algorithm

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.

Question A: Mapping. The two-sum problem is a popular algorithm problem. Given an array of integers and an integer target, return indices of the two numbers such that they add up to the target. You may assume that each input would have exactly one solution, and you may not use the same element twice. For example, suppose we have an array arr = [1,10,100]. If the target is 11, you should return [0,1] because arr[0] + arr[1] = 1+ 10 = 11. If the target is 101, you should return [0,2] because arr[0] + arr[2] = 1+ 100 = 101. Complete this problem in O(n). Hint: using a hash table.

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);

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

Given is a list of K distinct coin denominations (V1,...,Vk) and the total sum S>0. Find the minimum number of coins whose sum is equal to S (we can use as many coins of one type as we want), or report that it’s not possible to select coins in such a way that they sum up to S. Justify your explanation!

Please help with question: Determine the running time of the following algorithms. Write summations to represent loops and simplify. Show all work. If bounding is used, the upper and lower bounds must only differ by a constant. Note: This is not the line-by-line analysis method. Loops are inclusive.

Calculating the average of a list of integers by exploiting parallelism:Suppose we have an array of integers: 1, 10, 9, 100, 23, 4, 11, 12, 3, and 1. The size of this array is 10.Now if we want to calculate the average, we can simply do:average = sum of elements/ total elements.Now, if we have a large number of elements, then it will take a lot of time to calculate the average. Wecan utilize parallelism by dividing the task of finding the sum among different threads. Suppose a threadt1 finds the sum of first 4 elements:sum1=わ1+たす10+たす9+たす100=わ 120count=4And another thread t2 calculates the sums of remaining 6 elements:sum2=わ23+たす4+たす11+たす12+たす3=わ53count=6Then average calculated as:Total Sum = sum1+sum2= 120+53= 173Total Count= count1 + count2= 4+6=10Average= Total Sum/Total Count= 173/10= 17.3Assume that we want to compute the average of a list of numbers. The numbers are not in a single file,but they are placed in several files. Now write a program that is passed the names of files containingintegers...