Let A = [2, 2, 2, ......, 2] be an array where all of the elements are equal to one another. Determine whether Selection Sort or Insertion Sort sorts this array faster and carefully proving whether each algorithm is O(n), O(n log n), or O(n^2 ).

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

Consider sorting an array of length 10^12. Which algorithm would you recommend to implement to sort this array efficiently: selection sort, merge sort or quick sort? Why?

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'). ==

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; }

Can someone help me with this algorithm? No coding needed

Let A be an array, where each of the n elements is a randomly chosen digit between 0 and 9. For example, if n = 12, this array could be A = [3,5,1,0,5,7,9,2,2,8,8,6]. Determine whether Counting Sort or Merge Sort sorts this array faster.

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.

Let M[1 .. n] be an array, where each entry contains either a positive or a negative integer. Assume that M is already sorted in decreasing order. We want to decide whether there exists an entry M[r] such that M[r] is equal to r.