Recall the quicksort procedure we saw in class, where we pick a random element of the input array as the pivot, recursively sort the elements less than and larger than the pivot, and concatenate the solutions We saw that the expected running time is O(n logn) (a) 2 Using a basic implementation (base case being a singleton), find the constant in the O0 notation for the algorithm above (You may do this by picking any array, repeatedly running the procedure above, and averaging the values of running time divided by n log n ) (b) 2 Now, consider the following procedure for k 1 2 3, first pick (2k 1 random in(lices, and choose their median as the pivot Now report the constant in the O notation (c) 2 Explain your observations intuitively Recall the quicksort procedure we saw in class, where we pick a random element of the input array as the pivot, recursively sort the elements less than and larger than the pivot, and concatenate the solutions We saw that the expected running time is O(n logn) (a) 2 Using a basic implementation (base case being a singleton), find the constant in the O0 notation for the algorithm above (You may do this by picking any array, repeatedly running the procedure above, and averaging the values of running time divided by n log n ) (b) 2 Now, consider the following procedure for k 1 2 3, first pick (2k 1 random in(lices, and choose their median as the pivot Now report the constant in the O notation (c) 2 Explain your observations intuitively

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Recall the quicksort procedure we saw in class, where we pick a random element of the input array as the pivot, recursively sort the elements less than and larger than the pivot, and concatenate the solutions  We saw that the expected running time is O(n logn)  (a) 2  Using a basic implementation (base case being a singleton), find the constant in the O0 notation for the algorithm above  (You may do this by picking any array, repeatedly running the procedure above, and averaging the values of running time divided by n log n ) (b)  2  Now, consider the following procedure  for k   1 2 3, first pick (2k   1 random in(lices, and choose their median as the pivot  Now report the constant in the O notation  (c)  2  Explain your observations intuitively  Recall the quicksort procedure we saw in class, where we pick a random element of the input array as the pivot, recursively sort the elements less than and larger than the pivot, and concatenate the solutions  We saw that the expected running time is O(n logn)  (a) 2  Using a basic implementation (base case being a singleton), find the constant in the O0 notation for the algorithm above  (You may do this by picking any array, repeatedly running the procedure above, and averaging the values of running time divided by n log n ) (b)  2  Now, consider the following procedure  for k   1 2 3, first pick (2k   1 random in(lices, and choose their median as the pivot  Now report the constant in the O notation  (c)  2  Explain your observations intuitively

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Recall the quicksort procedure we saw in class, where we pick a random element of the input array as the pivot, recursively sort the elements

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