a) Show (diagrammatically in the form of a divide-and-conquer tree, in the same format shown in your text book and slides) all the steps involved in the quick sort on the following input sequence: 22 72 38 48 13 14 93 69 45 58 13 81 79. You should sort the sequence in the nondecreasing order. Clearly show the pivots chosen at each node. (Note: Though in practice the pivot for each input is chosen at random, you may choose pivots here of your choice which make the tree balanced, i.e. only choose good pivots).

b) Repeat part a) if the quick sort is performed in place.