[ 'chickenh[ 'tigerh[ ]='duckh[ 'duckh data ['bird''goat''pig''duck''dog''lion''tiger'nonenone'cow''cat'>print( [ ]none analysis of hashing we stated earlier that in the best case hashing would provide ( )constant time search technique howeverdue to collisionsthe number of comparisons is typically not so simple even though complete analysis of hashing is beyond the scope of this textwe can state some well-known results that approximate the number of comparisons necessary to search for an item the most important piece of information we need to analyze the use of hash table is the load factorconceptuallyif is smallthen there is lower chance of collisionsmeaning that items are more likely to be in the slots where they belong if is largemeaning that the table is filling upthen there are more and more collisions this means that collision resolution is more difficultrequiring more comparisons to find an empty slot with chainingincreased collisions means an increased number of items on each chain as beforewe will have result for both successful and an unsuccessful search for successful search using open addressing with linear probingthe average number of comparisons ) if we are using is approximately and an unsuccessful search gives chainingthe average number of comparisons is for the successful caseand simply comparisons if the search is unsuccessful sorting sorting is the process of placing elements from collection in some kind of order for examplea list of words could be sorted alphabetically or by length list of cities could be sorted by populationby areaor by zip code we have already seen number of algorithms that were able to benefit from having sorted list (recall the final anagram example and the binary searchthere are manymany sorting algorithms that have been developed and analyzed this suggests that sorting is an important area of study in computer science sorting large number of items can take substantial amount of computing resources like searchingthe efficiency of sorting algorithm is related to the number of items being processed for small collectionsa complex sorting method may be more trouble than it is worth the overhead may be too high sorting