UVA 10161 Ant on a Chessboard Solution

Problem Statement : 

 

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

#include <iostream>
#include <cstdio>
#include <cmath>

using namespace std;


int main()
{
    long N,i,j,k,l,n,x,y;

    while(scanf("%ld",&N) && N){
        n = sqrt(N * 1.);
        N -= n*n;
        if(!N){
            if(n & 1){
                x = 1;
                y = n;
            }
            else{
                x = n;
                y = 1;
            }
        }else{
            n++;
            x = y = n;
            if(n & 1){
                if(N <= n)
                    y = N;
                else
                    x -= N%n;

            }
            else{
                if(N <= n)
                    x = N;
                else
                    y -= N%n;
            }
        }
        printf("%ld %ld\n",x,y);

    }
    return 0;
}