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=,f=;char ch=getchar();
while(ch<''||ch>''){if(ch=='-')f=-;ch=getchar();}
while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
return x*f;
}
//************************************************************************************** int main()
{
ll n=read();
ll i=;
ll k=;
ll ans=;
while(n>=i)
{
n-=i;
ans+=i*k;
k++;
i=i*;
}
ans+=n*k;
cout<<ans<<endl;
}