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;elsecout << n - pow(a, 2) << " " << b << endl;}}return 0;}