$($Answer must be in your own hand$-$writing. Affix your signature

in each page of your answer.$)$

$($a$)$ Draw the ordered rooted tree whose in$-$order traversal is

$d,b,i,e,m,j,n,o,a,f,c,g,k,h,p,l.$

What is its post$-$order traversal?

$\%$

$($b$)$ Using Kruskal's algorithm, find a minimum spanning tree in the weighted

graph whose vertices are $A,B,C,D,L,M,N,S$ and the edges are

$\{S,L\},\{S,D\},\{S,C\},\{S,N\},\{L,D\},\{L,N\},\{C,B\},$

$\{C,N\},\{C,A\},\{A,N\},\{A,M\},\{N,B\},\{D,C\},\{N,M\}$

with corresponding weights

$75,140,175,245,120,230,130,110,100,115,90,50,130,165.$