user may attempt to insert entries with the same key - suppose we are given two ordered search tables and teach with entries (with and being implemented with arraysdescribe an (log )-time algorithm for finding the kth smallest key in the union of the keys from and (assuming no duplicatesc- give an (logn)-time solution for the previous problem - design variation of binary search for performing operation findall(kin dictionary implemented with an ordered search tableand show that it runs in time (logn )where is the number of elements in the dictionary and is the size of the iterator returned - describe the changes that must be made in the pseudo-code descriptions of the fundamental dictionary methods when we implement dictionary with hash table such that collisions are handled via separate chainingbut we add the space optimization that if bucket stores just single entrythen we simply have the bucket reference that entry directly - the hash table dictionary implementation requires that we find prime number between number and number implement method for finding such prime by using the sieve algorithm in this algorithmwe allocate cell boolean array asuch that cell is associated with the integer we then initialize the array cells to all be "trueand we "mark off all the cells that are multiples of and so on this process can stop after it reaches number larger than (hintconsider bootstrapping method for finding the primes up to - describe how to perform removal from hash table that uses linear probing to resolve collisions where we do not use special marker to represent deleted elements that iswe must rearrange the contents so that it appears that the removed entry was never inserted in the first place