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.

Consider the doctor-patient problem. There is a Doctor's clinic which has one Doctor, one patient chair, and n chairs for waiting for patients if there are any to sit on the chair. If there is no patient, then the Doctor sleeps in his own chair. When a patient arrives, he has to wake up the Doctor. If there are many patients and the Doctor is treating a patient, then the remaining patients either wait if there are empty chairs in the waiting room or they leave if no chairs are empty. Write a solution (Algorithm / Pseudocode) using semaphores.

do it

X-Kingdom has trapped n number of soldiers of their opponent. They want to execute them. They created a strategy so that the prisoners will kill each other and at the end one prisoner will be alive and eventually released. As part of the process, they assigned each trapped soldier a sequence number starting from 1 and ending at n.    If n = 5 and k = 2, then the safe position is 3. Firstly, the person at position 2 is killed, then person at position 4 is killed, then person at position 1 is killed. Finally, the person at position 5 is killed. So, the person at position 3 survives. If n = 7 and k = 3, then the safe position is 4. The people at positions 3, 6, 2, 7, 5, 1 are killed in order, and the person at position 4 survives.   Input:n and k Output:Print the list of prisoners in reverse order from n to 1Then reverse the list to print it in correct order from 1 to nDisplay the position number who will survive. You must have to use circular doubly linked list for your solution. You…