MadeEasy Test Series 2019: Programming & DS - Hashing

Question

Consider the hashing table with 'm' slots and 'n' keys. If the expected number of probes in unsuccessful search is 3. The expected number of probes in a successful search is_

Answer 1.647

Comments

Expected number of probes in open addressing in case of an unsuccessful search = 1/(1-$\alpha$) , where $\alpha$ denotes the load factor i.e. n/m.

So 1/(1-$\alpha$) = 3

Hence, $\alpha$ = 2/3

Now, Expected number of probes in open addressing in case of an successful search = (1/$\alpha$)*ln(1/(1-$\alpha$))

Putting $\alpha$=2/3 in the above formula, we get the expected probes for successful search as 1.647.

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why have you considered double hashing formula here? And why not linear probing?

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This is the formula that is used for open addressing..

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http://cs360.cs.ua.edu/notes/hashing_formulas.pdf

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thanks prashant jha 1 :)

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Now I think this question is incomplete , right @Somoshree Datta 5

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yes..they should have mentioned which hashing to use

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http://www.cs.tau.ac.il/~zwick/Adv-Alg-2015/Linear-Probing.pdf

visit this link..they have given this formula for uniform probing, not double hashing..

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http://web.ist.utl.pt/fabio.ferreira/material/asa/clrs.pdf

Visit page 210 of CLRS..here also they gave this formula for open addressing..

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thanks @prashant jha 1 @Somoshree Datta 5

most of the questions of test series are incomplete

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I followed the same path using the same logic. Please explain, why am I getting different answer.I  ain't getting 1.647.

1.5*ln(3)=1.098. Please someone explain. Silly thing though.😁

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You are doing calculation mistake

ln(3)= 1.0987..

1.5*1.0987=1.647

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https://gateoverflow.in/287833/madeeasy-test-series-programming-%26-ds-hashing

Answer 1

Number of probes in unsuccessful search  = $\displaystyle \frac{1}{1-x}$

Number Of Probes in successful search  = $\displaystyle \frac{1}{x } * \ln \displaystyle \frac{1}{1-x}$

where x= load factor of hash table

since, x = $\displaystyle \frac{n}{m }$

Therefore using above formula , x= $\displaystyle \frac{2}{3 }$ , as no. of probes in unsuccessful  search= 3.

Now using x=$\displaystyle \frac{2}{3 }$ ,  no of probes for successful search  = $\displaystyle \frac{3}{2 } * \ln3$ = 1.647