1049 Counting Ones (30分)

The task is simple: given any positive integer N, you are supposed to count the total number of 1's in the decimal form of the integers from 1 to N. For example, given N being 12, there are five 1's in 1, 10, 11, and 12.

Input Specification:

Each input file contains one test case which gives the positive N (≤).

Output Specification:

For each test case, print the number of 1's in one line.

Sample Input:

12

Sample Output:

5

题目分析：一道数学题 题目据说是《编程之美》上的一道题
具体的推法好像很麻烦的样子 之后有时间会看看

 #define _CRT_SECURE_NO_WARNINGS
 #include <climits>
 #include<iostream>
 #include<vector>
 #include<queue>
 #include<map>
 #include<set>
 #include<stack>
 #include<algorithm>
 #include<string>
 #include<cmath>
 using namespace std;

 int main()
 {
     int N;
     cin >> N;
     int count = ,left=,right=,now=,a=;
     while (N/a)
     {
         left = N / (a * );
         now = N / a % ;
         right = N % a;
         if (now == )count += left * a;
         else if (now ==)count += left * a + right + ;
         else if (now > )count += (left + ) * a;
         a *= ;
     }
     cout << count;
 }