Start from integer 1, remove any integer that contains 9 such as 9, 19, 29...
So now, you will have a new integer sequence: 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, ...
Given a positive integer n, you need to return the n-th integer after removing. Note that 1 will be the first integer.
Example 1:
Input: 9 Output: 10
Hint: n will not exceed 9 x 10^8.
Intuition
Let's write the first numbers and try to notice a pattern. Those numbers are:
1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, ... 80, 81, 82, 83, 84, 85, 86, 87, 88, 100, 101, 102, ...
These numbers look exactly like all base-9 numbers!
Indeed, every base-9 number is a number in this sequence, and every number in this sequence is a base-9 number. Both this sequence and the sequence of all base-9 numbers are in increasing order. The answer is therefore just the n-th base-9 number.
Complexity Analysis
Time Complexity: , since has at most 9 digits.
Space Complexity: .
Analysis written by: @awice.