poj 1019 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 <cstdio>
#include <cmath>
#define N 40000
using namespace std;
unsigned int a[N],sum[N];
void init()
{
a[1]=1;
sum[1]=1;
for (int i=2;i<31270;i++)
a[i]=a[i-1]+(int)log10((double)i)+1,sum[i]=sum[i-1]+a[i];
}
main()
{
int T,n;
init();
scanf("%d",&T);
while(T--)
{
scanf("%d",&n);
int i=1;
while(sum[i]<n) i++;
int pos=n-sum[i-1],ans=0;
for (i=1;ans<pos;i++)
ans+=(int)log10((double)i)+1;
printf("%dn",(i-1)/(int)pow(10.0,ans-pos)%10);
}
}