ZOJ Problem Set - 3566
The capital stock (or just stock) of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors. Stock is distinct from the property and the assets of a business which may fluctuate in quantity and value.
A warrant is a security that entitles the holder to buy the underlying stock of the issuing company at a fixed exercise price until the expiry date. Warrants and options are similar in that the two contractual financial instruments allow the holder special rights to buy securities. Both are discretionary and have expiration dates. The word warrant simply means to "endow with the right", which is only slightly different to the meaning of an option.
Warrant and stock are closely related, and warrant has a higher risk factor than the stock. There are a lot of technical terms and rules. But in this problem, you only need to know the rules as follows:
SXSTAR knows the closing price of one warrant's underlying asset today, and other basic information about the warrant. Coincidentally, the closing price of this warrant is the most nearly price to its intrinsic value (using rounding method). SXSTAR doesn't like to calculate. So, could you please calculate the possible range of warrant price tomorrow?
There are several test cases (<=200). You should process to the end of input. For each test case, the first line has one integers N, which means the warrant type, 1 is for call and 2 is for put. The second line is a positive real number (<= 100000, at most has 2 decimal places), which means the closing price of one warrant's underlying asset today. The second line is a positive real number (<= 100000, at most has 2 decimal places), which means the strike price of this warrant. The forth line is a positive real number (<= 100000, at most has 4 decimal places), which means the strike ratio of this warrant.
For each case, you should print a single line with two real numbers indicating the range of the warrant price tomorrow, and the first one should not be bigger than the second one. Two numbers should be separated by a space. Your answer should round to three decimal places.
1 200 100 1
Author: SHEN, Xin
Contest: ZOJ Monthly, December 2011