PAT-A-1049-Counting Ones

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

Code

#include <iostream>

using namespace std;

int main(){
	int n,a=1,ans=0;
	//从低位到高位遍历一个数，将其分为left now right三个部分，并讨论now=0、1、大于1三种情况下的结果
    int left,now,right;
	scanf("%d",&n);

    //从低位到高位遍历每个数
    while(n/a!=0){
        left = n/(a*10);
        now = n/a%10;
        //任何数取余1都为0
        right = n%a;
        if(now==0)
            ans+=left*a;
        else if(now==1)
            ans+=left*a+right+1;
        else
            ans+=(left+1)*a;
        a*=10;
    }

    printf("%d",ans);

	return 0;
}