Insert the following into an initially empty red$-$black tree: $4,7,12,15,3,5,14,18,16,17.$ When an insertion causes an RB property to be violated: stop, indicate the problem, and fix it before performing a new insertion. DRAW THE PICTURE.

Insert the following keys into a hash table of size $T=13$:$45,35,56,74,89,90,65,75,95,09,10,1.$ The primary hash function is key$\%$T$.$

a$.$ Using separate chaining.

$\backslash$table$[[,,,,,,,,,,,,],[0,1,2,3,4,5,6,7,8,9,10,11,12]]$

b$.$ Using linear probing.

$\backslash$table$[[,,,,,,,,,,,,],[0,1,2,3,4,5,6,7,8,9,10,11,12]]$

c$.$ Using quadratic probing; What is the load factor of the resulting hash table?

$\backslash$table$[[,,,,,,,,,,,,],[0,1,2,3,4,5,6,7,8,9,10,11,12]]$