1020 . Nowhere Money
Description
In Nowhere town, people use “coin and slot” as their money. There are 2 types of coins called
size1 and size2. Size2 coin is twice the thickness of size1. People stack their coins in slots and
use them as money. There are many size of slots. The slot of size n is able to stack up n size1
coins. Only filled-up slot is considered as legal money. The value of each filled-up slot is the
distinct ways its can stack coins inside. For example, for size-1 slot, there is only one way to
stack a single size1 coin inside. For size-2 slot, there are 2 ways to stack two size1 coins or one
size2 coin inside. And for size-5 slot, there are 8 ways to stack coins inside, which can be
illustrated as follow: 1 1 1 1 1, 1 1 1 2, 1 1 2 1, 1 2 1 1, 2 1 1 1, 1 2 2, 2 1 2, 2 2 1. So the value
of filled up slot with size-1, size-2 and size-5 are 1, 2 and 8 (monetary) units respectively
(regardless of the type of coins or the ways they are stacked).
Mr.Thinktwice is an owner of a grocery store in this town. He noticed that customers are likely
to go to the shop that can return the (money) change in the form that suits their customer. And
from his little survey, he found that most customers would like to get their amount of change in
the form according to these 2 simple constraints.
1. The number of slots is minimum.
2. The size of each slot must be different from each other by at least 2.
- This means that customers does not want any slots with the same size and it will be
easier for them to distinguish these
differences if the sizes are not too close.
So Mr.Thinktwice ask you to write a program that can give him a series of slot sizes for a given
amount of change according to the previous constraints. Moreover, the series must be sorted in
descending order. For more specific, any amount of change can be written in this formula.
For example:
Input Format
Input is a standard input which contains a set of integer. Each line of the input is an amount of
change which represents by a positive integer less than or equal to 5,000,000,000,000,000,000
or 5 * 1018
. The input is terminated when the EOF (EndOfFile) is reached.
Output Format
For each amount of change, generate 4 lines of output data. The first line is the amount of change
itself. The second line is a series of slot sizes (in descending order) separated by spaces. (The
maximum slot size is less than or equal to 90.) The third line is a series of corresponding slot
values. The fourth line is a blank line.
Sample Input 1
1 10 1000000
Sample Output 1
1 1 1 10 5 2 8 2 1000000 29 25 23 11 9 832040 121393 46368 144 55
Hints
Problem Source
Migrated from old NTUJ.
2009Phuket
Subtasks
| No. | Testdata Range | Score |
|---|