FactorialSystem | Topcoder Archive

Problem Statement

In the factorial number system the value of the first digit (from the right) is 1!, the value of the second digit is 2!, ..., and the value of the n-th digit is n!. This means that any decimal number d can be written in this system as: a_na_n-1...a₂a₁, where

d = a_n * n! + a_n-1 * (n-1)! + ... + a₂ * 2! + a₁ * 1! and 0 <= a_i <= i for all i.

Given an int num in decimal, return its representation in the factorial number system.

Definition

Class:: FactorialSystem
Method:: convert
Parameters:: int
Returns:: int
Method signature:: int convert(int num)
(be sure your method is public)

Notes

n! = 1 * 2 * ... * n

Constraints

num will be between 1 and 3628799 (10!-1), inclusive.

Examples

```
1
```
```
Returns: 1
```
```
24
```
```
Returns: 1000
```
24 = 4!
```
153
```
```
Returns: 11111
```
153 = 1! + 2! + 3! + 4! + 5!.
```
133
```
```
Returns: 10201
```
```
3628799
```
```
Returns: 987654321
```
Largest possible input.

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