660. Remove 9


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.


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Approach #1: Mathematical

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Intuition

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Let\'s write the first numbers and try to notice a pattern. Those numbers are:

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1, 2, 3, 4, 5, 6, 7, 8,\n10, 11, 12, 13, 14, 15, 16, 17, 18,\n20, 21, 22, 23, 24, 25, 26, 27, 28,\n...\n80, 81, 82, 83, 84, 85, 86, 87, 88,\n100, 101, 102, ...\n
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These numbers look exactly like all base-9 numbers!

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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.

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Complexity Analysis

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    Time Complexity: , since has at most 9 digits.

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    Space Complexity: .

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Analysis written by: @awice.

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