DS07_Ch07a - CHAPTER 7 HASHING What is hashing for? For...

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Unformatted text preview: CHAPTER 7 HASHING What is hashing for? For searching But we already have binary search in O( ln n ) time after sorting. And we already have algorithms for sorting in optimal time O( n ln n )... Wait a minute who said that O( n ln n ) is the optimal time? Theres a theorem saying that Any algorithm that sorts by comparisons only must have a worst case computing time of ( n log 2 n ). Then we just do something else besides comparison. Interpolation Search : Find key from a sorted list f [ l ].key , f [ l+1 ].key , ... , f [ u ].key . f[l].key f[u].key l u key i ? n elements l i key l f key n key l f key u f--- = ]. [ ]. [ ]. [ key l f key u f n key l f key l i ]. [ ]. [ ) ]. [ (- - + = If ( f [ i ].key < key ) l = i ; Else u = i ; Search by Formula Search by Formula 1/14 1 General Idea Symbol Table ( == Dictionary) ::= { < name, attribute > } Example In Oxford English dictionary name = since attribute = a list of meanings M[0] = after a date, event, etc. M[1] = seeing that (expressing reason) This is the worst disaster in California since I was elected. California Governor Pat Brown, discussing a local flood Example In a symbol table for a compiler name = identifier (e.g. int ) attribute = a list of lines that use the identifier, and some other fields 2/14 Objects : A set of name-attribute pairs, where the names are unique Operations : SymTab Create(TableSize) Boolean IsIn(symtab, name) Attribute Find(symtab, name) SymTab Insert(symtab, name, attr) SymTab Delete(symtab, name) Symbol Table ADT: 1 General Idea 3/14 Hash Tables [0] [1] [s- 1] ht [ 0 ] ht [ 1 ] ht [b- 1] b buckets s slots For each identifier x , we define a hash function f ( x ) = position of x in ht[ ] (i.e....
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DS07_Ch07a - CHAPTER 7 HASHING What is hashing for? For...

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