This project finds the running median of a stream of integers, returning the median in O(nlog(n)) time after every new integer.
This is accomplished through the use of two priority queues, on a max heap (gt) and one a min heap (lt). The max heap stores 
all elements less than the current median in ascending order. It will also contain the first element inputted. The min heap 
stores all elements greater than the median as negative numbers as to keep it in ascending order, with the smallest value 
on top of the queue. After every new integer input, the queues are rebalanced so that the difference in their size is 
no more than one. Thus, the median always lies at the top of whichever queue has more elements, or at the top of 
both stacks if they have the same number of elements.



median.cc contains four helper functions and a main function.

Median- returns the comparable median for use in determining
	where new integers are stored. Either returns the top
	value of lt or gt stack, depending on which stack has
	more elements.

balanceHeap- balances two queues so that their sizes differ
	     by no more than one.

insert- determines if a newly inputted integer is pushed in
	lt or gt. If it is greater than the median, it is 
	pushed to gt. Otherwise, it is pushed to lt.
	Calls balanceHeap to make sure the sizes of each 
	queue after the new element differ no more than 1.

printMed- prints either the top of the lt stack, the top of
	  the gt stack, or both. If lt has more elements,
	  lt.top() is printed. If gt has more elements,
	  gt,top() is printed. If they have the same number
	  of elements, both are printed.

main- prompts the user to enter 'p' to push or 'q' to quit,
      then promts the user for an integer to push if 'p'
      is selected. This process is repeated until the user
      chooses to quit. Each time an integer is entered,
      a call t insert is made to insert it in to the proper
      stack and balance the stacks, and then a call to
      printMed is made to print the appropriate median.



Makefile contains three commands: make, make run, and make clean

make- compiles median.cc to the exacuteable median

make run- runs median with ./median

make clean- removes the exacuteable median from the directory
	    with rm -r median



TIME COMPLEXITY REPORT:

median.cc itself executes in constant time, or O(1). There is no looping in any of the helper functions.
However, the use of priority queues, which take O(nlog(n)) time to insert values, makes the overall
runtime O(nlog(n)).