Suppose arrays A and B are both sorted in increasing order and both contain n elements. What is the time complexity to find the median of AUB, i.e., the set of elements in A or B? O O(n) O o(n log n) O O(n?) O O(log n)

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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)

1)If we consider Recurrences and Running Time, what is the running time T(n) for size of an array n? BINARY-SEARCH (A, lo, hi, x) { if (lo > hi) return FALSE mid = (lo + hi)/2 if x = A[mid]Assignment 1 return TRUE if (x < A[mid]) BINARY-SEARCH (A, lo, mid-1, x) if (x > A[mid]) BINARY-SEARCH (A, mid+1, hi, x) } 2)6. Based on T(n) that you found on previous question, solve recurrence with iteration method.

Suppose arrays A and B are both sorted in increasing order and both contain n elements. What is the time complexity to find the median of A U B, i.e., the set of elements in A or B?

Lets say we have an array of n items that we need to sort. Lets say that there is a sorting algorithm that has the property that in every step, no item moves more than log n places in the array in any step of the algorithm. Show that this algorithm runs in time at least Ω(n2 / log n) in the worst case.

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 the binary search algorithm 3. if value exists in alist, print "successful" otherwise print "unsuccessful" Question 10 options: O(2^n) O(n log n) O(log n) O(n^2) O(n) O(1)

We can sort n integers between 0 and 2n in O(n) time. True False Given a sorted array of n integers, we can find the median of them in O(1) time. True False If ƒ = 0(g), then g = 0(f). False True

What is the return value if B = {1, 3, 5}? Algorithm Ex5(A): Input: Arrays A and B each storing n ≥ 1 integers. Output: The number of elements in B equal to the sum of the prefix sums in A. c ← 0 for i ← 0 to n - 1 do s ← 0 for j ← 0 to i do s ← s + A[0] for k ← 1 to j do s ← s + A[k] if B[i] = s then c ← c + 1 return c

Algorthim of how to find the largest element missing in an unsorted array of n positive integers and the running time of the algorthim is in O(n). Example of this is that the n=6 array C= [5,90,8,6,26,9] The largest element missing in the array is 7

Question 2: Implement sequential search and binary search algorithms on your computer. Note down run time for each algorithm on arrays of size (1, 250, 500, 750, 1000, 1250, 1500, 5000). For both algorithms, store the values 0 throughn 1 in order in the array, and use a variety of random search values in the range 0 to n 1 on each size n. Graph the resulting times. When is sequential search faster than binary search for a sorted array? Solution: Execution Time for Input Size(N) Search Element Execution Time for Sequential Search(n) Binary Search(logn)

Given a Sorted Array of integers containing duplicates. Find the frequency of every unique element present in the array. Frequency is defined as the number of occurrence of any element in the array. Solve in Java

Given A[1...n] which is an increasingly sorted array of distinct positive integers, and t which is an integer; provide an O(n) algorithm deciding whether A contains two distinct elements x and y such that x + y = t.