tree.
  • Step 3: Finding an element in a balanced BST takes O(log n) time on average because the tree is structured to minimize the number of comparisons needed.
  • Step 4: After finding the element, you need to restructure the tree to maintain the BST properties. This restructuring also takes O(log n) time on average.
  • Step 5: Combine the time taken to find the element and the time taken to restructure the tree. Since both steps take O(log n) time, the overall time complexity for deleting an element in the average case is O(log n).
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