that for small values of nthe additional cost of sorting is probably not worth it in factwe should always consider whether it is cost effective to take on the extra work of sorting to gain searching benefits if we can sort once and then search many timesthe cost of the sort is not so significant howeverfor large listssorting even once can be so expensive that simply performing sequential search from the start may be the best choice self check suppose you have the following sorted list [ and are using the recursive binary search algorithm which group of numbers correctly shows the sequence of comparisons used to find the key suppose you have the following sorted list [ and are using the recursive binary search algorithm which group of numbers correctly shows the sequence of comparisons used to search for the key hashing in previous sections we were able to make improvements in our search algorithms by taking advantage of information about where items are stored in the collection with respect to one another for exampleby knowing that list was orderedwe could search in logarithmic time using binary search in this section we will attempt to go one step further by building data structure that can be searched in ( time this concept is referred to as hashing in order to do thiswe will need to know even more about where the items might be when we go to look for them in the collection if every item is where it should bethen the search can use single comparison to discover the presence of an item we will seehoweverthat this is typically not the case hash table is collection of items which are stored in such way as to make it easy to find them later each position of the hash tableoften called slotcan hold an item and is named by an integer value starting at for examplewe will have slot named slot named slot named and so on initiallythe hash table contains no items so every slot is empty we can implement hash table by using list with each element initialized to the special python value none figure shows hash table of size in other wordsthere are slots in the tablenamed through searching