Exercise $2$: Consider the following data : $\backslash (\backslash$left$\backslash \{\backslash$begin$\{$array$\}\{$lllllllll$\}175$ & $23$ & $71$ & $49$ & $113$ & $123$ & $61$ & $160$ & $160\backslash$end$\{$array$\}\backslash$right$.\backslash )\backslash (157\backslash \}\backslash ).$ Insert these keys in a hash table of size $\backslash ($ M$=19\backslash )$ using close hashing with linear probing. Use the hash function $\backslash (\backslash$mathrm$\{$h$\}(\backslash$mathrm$\{$K$\})=\backslash$mathrm$\{$K$\}\backslash$bmod $19\backslash )$

$```$

The data: $[175,23,71,49,113,123,61,160,160,157]$

The size of the hash table: $19$

The hash table with linear probing for the given data: $[-1.-1.-1.$

$-1.175.23.61.157.160.123.160.49.-1.-1.71.-1.-1.-1.$

$113.]$

$```$

Exercise $3$:

The load factor is defined as alpha $\backslash (=$N $/$ M $\backslash ),$ where $\backslash ($ N $\backslash )$ is the size of the input $($the number of keys$),$ and M is the output size $($the hash$\_$table$).$ If alpha is small, i$.$e$.,$ the hash table is large, there will be fewer chances of collision.

Modify your code in Exercise $1$ to do the following:

$1.$ Set alpha to $0\mathrm{.}5($which means $\backslash (\backslash$mathrm$\{$M$\}=2\backslash$mathrm$\{$~N$\}\backslash )).$ Use a random input and fill the hash table.

$2.$ Generate a random key and search it in the hash table. Count the number of comparisons you had to make $($regardless the search was successful or not$).$

$3.$ Do step $2($the search operation$)$ several times $($at least $10$ times$)$ for a different key in the same hash table. Every time note down the number of comparisons.

$4.$ Write the number of comparisons in table form and their average in the space provided below.