What is the worst-case time complexity of binary search?

Practice Questions

Q1
What is the worst-case time complexity of binary search?
  1. O(n)
  2. O(log n)
  3. O(n log n)
  4. O(1)

Questions & Step-by-Step Solutions

What is the worst-case time complexity of binary search?
  • Step 1: Understand what binary search is. It is a method to find an item in a sorted list by repeatedly dividing the search interval in half.
  • Step 2: Know that binary search starts with the entire list and checks the middle item.
  • Step 3: If the middle item is the target, the search is done. If not, it decides whether to search the left half or the right half of the list.
  • Step 4: Each time you check the middle item, you reduce the number of items to search by half.
  • Step 5: The worst-case scenario occurs when you keep halving the list until you have only one item left to check.
  • Step 6: The number of times you can halve a list of size n is log base 2 of n, which is written as log(n).
  • Step 7: Therefore, the worst-case time complexity of binary search is O(log n).
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