Suppose we know that an algorithm has 5 classes of complexity for a problem of size n. The complexities T1(n).. Ts(n) are given below. Regarding probabilities, suppose that p, is twice as likely as p2, p2 is twice as likely as p3, , p3 is twice as likely as p4 and p4 is twice as likely as p5. #2 T; for all instances: T(n) = n, T2(n) = 2n, T3(n) =3n4, T4(n) = 4n and T5(n) = 5n (a) Find all five probabilities p1, P2, P3, P4 , Ps. [Hint: the sum of all probabilities equal 1.0] (b) Find the A(n) for the algorithm.

no handwritten Alice and Bob are playing a match to see who is the first to win n games, for some fixed n > 0. Suppose Alice and Bob are equally competent, that is, each of them wins a game with probability 1/2. Further, suppose that they have already played i + j games, of which Alice won i and Bob won j. Give an efficient algorithm to compute the probability that Alice will go on to win the match. For example, if i = n − 1 and j = n − 3, then the probability that Alice will win the match is 7/8, since she must win any of the next three games.

Hi, could you create an algorithm using psuedocode for this problem:   Consider a problem in which you have a set of n keys and n locks. Every key corresponds to exactlyone lock, and every lock corresponds to exactly one key (this correspondence means that all items areunique, no duplicate keys or locks are present). Create an algorithm that efficiently (less than O(n2) time)pairs up every lock with its corresponding key. By fitting a lock and key together, you can see if fit iscorrect (the single match), if the lock is too small for the key, or if the lock is too large for the key. Aspart of this algorithm, you cannot compare lock A to lock B, nor key A to key B (no direct comparisonbetween members of the same set).