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Cormen Edition 3 Exercise 11.3 Question 4 (Page No. 269)
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Consider a hash table of size $m =1000$ and a corresponding hash function $h(k) =$ $\lfloor$ $m$$($$kA$ $mod$ $1$)$\rfloor$ for $A = \frac{(\sqrt{5} – 1)}{2}$ .Compute the locations to which the keys $61, 62, 63, 64,$ and $65$ are mapped.
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Apr 4, 2019
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61> 700
62> 318
63> 936
64> 554
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Jul 11, 2019
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puneetg788
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Cormen Edition 3 Exercise 11.3 Question 6 (Page No. 269)
Let $U$ be a set of $ntuples$ of values drawn from$\mathbb{\ Z_p}$ , let $B$ $=$ $\mathbb{\ Z_p}$ , where p is prime. Define the hash function $h_b :U \rightarrow B$ for $b$ $\in$\mathbb{\ Z_p}$ on an input $ ... $\mathscr{H}$ is $n(n1)/p$ universal according to the definition of the $\epsilon$ universal.
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Cormen Edition 3 Exercise 11.3 Question 5 (Page No. 269)
Define a family $\mathscr{H}$ of hash functions from a finite set $U$ to a finite set $B$ to be universal if for all pairs of distinct elements $k$ and $l$ in $U$, $Pr\{h(k) = h(l)\} \leq \epsilon$ where the probability is ... Show that an $\epsilon$universal family of hash functions must have $\epsilon \geq \frac{1}{B}  \frac{1}{U}$
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Cormen Edition 3 Exercise 11.3 Question 3 (Page No. 269)
Consider a version of the division method in which $h(k) =k$ $mod$ $m$, where $m = 2^p1$ and $k$ is a character string interpreted in $radix$ $2^p$. Show that if we can derive string $x$ from string $y$ by ... $y$ hash to the same value. Give an example of an application in which this property would be undesirable in a hash function.
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Cormen Edition 3 Exercise 11.4 Question 5 (Page No. 277)
Consider an openaddress hash table with a load factor $\alpha$ Find the nonzero value $\alpha$ for which the expected number of probes in an unsuccessful search equals twice the expected number of probes in a successful search.
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