You will perform graphical hand executions on B trees.

Sequence $1)$

Hand$-$insert the following sequence of keys into an initially empty B$-$Tree of ORDER $1,$ which means the root has $1$

to $2$ elements, and each child has $1$ to $2$ elements:

$1,2,3,4,9,8,7,6,5$

Sequence $2)$

Hand$-$insert the following sequence of keys into an initially empty B$-$Tree of ORDER $2,$ which means the root has $1$

to $4$ elements, and each child has $2$ to $4$ elements:

$20,30,40,50,60,70,80,90,45,55,65,15,25,35,75,85,95$

Sequence $3)$

Hand$-$insert the following sequence of keys into an initially empty B$-$Tree of ORDER $3,$ which means the root has $1$

to $6$ elements, and each child has $3$ to $6$ elements:

$20,30,40,50,60,22,32,42,52,62,72,82,92,47,70,80,90,45,55,65,15,25,35,75,85,95,21,31,41$

You MUST show all your work.

Turn in:

Lots of paper with lots of NEATLY DRAWN diagrams. Use a drawing program or do by hand NEATLY. Show all your

work, including:

Indicate the keys that are added to each node. Show any values that are moved in the arrays.

Show the tree before and after each split.

Indicate the keys that are moved when a node is split.