Complex Libraries
Using Hash Dictionaries 1
Playing Hash Table You are the new produce manager of the local grocery store. You want to use a dictionary to track your fruit inventory. Entries have the form (“banana”, 20) where o “banana” is the key o 20 is associated data, like the number of cases in stock Let’s observe your initial interactions with a hypothetical hash dictionary library 2
This is what This is what This is your side 0 is going on in is going on in the library the library 1 2 Client Implementation 3 4 You begin by 5 creating a Create a new hash dictionary 6 new dictionary 7 Here you go! 8 9 This library uses separate-chaining hash tables to implement dictionaries It decides on an initial capacity of 10 o it’s probably self -resizing 3
Client Implementation 0 1 Insert A = (“apple”, 20) 2 What’s the key of (A)? 3 4 new dictionary 5 Next, you insert 6 A = (“apple”,20) 7 8 9 Why is the library asking this? o it does not know what entries are (A) is just a pointer to some struct no sense of what’s in it You need to tell it 4
Client Implementation 0 1 Insert A = (“apple”, 20) 2 What’s the key of (A)? 3 4 “apple” new dictionary 5 What’s its hash value? Next, you insert 6 A = (“apple”,20) 7 8 9 Why is the library asking this? o it does not know the type of keys o even if it did, there are many ways to hash them You need to tell it 5
Key Hash Client Implementation "apple" -1290151091 0 "berry" -514151789 "banana" 207055587 1 Insert A = (“apple”, 20) "grape" -581390202 "lemon" -665562942 2 "lime" 2086736531 What’s the key of (A)? "pumpkin" -1189657311 3 4 “apple” new dictionary 5 What’s its hash value? Next, you insert 6 A = (“apple”,20) -1290151091 7 8 9 -1290151091 % 10 is -1 in C0 o not a valid array index! o the library needs a more robust way to compute the hash index Exercise! Let’s say it keeps the last digit 6
Key Hash Client Implementation "apple" -1290151091 0 "berry" -514151789 "banana" 207055587 1 A Insert A = (“apple”, 20) "grape" -581390202 "lemon" -665562942 2 "lime" 2086736531 What’s the key of (A)? "pumpkin" -1189657311 3 4 “apple” new dictionary 5 What’s its hash value? Next, you insert 6 A = (“apple”,20) -1290151091 7 Ok. The hash index is 1 . 8 9 This chain is empty. I can insert entry (A) there. Done The library asked for o the key of the entry o the hash value of the key Funny! Libraries didn’t ask for anything in the past 7
Key Hash Client Implementation "apple" -1290151091 0 "berry" -514151789 "banana" 207055587 1 A Insert B = (“banana”, 10) "grape" -581390202 "lemon" -665562942 2 "lime" 2086736531 What’s the key of (B)? "pumpkin" -1189657311 3 4 “banana” new dictionary insert A = (“apple”, 20) 5 What’s its hash value? 6 Next, you insert 207055587 7 B Ok. The B = (“banana”,10) hash index is 7 . 8 9 This chain is empty. I can insert entry (B) there. Done Same as for (A) 8
Key Hash Client Implementation "apple" -1290151091 0 "berry" -514151789 "banana" 207055587 1 A Insert C = (“pumpkin”, 50) "grape" -581390202 "lemon" -665562942 2 "lime" 2086736531 What’s the key of (C)? "pumpkin" -1189657311 3 4 “pumpkin” new dictionary insert A = (“apple”, 20) 5 insert B = (“banana”, 10) What’s its hash value? 6 -1189657311 7 Ok. The hash index is 1 . B Next, you insert It points to a node C = (“pumpkin”,50) 8 for entry (A) 9 What’s the key of (A)? Why is the library asking this? o it does not know what entries are (A) is just a pointer to some struct no sense of what’s in it You need to tell it 9
Key Hash Client Implementation "apple" -1290151091 0 "berry" -514151789 "banana" 207055587 1 A Insert C = (“pumpkin”, 50) "grape" -581390202 "lemon" -665562942 2 "lime" 2086736531 What’s the key of (C)? "pumpkin" -1189657311 3 4 “pumpkin” new dictionary insert A = (“apple”, 20) 5 insert B = (“banana”, 10) What’s its hash value? 6 -1189657311 7 Ok. The hash index is 1 . B Next, you insert It points to a node C = (“pumpkin”,50) 8 for entry (A) 9 What’s the key of (A)? “apple” Is it the same as “pumpkin” ? Why is the library asking this? o it does not know the type of keys o even if it did, there are many ways to compare them You need to tell it 10
Key Hash Client Implementation "apple" -1290151091 0 "berry" -514151789 "banana" 207055587 1 A C Insert C = (“pumpkin”, 50) "grape" -581390202 "lemon" -665562942 2 "lime" 2086736531 What’s the key of (C)? "pumpkin" -1189657311 3 In practice, it is 4 easier to insert “pumpkin” new dictionary new nodes at the insert A = (“apple”, 20) 5 beginning of a chain insert B = (“banana”, 10) What’s its hash value? 6 -1189657311 7 Ok. The hash index is 1 . B Next, you insert It points to a node C = (“pumpkin”,50) 8 for entry (A) 9 What’s the key of (A)? “apple” Is it the same as “pumpkin” ? There is no next node. I can insert entry (C) there. No The library asked for o the key of the entry Done o the hash value of the key o whether two keys are the same 11
Key Hash Client Implementation "apple" -1290151091 0 "berry" -514151789 "banana" 207055587 1 A C Look up “apple” "grape" -581390202 "lemon" -665562942 2 "lime" 2086736531 What’s its hash value? "pumpkin" -1189657311 3 4 -1290151091 new dictionary insert A = (“apple”, 20) Ok. The hash index is 1 . 5 insert B = (“banana”, 10) It points to a node 6 for entry (A) insert C = (“pumpkin”, 50) 7 B What’s the key of (A)? Next, you 8 look up “apple” “apple” 9 Is it the same as “apple” ? Yes Found (A) Looking up a key follows the same steps as inserting an entry 12
Key Hash Client Implementation "apple" -1290151091 0 "berry" -514151789 "banana" 207055587 1 A C Look up “lime” "grape" -581390202 "lemon" -665562942 2 "lime" 2086736531 What’s its hash value? "pumpkin" -1189657311 3 4 2086736531 Ok. The hash index is 1 . new dictionary It points to a node insert A = (“apple”, 20) 5 for entry (A) insert B = (“banana”, 10) 6 insert C = (“pumpkin”, 50) What’s the key of (A)? look up “apple” 7 B “apple” 8 Next, you look up “lime” 9 Is it the same as “lime” ? The library goes through the chain node by node 13
Key Hash Client Implementation "apple" -1290151091 0 "berry" -514151789 "banana" 207055587 1 A C Look up “lime” "grape" -581390202 "lemon" -665562942 2 "lime" 2086736531 What’s its hash value? "pumpkin" -1189657311 3 4 2086736531 Ok. The hash index is 1 . new dictionary It points to a node insert A = (“apple”, 20) 5 for entry (A) insert B = (“banana”, 10) 6 insert C = (“pumpkin”, 50) What’s the key of (A)? look up “apple” 7 B “apple” 8 Next, you look up “lime” 9 Is it the same as “lime” ? No Ok. The next node has entry (C) What’s the key of (C)? The library goes through the “pumpkin” chain node by node Is it the same as “lime” ? 14
Key Hash Client Implementation "apple" -1290151091 0 "berry" -514151789 "banana" 207055587 1 A C Look up “lime” "grape" -581390202 "lemon" -665562942 2 "lime" 2086736531 What’s its hash value? "pumpkin" -1189657311 3 4 2086736531 Ok. The hash index is 1 . new dictionary It points to a node insert A = (“apple”, 20) 5 for entry (A) insert B = (“banana”, 10) 6 insert C = (“pumpkin”, 50) What’s the key of (A)? lookup “apple” 7 B “apple” 8 Next, you look up “lime” 9 Is it the same as “lime” ? No Ok. The next node has entry (C) What’s the key of (C)? Looking up a key can “pumpkin” o return the associated Is it the same as “lime” ? entry, or o signal there is no entry There is no No next node with this key I have no “lime” 15
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