Problem:
JPEG Compression

The fundamental idea in the JPEG compression algorithm is to sort coeffi-
cient of given image by zigzag path and encode it. In this problem, we don’t
discuss about details of the algorithm, but you are asked to make simple pro-
gram. You are given single integer N , and you must output zigzag path on
a matrix where size is N by N . The zigzag scanning is start at the upper-left
corner (0, 0) and end up at the bottom-right corner. See the following Figure
and sample output to make sure rule of the zigzag scanning. For example, if you
are given N = 8, corresponding output should be a matrix shown in right-side
of the Figure. This matrix consists of visited time for each element.

Input

Several test cases are given. Each test case consists of one integer N (0 < N <
10) in a line. The input will end at a line contains single zero.

Output

For each input, you must output a matrix where each element is the visited
time. All numbers in the matrix must be right justified in a field of width 3.
Each matrix should be prefixed by a header “Case x:” where x equals test case
number.

Sample Input

3
4
0

Output for the Sample Input

Case 1:
1 2 6
3 5 7
4 8 9
Case 2:
1 2 6 7
3 5 8 13
4 9 12 14
10 11 15 16

Solution in JAVA (judge verdict: Accepted)

import java.util.*;

class Main {

    static void solve (int n) {
        int[][] jpeg = new int [n][n];
        int x = 0;
        int y = 0;
        boolean ascending = true;

        for (int i = 1; i <= n * n; i++) {
            jpeg[x][y] = i;
            if ( ascending && y == 0 && x != n-1 )  {
                x += 1;
                ascending = false;
            } else if ( (!ascending) && x == 0 && y != n-1) {
                y += 1;
                ascending = true;
            } else if ( ascending && x == n-1) {
                y += 1;
                ascending = false;
            } else if ( (!ascending) && y == n-1) {
                x += 1;
                ascending = true;
            } else if (ascending) {
                x += 1;
                y -= 1;
            } else {
                x -= 1;
                y += 1;
            }
        }

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                System.out.printf("%3d", jpeg[j][i]);
            }
            System.out.println("");
        }
    }


    public static void main (String [] args) {

        Scanner sc = new Scanner(System.in);
        int times = 1;

        while (true) {
            int n = sc.nextInt();
            if (n == 0) break;

            System.out.printf("Case %d:\n", times);
            solve(n);
            times += 1;
        }

    }
}