1049. Counting Ones (30)

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 (<=2³⁰).

Output Specification:

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

Sample Input:

12

Sample Output:

5

 1 #include <iostream>
 2 #include <cmath>
 3 #include <string>
 4
 5 using namespace std;
 6
 7 int ToInt(string num)
 8 {
 9     int res = 0;
10     for (int i = 0; i < num.size(); i++)
11         res = res * 10 + num[i] - ‘0‘;
12     return res;
13 }
14
15 int CountingOnes(string num)
16 {
17     if (num.size() == 1)
18     {
19         if (num == "0")
20             return 0;
21         else
22             return 1;
23     }
24     else
25     {
26         int total = 0;
27         int first = num[0] - ‘0‘;
28         string sub = string(num.begin() + 1, num.end());
29         if (first == 1)
30             total += (ToInt(sub) + 1);
31         else if (first > 1)
32             total += pow(10, sub.size());
33         total += CountingOnes(sub) + first * CountingOnes(string(sub.size(), ‘9‘));
34         return total;
35     }
36 }
37
38 int main()
39 {
40     string num;
41     cin >> num;
42
43     cout << CountingOnes(num);
44 }