poj 1019(组外偏移->组内偏移)

Number Sequence

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 31916		Accepted: 9075

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

简单的组合数学。思路是：先判断num是在第几组（题目中的Sk）,再计算出组内偏移（用num减去这个组之前的累计数字个数）。然后计算出 那个组的组内偏移位置数字是多少。

需要细心一些。第一次样例没有过是因为sum[i] - num这个计算出来的实际上是组内的倒着数的偏移量，因此需要用belong[i]减去这个值才能得到正数偏移量。

每时每刻都需要知道每个值是 从0计数还是从1计数。为了安全起见，本程序所有计数都 统一从1开始。

提交记录：

1、Accepted！

代码：