Let A [1...n] be an array of distinct numbers and assume that n is divisible by 3. Give an O(n)-time algorithm that outputs the n/3 largest numbers in A; that is, the numbers that will appear at indices/positions 2n/3+1, …, n of A if A is sorted in increasing order. (Hint. Use the algorithm Select ()

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.

Let A[1, ., n] be a sorted array of distinct integers. Write an efficient algorithm with proper pseudocode for finding whether an element exists such that: A[i] i, for 1 <= i <= n. (i.e., an element whose index and value are both equal to 'i'). ==

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; }

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)

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.