Given a string S[1, . . . , n] and a dictionary of strings S, return true if S[1, . . . , n] can be segmented into a space-separated sequence of one or more dictionary words. Note that the same word in the dictionary may be reused multiple times in the segmentation. Precisely define the subproblem. Provide the recurrence equation. Describe the algorithm in pseudocode to compute the optimal value. Describe the algorithm in pseudocode to print out an optimal solution.

I have to use the Binary Search Algorithm to determine whether the number 17 appears in the sequence s : 3, 6, 7, 8, 15, 17, 19, 23, 24. Can someone give a step by step description of what the algorithm does in this case.

We talked about the trade-off between using sequential search on an unsorted list as opposed to sorting the list and then using binary search. If the list size is n = 9,000, about how many worst-case searches must be done before the second alternative is better in terms of number of comparisons? (Hint: Let p represent the number of searches done.) Use selection search to sort the binary search list.

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…

Find the running time for each of the following algorithms. Show work by finding a table of values for each while loop, writing the summations, then solving. Be sure to show work on both the upper bound and lower bound, justify the split, and check that the bounds differ by only a constant factor. Use asymptotic notation to write the answer. b) Func3(n) 1 2 3 4 5 6 7 8 9 10 11 S← 0; i+n; while (i 8) do s+ s + i - j; j← lj/⁹]; end i + 4 x i; end return (s);

Use the Transform-and-Conquer algorithm design technique with Instance Simplification variant to design an O(nlogn) algorithm for the problem below. Show the pseudocode. Given a set S of n integers and another integer x, determine whether or not there exist two elements in S whose sum is exactly x.

1. Let S be a set of n arbitrary but distinct numbers. (a) Give a deterministic algorithm to output the largest n³/4 of the numbers in S in sorted order. Your algorithm must use O(n) comparisons. (b) Show that any deterministic comparison-based algorithm that correctly outputs the median on inputs of n distinct elements must use at least n 1 comparisons. To be completely precise, the median is defined to be the [n/2]th smallest element.

Find the running time for each of the following algorithms. Show work by finding a table of values for each while loop, writing the summations, then solving. Be sure to show work on both the upper bound and lower bound, justify the split, and check that the bounds differ by only a constant factor. Use asymptotic notation to write the answer. a) Func2(n) 1 2 3 4 5 6 7 S ← 0; j←7n²; while (j > 8) do s+ s + i- j; je lj/9]; end return (s);

The standard Mergesort (the implementation in the textbook) is an in-place sorting. True False The erpected running time of the randomized quicksort algorithm (that chooses the pivot randomly) is O(n log n) for all inputs. True False If we solve T(n) = T(}n) + O(n), we obtain T(n) = 0(n log n). False True

Consider the following algorithm that uses a sorted list of n elements (alist). What is the worst case runtime of this algorithm? for each element in alist    1. ask the user for an input, call it value    2. search value in alist using binary search    3. if value exists in alist, print "successful"       otherwise print "unsuccessful"      Question options: a. O(log n) b. O(n) c. O(n log n) d. O(2^n) e. O(n^2) f. O(1)