Graph the equations T(n) = log2 n and T(n) = n= loge n. Which gives the better performance, binary search on a sorted list, or sequential search on a list ordered by frequency where the frequency conforms to a Zipf distribution? Characterize the difference in running times.

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QuickSort is run for an array A in a manner that PARTITION consistently produces a 5:1 split for the (sub)arrays to be sorted (recursively) next. In this case, the recurrence equation for QuickSort's runtime is what? Group of answer choices T(n) <= T(5n/10) + T(n/10) + Theta(n) T(n) <= T(5/n) + T(1/n) + Theta(n) T(n) <= T(5n/6) + T(n/6) + Theta(n) T(n) <- T(6n/5) + T(6n) + Theta(n)

A given implementation of bubble-sort takes on average 1 second to sort an array of 1000 elements. How many seconds do you expect sorting an array of 8000 elements will take? A given implementation of quicksort takes on average 0.1 seconds to sort an array of 1000 elements. How many seconds do you expect sorting an array of 8000 elements will take?

A sequential search of a sorted list can halt when the target is less than a given element in the list. Define a modified version of this algorithm and state the computational complexity, using big-O notation, of its best-, worst-, and average- case performances.

For each question, an algorithm will be described that operates on N elements, and your answer should include: (a) a big-O expression that describes the total number of operations in the worst case (for ex- ample, O(N³)) (b) a description of how to achieve the same effect as the algorithm described, but achieved with a better big-O time bound (for example, "use mergesort instead of insertion sort") (c) the big-O time bound for your improved approach. Your improved algorithm does not need to be provably the best possible, but it should have a different and better big-O bound. (It may not be as simple as substituting one named algorithm for another; consider what is redundant about the work done by the existing algorithm.) You don't need to use pseudocode to describe your algorithms - the style used in the problem descriptions is also sufficient for your solutions. You can use pseudocode if you like. Do not write real code. If you wish to use an algorithm described in class, you can name…

By choosing an acceptable pivot and an appropriate cut-off value for the sort, a quicksort's performance may be enhanced.

Consider the following problem:L is a sorted list containing n signed integers (n being big enough), for example [-5, -2, -1, 0, 1, 2, 4] (here, nhas a value of 7). If L is known to contain the integer 0, how can you find the index of 0 ?

Performing sequential search for an item that is not present in an unsorted list has Best-Case running time equals to:           1     log(n)     n     n2

By choosing an acceptable pivot and a reasonable cut-off value for the sort, one may enhance the performance of a quicksort.