Problems

$(20$ points$)$ Problem $1$: Hash Tables.

$($a$)$ A hash code is using polynomial accumulation as follows $h_1(x)=-24+8x-12x^2+$

$4x^3-6x^4+2x^5.$ Use Horner's method to evaluate $h_1(-2).$

$($b$)(5$ points$)$ Draw the $11-$entry hash table that results from using the hash function

$h(i)=(3i+5)mod11,$ to hash the keys $12,44,13,88,23,94,11,39,20,16,5,$

assuming collisions are handled by chaining.

$($c$)(5$ points$)$ Repeat part $($b$)$ but now resolve collisions using linear probing.

$($d$)(5$ points$)$ Repeat part $($b$)$ but now resolve collisions using double hashing where the

secondary hash function is defined as $h^{\text{'}}(k)=7-(kmod7).$