1049. Counting Ones (30)-PAT

1049. Counting Ones (30)

时间限制

10 ms

内存限制

32000 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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

推荐指数：※※

来源：http://pat.zju.edu.cn/contests/pat-a-practise/1049

这道题在剑指offer上面也有，不错个人觉得http://blog.youkuaiyun.com/sunbaigui/article/details/8672335分别计算每一位1更为高效和好理解。

#include <iostream>
using namespace std;
int Count(int n)
{
	int sum,now,left,right;
	int base;
	base=1;
	sum=0;
	while(n/base!=0){
		now=(n/base)%10;/*the number of now*/
		left=n/(base*10);/*the number of left*/
		right=n%base;/*the number of right*/
		if(now==0){
			sum+=left*base;
		}
		else if(now==1)
		{
			sum+=left*base+right+1;
		}
		else
		{
			sum+=(left+1)*base;
		}
		base=base*10;
	}
	return sum;
}
int main()
{
	int n;
	cin>>n;
	cout<<Count(n)<<endl;
	return 0;
}