Question 2: Let S be a set of n points in R 2 . We consider each point of S to be the location of a city. With each point of S, we are also given the size of the population of the city represented by this point. Describe a data structure of size O(n log n) that supports the following type of query in O(log2 n) time: Given a query point q in R 2 and a query range [a, b], report the city with a population in the range [a, b] that is closest to q. Justify the size and query time of your data structure.

Assume that linear probing is used for hash-tables. To improve the time complexity of the operations performed on the table, a special AVAILABLE object is used to mark a location when an item is removed from the location. Assuming that all keys are positive integers, the following two techniques were suggested instead of marking the location as AVAILABLE: i) When an entry is removed, instead of marking its location in the table as AVAILABLE, indicate the key in the location as the negative value of the removed key (e.g., if the removed key was 16, indicate the key as -16). Searching for an entry with the removed key would then terminate once a negative value of the key is found (instead of continuing to search if AVAILABLE is used). ii) Instead of using AVAILABLE, find a key in the table that should have been placed in the location of the removed entry, then place that key (the entire entry of course) in that location (instead of setting the location as AVAILABLE). The motive is to…

Question 4 Please answer them correctly

Given a list of non-overlapping intervals ofitems, write a function that takes an item as argument and determines in which, ifany, interval that item lies. For example, if the items are integers and the intervals are1643-2033, 5532-7643, 8999-10332, 5666653-5669321, then the query point 9122lies in the third interval and 8122 lies in no interval.