233 Number of Digit One

Given an integer n, count the total number of digit 1 appearing in all non-negative integers less than or equal to n.

For example:
Given n = 13,
Return 6, because digit 1 occurred in the following numbers: 1, 10, 11, 12, 13.

输入一个整数n，求从1到n这n个整数的十进制表示中1出现的次数。

C++:

class Solution {
public:
    int countDigitOne(int n) {
        int cnt = 0 ;
        for(long long  m = 1 ; m <= n ; m*=10){
            int a = n/m ;
            int b = n%m ;
            cnt += (a+8)/10 * m + ((a%10 == 1) ? b+1 : 0) ;
        }
        return cnt ;
    }
};