a$.$ Suppose A$[1$ n$]$ and B$[1$ n$]$ are heaps storing key values. Does

C$[1$ n$]$ where C$[$i$]=$ A$[$i$]+$ B$[$i$]$ for i $=1,...,$ n represent a heap? Why or why not?

b$.$ Again, let A$[1$ n$]$ store the keys of a heap. Write a pseudocode for the

method replaceKey$($i$,$ k$)$: Replace the key at A$[$i$]$ with k$.$

You must incorporate the pseudocode for BubbleUp and BubbleDown in your algorithm. Briefly explain why your implementa$$on is correct and why its running time is O$($log n$).$