Problem Statement

We have a book with N pages, numbered 1 to N. How many times does each digit occur in the page numbers?
You are given an int N. Return a int[] with 10 elements, where for all i between 0 and 9, inclusive, the element i will be the number of times digit i occurs when we write down all the numbers between 1 and N, inclusive.

Definition

Class:
PageNumbers
Method:
getCounts
Parameters:
int
Returns:
int[]
Method signature:
int[] getCounts(int N)
(be sure your method is public)


Notes
-
You may assume that for any valid input each of the output values fits into an int.
Constraints
-
N will be between 1 and 1,000,000,000, inclusive.
Examples
0)

????
7
Returns: {0, 1, 1, 1, 1, 1, 1, 1, 0, 0 }
The page numbers in this case are simply 1, 2, 3, 4, 5, 6, and 7.
1)

????
11
Returns: {1, 4, 1, 1, 1, 1, 1, 1, 1, 1 }
In comparison to the previous case, we added the pages 8, 9, 10, and 11. Now we have each digit exactly once, except for the digit 1 that occurs four times: once in 1 and 10, and twice in 11.
2)

????
19
Returns: {1, 12, 2, 2, 2, 2, 2, 2, 2, 2 }
Digits 2 to 9 now occur twice each, and we have plenty of occurrences of the digit 1.
3)

????
999
Returns: {189, 300, 300, 300, 300, 300, 300, 300, 300, 300 }
Due to symmetry, each of the digits 1 to 9 occurs equally many times in the sequence 1,2,...,999.
4)

????
543212345
Returns: 
{429904664, 541008121, 540917467, 540117067, 533117017, 473117011, 429904664,
 429904664, 429904664, 429904664 }
Watch out for the time limit.
 
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