1. Implement a heap-based priority queue that supports the following additional operation in linear time:

replaceComparator(c): Replace the current comparator with c. After changing the comparator, the heap will need to be restructured.

2. Write a program that can process a sequence of stock buy and sell orders as described in Exercise C-8.1.

C-8.1 An online computer system for trading stock needs to process orders of

the form “buy 100 shares at $x each” or “sell 100 shares at $y each.” A

buy order for $x can only be processed if there is an existing sell order

with price $y such that y ≤ x. Likewise, a sell order for $y can only be

processed if there is an existing buy order with price $x such that x ≥ y.

If a buy or sell order is entered but cannot be processed, it must wait

for a future order that allows it to be processed. Describe a scheme that

allows for buy and sell orders to be entered in O(logn) time, independent

of whether or not they can be immediately processed.