Show QuickSort recursion depth O(log n) with high probability
Analyze the show quicksort recursion depth o(log n) with high probability.
Examples
Input:"test_input_1"
Output:"output_1"
Input:"test_input_2"
Output:"output_2"
Hints
Recall that quicksort's recursion depth is influenced by pivot selection; randomized pivot selection helps achieve average-case O(log n) depth.
Consider the probabilistic analysis of quicksort: the probability of worst-case O(n) depth decreases exponentially with each recursive call when pivots are chosen randomly.
To prove O(log n) depth with high probability, analyze the expected number of pivots that split the array into subarrays of size ≤ 3n/4, using Chernoff bounds or similar probabilistic tools.
Show QuickSort recursion depth O(log n) with high probability
Analyze the show quicksort recursion depth o(log n) with high probability.