Solution for https://www.coderbyte.com/editor/guest:Correct%20Path:Java

solution.java

import java.awt.Point;
import java.util.Scanner;

class Main {
  
  public static String CorrectPath(String str) { 
    return findWay(new Point(0, 0), str);
  }
  
  public static String findWay(Point from, String using) {
	  // check if we are out of the grid
      if (from.x < 0 || from.x >= 5) return null;
      if (from.y < 0 || from.y >= 5) return null;
      // check if we reached the target (4, 4)
      if (using.length() == 0) {
    	  if (from.x == 4 && from.y == 4) return "";
    	  else return null;
      }
      
      // check in which directions we are allowed to continue
      String fst = using.substring(0, 1);
      Movement[] movementsToExplore;
      if ("?".equals(fst)) {
    	  movementsToExplore = Movement.values();
      } else {
    	  movementsToExplore = new Movement[1];
    	  movementsToExplore[0] = Movement.valueOf(fst);
    	  if (movementsToExplore[0] == null) {
    		  throw new RuntimeException("Invalid question");
    	  }
      }
      
      // for each direction continue recursively
	  for (Movement m : movementsToExplore) {
		  Point nextTile = new Point(from.x + m.x, from.y + m.y);
		  String way = findWay(nextTile, using.substring(1));
		  if (way != null) {
			  return m.toString() + way;
		  }
	  }
	  
	  // there was no way
	  return null;
  }
  
  public static void main (String[] args) {  
    // keep this function call here     
    Scanner s = new Scanner(System.in);
    System.out.print(CorrectPath(s.nextLine())); 
  }
  
  private static enum Movement {
      l(-1, 0), r(1, 0), u(0, -1), d(0, 1);
      
      final int x;
      final int y;
      
      Movement(int x, int y) {
          this.x = x;
          this.y = y;
      }
  }
  
}