Would someone be able to help me with these questions?

Due in class on Thursday, March 2. 2017 Josephus figured out where to stand in the vicious circle and survived. He also saved his friend, the penultimate winner. For some small values of n. write down the position of the penultimate winner. I(n). You may extend the following table as much as you like. Give a recurrence relation for I(n). Give an O(n log k)-time algorithm that merges k sorted lists with a total of n elements into one sorted list. There are many duplications in the input sequence of n numbers. such that only O(log n) numbers are distinct. Give an O(n log log n) worst-case time algorithm to sort such a sequence. Design an O(n log n) worst-case time algorithm that counts the number of inversions in an array of n numbers. The K-th quantiles of a set of n numbers are the k - 1 numbers that divide the sorted sot into k equal-sized seta (to within 1). For example, if the set is {1, 2, 3, 99}, the 10-th quantiles are 10, 20, ....90. Design an O(n log K) time algorithm to find the K-th quantiles of a set