Please include solution. Thank you We are given a collection of n key-value pairs (k,m) in which k is a positive integer number in a range [0,N-1] for small enough N. Assume that we may have multiple values for the same keys. a) If m is a positive number in a range [0,M-1] for some small enough integer M, design a lookup table for storing these items such that the time complexity of search, insert and delete are constant. b) If m is an arbitrary integer number, design a lookup table for storing these items such that the time complexity of search is log n.

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Hash Table

A hash table also called a hash map, is a data structure that maps key-value pairs. The hash table can be used in complex systems to provide fast access and compact storage. A hash table is a structure that stores data in an abstract data type kind of associative array. It keeps data in an array format, with a distinct index value for every data value. If the index of the required data is known, then the data can be accessed very easily.