Discussion
Suppose that the splits at every level of quicksort are in the proportion \((1 - \alpha)\) to \(\alpha\), where \(0 \lt \alpha \le \frac{1}{2}\) is a constant. The minimum depth of a leaf in the recursion tree is approximately given by
Answer: C
The minimum depth is \(-\lg n / \lg \alpha\).
The shallowest path always follows the smaller part \(\alpha\) of each split. After \(k\) levels the subproblem has size \(\alpha^{k} n\) and the leaf is reached when \(\alpha^{k} n = 1\), giving \[ k = -\frac{\lg n}{\lg \alpha}. \]
The expression with \(\lg(1 - \alpha)\) is the maximum depth, which follows the larger part, and the expressions with \(\lg n\) in the denominator are not depths.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development