Solution for a question, that there is a chesstable 4x4, you are starting from left lower corner to right upper corner. You should print all alternative paths to go, and solution should be recursive? (There are 2 different solutions below. 2nd solution below is a simple search algorithm, 1st solution is a simpler DFS solution)

ChessPath.java

public class ChessPath {
	private static int length = 4;
	public static void main(String[] args) {
		String headStr = "";
		getPath(1, 0, false, headStr);
		getPath(0, 1, true, headStr);
	}
	
	public static void getPath(int xC, int yC, boolean upD, String path) {
		if(xC == length || yC == length) return;
		if(upD) path += "U";
		else path += "R";
		if(xC == (length - 1) && xC == yC) {
			System.out.println(path);
			return;
		}
		getPath(xC + 1, yC, false, path);
		getPath(xC, yC + 1, true, path);
	}
}

PathFinding.java

public class PathFinding {

	static int GRID_LENGTH = 4;
	static PathFinding pathFinding = new PathFinding();
	public static void main(String[] args) {
		String str = "";
		Node head = pathFinding.new Node(0, 0, str);
		searchNode(head);
	}
		
	public static void searchNode(Node node) {
		List<Node> nodeList = node.getAvailableNodes();
		if(nodeList.size() == 0) {
			System.out.println(node);
			return;
		} else {
			for(Node iNode : nodeList) {
				searchNode(iNode);
			}
		}
	}

	class Node {
		int rightC = 0;
		int upC = 0;
		String str = "";
		
		public Node(int rightC, int upC, String str) {
			this.rightC = rightC;
			this.upC = upC;
			this.str = str;
		}
		
		public List<Node> getAvailableNodes() {
			List<Node> availableNodes = new ArrayList<Node>();
			if(rightC < GRID_LENGTH - 1) {
				String newStr = new String(str + "R");
				Node rightNode = new Node(rightC + 1, upC, newStr);
				availableNodes.add(rightNode);
			}
			if(upC < GRID_LENGTH - 1) {
				String newStr = new String(str + "U");
				Node upNode = new Node(rightC, upC + 1, newStr);
				availableNodes.add(upNode);
			}
			return availableNodes;
		}
		
		@Override
		public String toString() {
			return str;
		}
	}
}