Q$1.$ Find the topological sorting problem for the given graph A and $B.$

Q$2.$ Apply Quick to sort the list, M$,$ U$,$ L$,$ T$,$ I $,$ M$,$ E$,$ D$,$ I $,$ A in alphabetical

order.

Q$3.$ Explain Master Theorem $.$Using Master Theorem solved the following recurrence.

a$)T(n)=9T(\frac{n}{3})+n^{2}logn$

b$)T(n)=64T(\frac{n}{32})+\sqrt[\phantom{2}]{n}$

Q$4.$ Write the Recursive algorithm for Merge Sort $.$Consruct the recurrence relation for

recursive algorithm and solve using bachward Subtution.

$(2$ Mark$)$

Q$5.$ Solve the following equations using Gaussian Elimination Method:

$(2$ Mark$)$

$-61+52-33=6$

$21+72-83=10$

$-31+82-23=15$