hihocoder#1349 : Nature Numbers(思维)

时间限制:10000ms

单点时限:1000ms

内存限制:256MB

描述

Consider the following sequence S which is constrcuted by writting nature numbers one by one: "012345678910111213...".

The first digit of S, S[0], is 0. The second digit S[1] is 1. And the 11th digit S[10] is 1.

Given an integer N, can you find the digit S[N]? 

输入

An integer N. (0 <= N <= 1018)

输出

Digit S[N].

样例输入

17

样例输出

3

思路：易知1位数有9个(不包括0)，2位数有90个，3位数有900个，4位数有9000个，以此类推。。。可以算出s[n]在几位数里面。然后算出s[n]在哪个整数里面。答案就出来了。

#include<bits/stdc++.h>using namespace std;int main(){long long n,s,num,i,ans;cin>>n;if(n==0)puts("0");else    {        s=0,num=9,i=1;//i代表位数，num代表i位数有多少个        while(n>=s+num*i)        {            s+=num*i;            i++;            num*=10;        }        n-=s;        num=(num/9)-1;        num+=n/i;//num代表s[n]所在的整数        n%=i;        if(n==0)printf("%d\n",num%10);        else        {            num++;            stack<int>p;            while(num)p.push(num%10),num/=10;            while(n)            {                ans=p.top();                p.pop();                n--;            }            cout<<ans<<endl;        }    }return 0;}