Number Sequence

Number Sequence

描述
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

输入
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)

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

样例输入
2
8
3
样例输出
2
2

#include 
#include 
#include 
using namespace std;

int len[32000] = {};
 
int main()
{
    int t, n, i, sum = 0;
 
    for(i = 1; sum >= 0; i ++)
    {
        len[i] = len[i-1] + (int)log10(i) + 1;
        sum += len[i];
    }
 
    cin >> t;
 
    while(t--)
    {
        cin >> n;
        //获得最后的sk
        i = 1;
        while(len[i] < n)
            n -= len[i++];
        //获得sk中的最后一个数
        i = 1;
        while((int)log10(i) + 1 < n)
        {
            n -= (int)log10(i) + 1;
            i++;
        }
        //i就是这个数
        i /= pow(10, (int)log10(i) + 1 - n);//没有被打印出来的位数作为幂，没被打出来的是后半部分，直接除掉
        i %= 10;//最后一位
        cout << i << endl;
    }
}