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 = 0,left=0,right=0,now=1,a=1;
    while (N/a)
    {
        left = N / (a * 10);
        now = N / a % 10;
        right = N % a;
        if (now == 0)count += left * a;
        else if (now ==1)count += left * a + right + 1;
        else if (now > 1)count += (left + 1) * a;
        a *= 10;
    }
    cout << count;
}