Codeforces Round #308 (Div. 2)B. Vanya and Books 数学

B. Vanya and Books

Time Limit: 20 Sec

Memory Limit: 256 MB

题目连接

http://codeforces.com/contest/552/problem/B

Description

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.

Sample Input

13

Sample Output

17

HINT

题意

要写n个数，然后问你一个写了多少个数字

比如17这个数，就写了2个数字

题解：

数学题，每一位都是9*10^n个

代码：

#include <cstdio>
#include <cmath>
#include <cstring>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <set>
#include <vector>
#include <sstream>
#include <queue>
#include <typeinfo>
#include <fstream>
#include <map>
#include <stack>
typedef long long ll;
using namespace std;
//freopen("D.in","r",stdin);
//freopen("D.out","w",stdout);
#define sspeed ios_base::sync_with_stdio(0);cin.tie(0)
#define test freopen("test.txt","r",stdin)  
#define maxn 1000010
#define mod 1000000007
#define eps 1e-6
const int inf=0x3f3f3f3f;
const ll infll = 0x3f3f3f3f3f3f3f3fLL;
inline ll read()
{
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
//**************************************************************************************

int main()
{  
    ll n=read();
    ll i=9;
    ll k=1;
    ll ans=0;
    while(n>=i)
    {
        n-=i;
        ans+=i*k;
        k++;
        i=i*10;
    }
    ans+=n*k;
    cout<<ans<<endl;
}