codeforces 552B Vanya and Books

最新推荐文章于 2018-04-13 21:36:02 发布

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本文介绍了一种计算从1到n所有整数位数总和的方法，并提供了完整的C++实现代码。通过分析不同位数的贡献，实现了高效计算。

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Vanya got an important task — he should enumerate books in the library and label each book with its number. Each of the n books should be assigned with a number from 1 to n. Naturally, distinct books should be assigned distinct numbers.

Vanya wants to know how many digits he will have to write down as he labels the books.

Input

The first line contains integer n (1 ≤ n ≤ 109) — the number of books in the library.

Output

Print the number of digits needed to number all the books.

        Examples
      
          input
        
13

          output
        
17

          input
        
4

          output
        
4

Note

Note to the first test. The books get numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, which totals to 17 digits.

Note to the second sample. The books get numbers 1, 2, 3, 4, which totals to 4 digits.

题意：求1到n的所有位数和。

设x∈[1,n]，当x不包含最高位时，9+90*2+900*3……+最多位的位数和。

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
int mod=1000000000;
int main()
{
    char s[15];
    while(cin>>s)
    {
        int len=strlen(s);
        ll n=0;
        for(int i=0;i<len;i++)
            n=n*10+s[i]-'0';
        ll mo=1;
        for(int i=1;i<len;i++)
            mo*=10;
        ll a=(n-mo+1)*len,b=0,k=9;
        for(int i=0;i<len-1;i++)
        {
            b+=k*(i+1);
            k*=10;
        }
        cout<<a+b<<endl;
    }
    return 0;
}