uva 10161 Ant on a Chessboard（蛇型矩阵）

Problem A.Ant on a Chessboard

 

Background

  One day, an ant called Alice came to an M*M chessboard. She wanted to go around all the grids. So she began to walk along the chessboard according to this way: (you can assume that her speed is one grid per second)

  At the first second, Alice was standing at (1,1). Firstly she went up for a grid, then a grid to the right, a grid downward. After that, she went a grid to the right, then two grids upward, and then two grids to the left…in a word, the path was like a snake.

  For example, her first 25 seconds went like this:

  ( the numbers in the grids stands for the time when she went into the grids)

 

25	24	23	22	21
10	11	12	13	20
9	8	7	14	19
2	3	6	15	18
1	4	5	16	17

5

4

3

2

1

 

1          2          3           4           5

At the 8^th second , she was at (2,3), and at 20^th second, she was at (5,4).

Your task is to decide where she was at a given time.

(you can assume that M is large enough)

 

 

Input

  Input file will contain several lines, and each line contains a number N(1<=N<=2*10^9), which stands for the time. The file will be ended with a line that contains a number 0.

 

 

Output

  For each input situation you should print a line with two numbers (x, y), the column and the row number, there must be only a space between them.

 

 

Sample Input

8

20

25

0

 

 

Sample Output

2 3

5 4

1 5

题目大意：找到数字对应的行和列。

解题思路：找规律，奇数行，起始为行数的平方。偶数列，起始为列数的平方。行和列有与数字匹配的规律。

#include<iostream>
#include<math.h>
using namespace std;

int main()
{
	int n;

	while (cin >> n, n)
	{
		int a, b;
		// Find.
		for (int i = 0; ; i++)
			if (n <= pow(i + 1, 2))
			{	a = i;
				b = i + 1;
				break;
			}

		int t = pow(b, 2) - n;

		// Print.
		if (b % 2)
		{
			if (t < b)
				cout << t + 1 << " " << b << endl;
			else 
				cout << b << " " << n - pow(a, 2) << endl;
		}
		else 
		{
			if ( t < b)
				cout << b << " " << t + 1 << endl;
			else
				cout << n - pow(a, 2) << " " << b << endl;
		}
	}
	return 0;
}