Leetcode 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.

Hint:

1. Beware of overflow.

Problem Solving Ideas:

To see the answer. Very burning brain, did not see very clearly.

This problem is actually equivalent to a law-finding problem. So to find out the rules, let's start by listing all the numbers that contain 1, and count each of the 10, as follows:

Number of

1           numbers with 1                                                                             Number range

1                    1                                                                                         [1, 9]

11 10 11 12 13 14 15 16 17 18 19 [10, 19]

1 21 [20, 29]

1                    31                                                                                       [in]

1                    41                                                                                       [+]

1                    51                                                                                       []

1                    61                                                                                       [up]

1                    71                                                                                       [+]

1                    81                                                                                       [+]

1 91 [90, 99]

11 100 101 102 103 104 105 106 107 108 109 [100, 109]

21 110 111 112 113 114 115 116 117 118 119 [110, 119]

11 120 121 122 123 124 125 126 127 128 129 [120, 129]

...                  ...                                                                                  ...

As we can see from the above list, there are only 1 of the numbers within 100, except for 11 ' 1 ' between 10-19. If we don't consider the more than 10 ' 1 ' on the [10, 19] interval, then we can add two more to the number of 10 digits (plus 1) on any 1-digit, 10-digit number. For example, 56 have (5+1) +10=16. How to know whether to add more than 10, we have to see whether the number on the 10-bit is greater than or equal to 2, is to add the extra 10 ' 1 '. Then we can use (x+8)/10来 to determine whether a number is greater than or equal to 2. The same is true for three-bit numbers, except for the 10 numbers that are extra between [110, 119] and the remaining 10 ' 11 ', the same method can be used to determine and accumulate the number of 1.

Java Code:

 Public class Solution {    publicint countdigitone (int  n) {        int res = 0 , a = 1, b = 1;          while (n > 0) {            + = (n + 8)/ten * a + (n% = = 1? b:0)            ; + = n% * A;             *=;             /=;        }         return res;    }}

Reference:

1. http://www.cnblogs.com/grandyang/p/4629032.html

2. Https://leetcode.com/discuss/44281/8-lines-o-log-n-c-java-python

Leetcode Number of Digit one