Searching in the "roundly" sorted square 2^n x 2^n matrix

RoundSortSearch.java

import static java.nio.charset.StandardCharsets.US_ASCII;

import java.io.IOException;
import java.nio.file.Files;
import java.nio.file.Path;
import java.util.Scanner;

public class RoundSortSearch {

	public static void main(String[] args) throws IOException {
		var reader = Files.newBufferedReader(Path.of("matrix.txt"), US_ASCII);
		var scanner = new Scanner(reader);
		var a = readMatrix(scanner);
		int x = scanner.nextInt();
		
		if (search(a, x)) {
			System.out.println("Found");
		} else {
			System.out.println("Not found");
		}
	}

	private static int[][] readMatrix(Scanner scanner) {
		int n = scanner.nextInt();
		var mat = new int[n][n];
		
		for (int i = 0; i < n; ++i) {
			for (int j = 0; j < n; ++j) {
				mat[i][j] = scanner.nextInt();
			}
		}
		
		return mat;
	}
	
	private static boolean search(int[][] mat, int num) {
		if (!square(mat)) {
			throw new IllegalArgumentException("matrix is not square");
		}
		
		int dim = mat.length;
		int topRow = 0;
		int leftColumn = 0;
		
		while (dim > 1) {
			if (dim % 2 != 0) {
				throw new IllegalArgumentException("matrix dimension is not a power of two");
			}
			
			int qdim = dim / 2; // quarter dimensions
			
			// Order of checks is important.
			if (num >= mat[topRow + qdim][leftColumn]) {
				// has to be in the bottom left quarter
				topRow += qdim;
			} else if (num >= mat[topRow + qdim][leftColumn + qdim]) {
				// has to be in the bottom right quarter
				topRow += qdim;
				leftColumn += qdim;
			} else if (num >= mat[topRow][leftColumn + qdim]) {
				// has to be in the top right quarter
				leftColumn += qdim;
			}

			// If all the conditions above give false, it's in the top left quarter
			// and topRow and leftColumn don't change.
			
			dim = qdim;
		}
		
		return mat[topRow][leftColumn] == num;
	}
	
	private static boolean square(int[][] mat) {
		int n = mat.length;
		int i = 0;
		
		while (i < n && mat[i].length == n) {
			++i;
		}
		
		return i == n;
	}
}

https://stackoverflow.com/q/70640297/17695211