think of each column as bucket in which we throw all the elements which give particular result when the hash function is suppliedso the fifth column contains all the keys for which the hash function evaluates to then we could put hkg into the slot 'beneathphland gla in the one beneath oryand continue filling the table in the order given until we reach lax dca phl hkg fra gcm akl ory gla the disadvantage of this approach is that it has to reserve quite bit more space than will be eventually requiredsince it must take into account the likely maximal number of collisions even while the table is still quite empty overallcollisions will become increasingly likely moreoverwhen searching for particular keyit will be necessary to search the entire column associated with its expected positionat least until an empty slot is reached if there is an order on the keysthey can be stored in ascending orderwhich means we can use the more efficient binary search rather than linear searchbut the ordering will have an overhead of its own the average complexity of searching for particular item depends on how many entries in the array have been filled already this approach turns out to be slower than the other techniques we shall considerso we shall not spend any more time on itapart from noting that it does prove useful when the entries are held in slow external storage direct chaining rather than reserving entire sub-arrays (the columns abovefor keys that collideone can instead create linked list for the set of entries corresponding to each key the result for the above example can be pictured something like this lax phl fra dca hkg gcm akl ory gla this approach does not reserve any space that will not be taken upbut has the disadvantage that in order to find particular itemlists will have to be traversed howeveradding the hashing step still speeds up retrieval considerably we can compute the size of the average non-empty list occurring in the hash table as follows with items in an array of size mthe probability than no items land in particular slot is (nmm- so the number of slots with at least one item falling in it is nn (nmm (nmm