Search path of a word in a matrix

SearchPathOfAWordInMatrix.java

public class WordPath{
  class Coordinate{
    public int x;
    public int y;
    public Coordinate(int x, int y){
      this.x = x;
      this.y = y;
    }
  }

  char[][] matrix = {{'a', 'b', 'c', 'd', 'e'},
                     {'f', 'g', 'h', 'i'},
                     {'j', 'k', 'l', 'm', 'n'},
                     {'o', 'p', 'q', 'r', 's'},
                     {'t', 'u', 'v', 'w'},
                     {'x', 'y', 'z'}};

  public static void main(String[] args){
    String word = "google";
    WordPath wP = new WordPath();
    String path = wP.searchPath(word.toLowerCase());
    System.out.println(path);
  }

  public String searchPath(String word){
    if(word == null || word.length() == 0){
      return null;
    }
    HashMap<Character, Coordinate> map = new HashMap<Character, Coordinate>();
    for(int i = 0; i < matrix.length; i++){
      for(int j = 0; j < matrix[i].length; j++){
        map.put(matrix[i][j], new Coordinate(i, j));
      }
    }
    StringBuilder path = new StringBuilder();
    Coordinate previous = null, current = null;
    String p;
    for(int i = 0; i < word.length(); i++){
      current = map.get(word.charAt(i));
      if(previous == null){
        p = getDirection(new Coordinate(0, 0), current);
        path.append(p);
        previous = current;
      } else{
        p = getDirection(previous, current);
        path.append(p);
        previous = current;
      }
    }
    return path.toString();
  }

  private String getDirection(Coordinate prev, Coordinate curr){
    StringBuilder path = new StringBuilder();
    int xDiff = curr.x - prev.x;
    int yDiff = curr.y - prev.y;
    if(xDiff == 0 && yDiff == 0){ // Same Location
      path.append('!');
    }
    if(xDiff > 0){ // Go Down
      appendNTimes(path, 'D', xDiff);
    } else if(xDiff < 0){ // Go Up
      appendNTimes(path, 'U', Math.abs(xDiff));
    }
    if(yDiff > 0){ // Go Right
      appendNTimes(path, 'R', yDiff);
    } else if(yDiff < 0){ // Go Left
      appendNTimes(path, 'L', Math.abs(yDiff));
    }
    return path.toString();
  }

  private void appendNTimes(StringBuilder path, char direction, int n){
    for(int i = 0; i < n; i++){
      path.append(direction);
    }
  }
}