You should do the following problems on paper. The problems are all quite easy, and will give you practice with balanced trees. You will hand in your answers in on d$2$l in the folder labeled hw$4$a $-$ Balanced Tree Problems.

$2-3$ Trees:

$3\mathrm{.}3\mathrm{.}1$

$3\mathrm{.}3\mathrm{.}2$

$3\mathrm{.}3\mathrm{.}3$

$3\mathrm{.}3\mathrm{.}5---$ structurally different means that they are different even

if all you ignore the values $($take all values to be equal$)$

and you also ignore the order of the children

Red$-$Black Trees:

$3\mathrm{.}3\mathrm{.}9$

$3\mathrm{.}3\mathrm{.}10$

$3\mathrm{.}3\mathrm{.}11$

$3\mathrm{.}3\mathrm{.}14$

$3\mathrm{.}3\mathrm{.}15$