HashMaps

OverviewWhat are HashMaps?Implementing DictionaryADT with HashMaps

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HashingWhat if:We could store everything in our dictionary in an array?We could somehow take any key and turn it into an index

into the array in constant time?What would the cost of insert, delete, and find be then?

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Designing a hashtableThere are three main design questions:

What hash function to use (the function that turns a key into an array index)

What size to make the arrayWhat to do if two items index into the same spot (a

“collision”)

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Step 1: what if your key isn’t an integer?Suppose the keys are individual letters, stored as Strings.

What happens if the hash function returnsA number from 0-25?The ASCII code (or Unicode) of the letter?

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Choosing a hash function for StringsWhat if the hash function for a String returnsThe value of the hash function for the first letter of the

String?The sum of the values of the hash functions for all the

letters?Java’s solution: For a String of length n:

s[0] *31n-1 + s[1]*31n-2 + … + s[n-1]*310

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Step 2: get the right integerOnce your key has been converted into an integer, then

what?Is it in the right range to index into the array?Easy solution: index = hashCode % arraySize;Harder question: what if two keys hash to the same array

index (a collision)?

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Resolving collisions 1: chaining What is chaining? Suppose we insert the following names into a table of

size 26 using chaining (with the hash function h(A)=0, h(B)=1, etc.)Ann, Andrew, Bob, Doug, Elizabeth, Betty, Barbara, Hal, Bill, Mary, Tim,

Walter, Xena

What does the table look like after the inserts?

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Resolving collisions: chainingA chained hashtable has an array size of 512. What is the

maximum number of entries that can be placed in the table?

A.256B.511C.512D.164E.There is no maximum.

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Resolving collisions: linear probingWhat is linear probing?Suppose we insert the following names into a table of

size 26 using linear probing (with the hash function h(A)=0, h(B)=1, etc.)Ann, Andrew, Bob, Doug, Elizabeth, Betty, Barbara, Hal, Bill,

Mary, Tim, Walter, Xena

What does the hashtable look like after the inserts?

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Resolving collisions: Quadratic probingWhat is quadratic probing?Suppose we insert the following names into a table of

size 26 using quadratic probing (with the hash function h(A)=0, h(B)=1, etc.)Ann, Andrew, Bob, Doug, Elizabeth, Betty, Barbara, Hal, Bill,

Mary, Tim, Walter, Xena

What does the hashtable look like after the inserts?

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Resolving collisions: Double HashingWhat is double hashing?What are its pros and cons?

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Deleting elements from a hashtableHow does this work if collisions are handled using

chaining?How does this work if collisions are handled using linear

probing or another strategy that stores data in the table?

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Load factorSuppose you place m items in a hashtable with an

array size of s. What is the correct formula for the load factor?

A.s+mB.s-mC.m-sD.m*sE.m/s

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Java’s HashMap classWhat does Java mean by a map?What is Java’s default value for the load factor for the class

HashMap?What are the HashMap operations for insert, delete, and

find?

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Coming attractionsNext time, we’ll look at a new data structure that

allows us to model the Internet, airplane routes, and a variety of other data connected in ways that may be neither linear nor hierarchical: graphs.

Homework: read chapter 13 Graphs (or the equivalent in the earlier edition).

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