233. Number of Digit One

Topic:

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.

Links: http://leetcode.com/problems/number-of-digit-one/

Exercises

is a mathematical problem, the main idea is to do it by hand. There are some other solutions, two brushes to understand the best solution.

Let's step through the analysis:

1. N < 1 o'clock with a result of 0
2. 1 <= N < 10 o'clock with a result of 1
Assuming n = 312, we break this calculation process down into several steps:
1. (1 ~ 99) with a result of Countdigitone (99)
2. (100 ~ 199), result is + countdigitone (99)
3. (200 ~ 299) with a result of Countdigitone (99)
4. (300 ~ 312) with a result of Countdigitone (12)
3. Assuming n = 112, we also decompose this calculation process:
   1. (1 ~ 99) with a result of Countdigitone (99)
   2. (100 ~ 112), result 112-100 + 1 + countdigitone (12)
4. As a result, we can introduce the general formula

Time Complexity-o (log10n), Space complexity-o (log10n)

 Public classSolution { Public intCountdigitone (intN) {if(N < 1)            return0; if(N < 10)            return1; intBaseinten = (int) Math.pow (string.valueof (n). Length ()-1); intHighestdigit = N/baseinten;//get the highest digit of n                if(Highestdigit = = 1)            returnCountdigitone (baseInTen-1) + (N-baseinten + 1) + countdigitone (n%Baseinten); Else            returnHighestdigit * Countdigitone (baseInTen-1) + Baseinten + countdigitone (n%Baseinten); }}

Reference:

Https://leetcode.com/discuss/44281/4-lines-o-log-n-c-java-python

Https://leetcode.com/discuss/44279/clean-c-code-of-log10-complexity-with-detailed-explanation

Https://leetcode.com/discuss/44314/accepted-solution-using-counting-principle-with-explanation

Https://leetcode.com/discuss/44465/my-ac-java-solution-with-explanation

Https://leetcode.com/discuss/44617/my-recursion-implementation

Https://leetcode.com/discuss/47774/0ms-recursive-solution-in-c-8-line-code

Https://leetcode.com/discuss/46366/ac-short-java-solution

Https://leetcode.com/discuss/64604/my-simple-and-understandable-java-solution

Https://leetcode.com/discuss/64962/java-python-one-pass-solution-easy-to-understand

Https://leetcode.com/discuss/54107/0-ms-recursive-solution

Https://leetcode.com/discuss/58868/easy-understand-java-solution-with-detailed-explaination

233. Number of Digit One