Problem B
Urn-ball Probabilities!
Input: standard input
Output: standard output
Time Limit: 3 seconds
Assume that you have two urns before you. Initially, one urn has one
ball and the other urn has two balls and exactly one ball in each urn is red.
At this initial stage you are asked to pick up two balls, one from each urn.
Then one white ball is added in each urn and you are again asked to pick up one
ball from each urn then again one white ball is added in each urn. This process
continues for a certain time. Remember that you place the picked ball back to
the urn after each pick up. You will have to determine the probability that in any
of your pickups both of the picked balls were red and also the probability that
all of your picked balls were red after certain steps.
Input
The input file contains several lines of inputs. Each line of the input file contains an unsigned integer N (N<1000000) indicating how many times you will pick up. Of course after each pick up an increment in balls occurs as described previously.
Output
For each line of input print a single line of output containing a floating point number and an integer. The floating-point number indicates the probability that you have picked up two red balls in at least one of your pick-ups and the second integer denotes how many consecutive zeros are there after decimal point in the probability value that all of your pick ups has both balls as red.
Sample Input:
Sample
Output:
Shahriar
Manzoor
“The contest judges do not check whether your algorithm is correct or not,
they just want certain output for their given input. But still it is the fastest
and best way of judging
whether your algorithm is correct.”