UVa 10161 Ant on a Chessboard (简单数学)

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 8th second , she was at (2,3), and at 20th 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
。.....A.C.............................................................................................................................................................................

#include<stdio.h>

#include<math.h>

int main()

{
int step;  

    while (scanf("%d",&step)!=EOF,step>=1)  

    {  

        int column = (int)ceil(sqrt(step)); 

        int diagonal = column * (column - 1) + 1;  

        if (column&1)//判断奇偶性  

        {  

            if (step >= diagonal)  

                printf("%d %d\n",column - (step - diagonal),column);  

            else  

                printf("%d %d\n",column,column - (diagonal - step));   

        }  

        else//奇数 

        {  

            if (step >= diagonal)  

               printf("%d %d\n",column,column-(step-diagonal));  

            else  

               printf("%d %d\n",column-(diagonal-step),column);  

        }  

    }  

    return 0;  

}