PAT Counting Ones

链接： https://www.nowcoder.com/questionTerminal/eb1e0fc83a25461e93b8bf2039e871b9
来源：牛客网

[编程题]Counting Ones (30)

• 热度指数：399时间限制：1秒空间限制：65536K
• 算法知识视频讲解

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

输入描述:

Each input file contains one test case which gives the positive N (<=230).

输出描述:

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

示例1

输入

12

输出

5

这道题目求小于等于一个数的所有数中1的个数。按位从高到低来计算，计算每一位对应的小于这个数的数的数目，相加就可以了。

if the number of the digit is bigger than 1,then the amount is (the number composed of the left digtis+1)*10^(how many digits on the right )

if the number of the digit equals 1,then the amount is (the number composed of the left digits)*10^(how many ……)+(the number composed of the right digits+1)

if smaller then 1,the amount will be (the number composed of the left digits )*10^(how many……)

we can see that all the possibilities lie in three parts.

// pat.cpp : 定义控制台应用程序的入口点。
//

//#include "stdafx.h"
#include
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#include