Give a complete justification of Proposition 12.1. In the merge-sort tree shown in Figures 12.2 through 12.4, some edges are drawn as arrows. What is the meaning of a downward arrow? How about an...

Give a complete justification of Proposition 12.1.

In the merge-sort tree shown in Figures 12.2 through 12.4, some edges are

drawn as arrows. What is the meaning of a downward arrow? How about

an upward arrow?

Show that the running time of the merge-sort algorithm on an
n-element

sequence is
O(nlog
n), even when
n
is not a power of 2.

Is our array-based implementation of merge-sort given in Section 12.2.2

stable? Explain why or why not.