Let A[1..n] be an array of n integers that each is larger than 1. give an O(n lg n)-time algorithm that decides if there are two integers x,y in A such that x=y2 (multiplication takes O(1) time)

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

write a computer program that produces the desired output from the given input. Input: Elements in a finite set SOutput: Elements in ℘(S)Algorithm: Use recursion.

Let A be an array of n integers: (a) Write a pseudo code for a divide-and-conquer algorithm that computes the MAX and MIN values in array A . (b) Write the recurrence for this algorithm. (c) Solve the recurrence using the substitution method.

The algorithm below searches for the maximum in an input array A. Assume A is a random sequence containing n distinguishable real numbers, what is the probability for line #4 to be executed exactly once? (The phrase "random sequence" here means the n numbers can appear in any order with equal chance.) mymax(A, n) { 1: max = A[1]; 2: for i = 2:n 3: if A[i]> max 4: max = A[i); 5: end; 6: end; 7: return max; }

For any input array of n 3-digit numbers, prove that Radix Sort is guaranteed to correctly sort these n numbers, with the algorithm running in O(n) time.

Consider the window size is 10, bandwidth is 1500 bps, transmission delay is 2 ms and propagation delay is 50 ms. What is the throughput using Go Back N protocol? a) 294.11 b) 140.23 c) 96 d) 154.21

Let M(n) be the minimum number of comparisons needed to sort an array A with exactly n ele- ments. For example, M(1) = 0, M(2) = 1, and M(4) = 4. If n is an even number, clearly explain why M(n) = 2M(n/2) + n/2.

Write pseudocode for a divide-and-conquer algorithm for finding the position of the largest element in an array of n numbers.