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
Source
Tehran 2002, First Iran Nationwide Internet Programming Contest
题目大意就是给你这一串数字11212312341234512345612345671234567812345678912345678910123456789101112345678910……(未列完)
要我们求出第n个数是多少(从左到右看),例如第2个是1,第三个是2,第八个是2;
如果仔细观察这一串数字,可以发现他可以还分为很多小串,假设第i小串是123……i,假设第i小串所占的空间是a[i],则通过对比a[i]与a[i+1]发现,
第i+1串只比第i串多一个数,即i+1,故他们所占的空间差就是第i+1所占的空间。
对任意一个数所占的空间很好求,即 (int)log10(k)+1;
然后就可以求出每一个串的起始位置,通过与n比较就可以确定n出现在那一个串里,最后在求出n在这个串里的相对位置,就可以求出该题的解
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