Princeton Alogorithm COS226 Week

in previous lecture, we learn symbol table implemented by bst. and have lg n time complexity in worst case.
Can we do better?
yes, but with different access to the data.
it is the famous data structure, hash table.
the key of hash table is the hash function, the issue of hash function is the hash collision. so when implement hash table, we need to handle two keys that hash to the same array index.
so i will introduce hash function.

hash function

hash function is a function convert any object to a int.
idealistic goal is that scramble the keys uniformly to produce a table index

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uniform hash assumption

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separate chainning

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linear probing

open addressing, when a new key collides, find next empty slot, and put it there

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knuth's parking problem
cars arrive at one-way street with M parking spaces. each desire a random space i: if space i is taken, try i+1, i+2 etc
what is mean displacement of a car?

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algorithmic complexity attack on java

goal: find family of strings with the same hash code.

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so we need a one-way hash function, it is hard to find a key that will hash to a desired value(or two keys that hash to some value)

spearate chaining vs linear probing

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QUIZ

Q1

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we assume we have uniform hashing assumption, then we can use hashmap to record all the n^2 pair , then we can use O(N) to find the result, be care find the two pair with some same indices.

Q2

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if you override hashCode() but not equals(), only same reference will be dedup in hashmap.

if you override equals() but not hashCode().
only same reference will be dedup, but equal may return false on same reference

if you override hashCode() but implement wrong equals signature

public boolean equals(OlympicAthletethat)
have no use in dedup of hashmap.

Searching application

exception filter application

read in a list of words from one file, print out all words from standard input that are {in, not in} the list

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and dictionary lookup

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File indexing

goal: given a list of files specified, create an index so that you can efficiently find all files containing a given query string

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Concordance

goal: preprocess a text corpus to support concordance queries: given a word, find all occurrences with their immediate contexts

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Sparse matrix-vector multiplication

assumption: matrix dimension is 10,000; average nonzeros per row ~10

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course quiz and project : https://github.com/yixuaz/algorithm4-princeton-cos226