poj 1019 Number Sequence 二分

Number Sequence

Description

A single positive integer i is given. Write a program to find the digit located in the position i in the sequence of number groups S1S2...Sk. Each group Sk consists of a sequence of positive integer numbers ranging from 1 to k, written one after another.

For example, the first 80 digits of the sequence are as follows:

11212312341234512345612345671234567812345678912345678910123456789101112345678910

Input

The first line of the input file contains a single integer t (1 ≤ t ≤ 10), the number of test cases, followed by one line for each test case. The line for a test case contains the single integer i (1 ≤ i ≤ 2147483647)

Output

There should be one output line per test case containing the digit located in the position i.

Sample Input

2
8
3

Sample Output

2
2

#include<iostream>
#include<cstring>
#include<cmath>
using namespace std;
typedef long long ll;

const ll maxn=40000;
ll a[maxn],b[maxn];
void init(){
    a[1]=b[1]=1;
    for(ll i=2;i<maxn;i++){
        a[i]=a[i-1]+(int)log10((double)i)+1;
        b[i]=b[i-1]+a[i];
    }
    return ;
}

ll f(ll m){
    ll i=1;
    while(b[i]<m)   i++;
    int p=m-b[i-1];
    int len=0;
    for(i=1;len<p;i++)
        len+=(int)log10((double)i)+1;
    return (i-1)/(int)pow((double)10,len-p)%10;
}

int main(){
    init();
    int T;
    cin>>T;
    while(T--){
        ll n;
        cin>>n;
        cout<<f(n)<<endl;
    }
}