UVa 10427 - Naughty Sleepy Boys

　　题目大意：从1开始往后写数字，构成一个如下的字符串 123456789101112... 。求第n位的数字是多少。

　　找规律，按数字的位数可以构建一个类似杨辉三角的东西，求出第n位是哪个数的第几位即可。

#include <cstdio>
#include <cmath>

int main()
{
#ifdef LOCAL
    freopen("in", "r", stdin);
#endif
    int table[9] = {0};
    int base = 9;
    for (int i = 1; i <= 8; i++)
    {
        table[i] = i * base;
        base *= 10;
    }
    for (int i = 1; i <= 8; i++)
        table[i] += table[i-1];
    int n;
    while (scanf("%d", &n) != EOF)
    {
        int k = 1;
        while (table[k] < n)   k++;
        double t1 = 1.0 * (n - table[k-1]) / k;
        int offset = (int)ceil(t1);  // n is offset-th num of k-th row
        int t2 = (n - table[k-1] - 1) % k + 1;  // the t2-th digit of the num    
        int t3 = 0;
        for (int i  = 1; i <= k-1; i++)
            t3 = t3*10 + 9;
        int m = t3 + offset;  // the compete num  
        for (int i = 0; i < k-t2; i++)   m /= 10;
        printf("%d\n", m % 10);
    }
    return 0;
}