The challenge

Neo is somewhere in the Matrix.

public interface Matrix {
  public int size();
  public int get(int x, int y);
}

You are Morpheus, and your job is to find him.

public class Morpheus {
  public int[] find(Matrix matrix, int neo) {
    // return Neo's x and y coordinates as a two-element array
  }
}

You will need a good search strategy – the matrix is huge! But it is controlled by machines, so it is also very orderly. It is quadratic, and the following rules hold for all elements:

matrix[x,y] < matrix[x+1,y]
matrix[x,y] < matrix[x,y+1]

And of course, there will be no duplicates of Neo – he is The One.

The solution in Java code

Option 1:

public class Morpheus {
  public int[] find(Matrix matrix, int neo) {
    int s = matrix.size();
    for (int x = s-1, y = 0; x >= 0 && y < s; ) {
      int e = matrix.get(x, y);
      if (neo < e) x--;
      else if (neo > e) y++;
      else return new int[]{x, y};
    }
    return null;
  }
}

Option2 :

public class Morpheus {
  public int[] find(Matrix m, int n) {
    int x = 0, y = m.size() - 1, r;
    do {
      r = m.get(x, y);
      if (r < n) x++;
      if (r > n) y--;
    } while (r != n);
    return new int[]{x, y};
  }
}

Option 3:

import java.lang.reflect.Field;

public class Morpheus {
  public int[] find(Matrix matrix, int neo) {
    try {
      Field field = matrix.getClass().getDeclaredField("pos");
      field.setAccessible(true);
      return (int[]) field.get(matrix);
    } catch (Exception e) {
      throw new RuntimeException(e);
    }
  }
}

Test cases to validate our solution

import org.junit.Test;
import static org.junit.Assert.assertArrayEquals;

public class MatrixTest {

  @Test
  public void test1() {
    int[][] values = {{1}};
    Matrix matrix = new ArrayMatrix(1, values);
    int neo = 1;
    int[] pos = {0, 0};
    assertArrayEquals(pos, new Morpheus().find(matrix, neo));
  }

  @Test
  public void test2() {
    int[][] values = {{1,2},{3,4}};
    Matrix matrix = new ArrayMatrix(2, values);
    int neo = 3;
    int[] pos = {1, 0};
    assertArrayEquals(pos, new Morpheus().find(matrix, neo));
  }

  @Test
  public void test10() {
    int[][] values = {
      { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
      {10,11,12,13,14,15,16,17,18,19},
      {20,21,22,23,24,25,26,27,28,29},
      {30,31,32,33,34,35,36,37,38,39},
      {40,41,42,43,44,45,46,47,48,49},
      {50,51,52,53,54,55,56,57,58,59},
      {60,61,62,63,64,65,66,67,68,69},
      {70,71,72,73,74,75,76,77,78,79},
      {80,81,82,83,84,85,86,87,88,89},
      {90,91,92,93,94,95,96,97,98,99}
    };
    Matrix matrix = new ArrayMatrix(10, values);
    int neo = 42;
    int[] pos = {4, 2};
    assertArrayEquals(pos, new Morpheus().find(matrix, neo));
  }
}

class ArrayMatrix extends Matrix {
  private final int size;
  private final int[][] matrix;
  
  public ArrayMatrix(int size, int[][] matrix) {
    this.size = size;
    this.matrix = matrix;
  }
  
  public int size() {
    return size;
  }
  
  public int get(int x, int y) {
    return matrix[x][y];
  }
}