Timus 1209. 1, 10,100,100 0...

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Timus 1209. 1, 10,100,100 0... requires that the value at the specified position of a specific sequence be given.

1209. 1, 10,100,100 0... time limit: 1.0 second
Memory limit: 16 mblet's consider an infinite sequence of digits constructed of ascending powers of 10 written one after another. Here is the beginning of the sequence: 110100100010000... You are to find out what digit is located at the definite position of the sequence. inputthere is the only positive integer number NIn the first line, N& Lt; 65536. I-Th NLeft lines contains the positive integer Ki-The number of positions in the sequence. It's given that Ki<231. outputyou are to output NDigits 0 or 1 separated with a space. More precisely, I-Th digit of output is to be equal to Ki-Th digit of described above sequence. Sample

Input	Output
4 3 14 7 6	0 0 1 0

Problem Author:Alexey lakhtin
Problem Source:USU open Collegiate Programming Contest October '2002 Junior session

This question is, let's consider an infinite sequence consisting of 10 non-negative integer power connections in turn: 110100100010000 .... Your task is to give the value of the specified position of the sequence.

Through careful observation, we can see that the first 1 in the sequence (x + 1) is located in the nth = 1 + (1 + 2 +... x) = 1 + x (x + 1)/2 positions. Solve the quadratic equation of x and obtain the non-negative root of X = (√ 8n-7-1)/2. Therefore, when X is an integer, the value of the nth position in the sequence is 1, and the value of other positions is 0.

The corresponding C # program is as follows:

1 using system;
2
3 // http://acm.timus.ru/problem.aspx? Space = 1 & num = 1209
4 class t1209
5 {
6 static void main ()
7 {
8 For (INT I = int. parse (console. Readline (); I> 0; I --)
9 {
10 double X = (math. SQRT (8.0 * Int. parse (console. Readline ()-7)-1)/2;
11 console. Write (x = (INT) x )? 1: 0) + "");
12}
13}
14} Returned directory