Question $1(25$ marks$)$

a$.$ The INORDER traversal output of a binary tree is $A,B,N,O,R,M,A,L,L,Y$ and the PREORDER traversal output of the same tree is $Y,N,A,B,M,O,R,L,A,L.$ Construct the tree and determine the output of the POSTORDER traversal output.

$(6\mathrm{.}0$ marks$)$

b$.$ Given the following undirected graph:

Represent the graph as:

$($i$)$ Adjacency matrix

$(3\mathrm{.}0$ marks$)$

$($ii$)$ Adjacency list

$(3\mathrm{.}0$ marks$)$

$($iii$)$ Incidence matrix

$(3\mathrm{.}0$ marks$)$

c$.$ Starting with an empty $2-4$ tree, construct a $2-4$ tree with the following keys. Show the major working steps.

$14,12,11,13,16,15$

$(10\mathrm{.}0$ marks$)$

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