Remove 9

Hard Mathematics

LeetCode: https://leetcode.com/contest/leetcode-weekly-contest-45/problems/remove-9/

Question

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

Input: 9
Output: 10

Hint: n will not exceed 9 x 10^8.

Thinking

This is a radix problems. The radix is 9. How to convert the value form radix 10 to radix 9?
see: 二、八、十、十六进制转换（图解篇）

Solution

Java

public class Solution {
    public int newInteger(int n) {
        int num = 0;
        int base = 1;
        while (n > 0) {
            num = base * (n % 9) + num;
            n = n / 9;
            base = base * 10;
        }
        return num;
    }
}