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

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