Please answer all parts of the question

(a) Consider the following algorithm: Input: n (a non-negative integer), A[0], A[1], A[2], ellipsis, A[n] (a array of an integers). for I = 0 to n for j = I + 1 to n if (A[i] + A[j] = k) return true return false (i) What does the algorithm compute? (ii) Express the worst-case running time of the algorithm using the Big-Oh notation. Give details of your working. (iii) If it takes 10 seconds to run the algorithm on an array of 10000 elements, how long will it take to run the algorithm on an array with 40000 elements? (b) Prove or disprove each of the following statements. (i) log n! = O(nlog(n)) (ii) If f(n) is O(g(n)), then g(n) is O(f(n)) (c) (i) A pointer start points to the first clement of a singly-linked list L.Write an algorithm that inserts a new node (with data field val) at thebeginning of the linked list L and returns start. What is the worst-caserunning time of your algorithm? (ii) A priority queue is implemented using an array. Items stored in thearray are ordered by the values of their keys in non-decreasing order.Write an algorithm to insert a new item with a specified key into thearray