Just keep track of the last burger joint you saw and the last restaurant you saw. You can solve this greedily. If you ever find a ‘Z’ then the answer is immediately always 0.

import java.io.PrintWriter;
import java.util.Scanner;

/**
 * 
 * @author Sanchit M. Bhatnagar
 * @see http://uhunt.felix-halim.net/id/74004
 * 
 */
public class P11661 {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);

    while (sc.hasNextLine()) {
      int L = Integer.parseInt(sc.nextLine());
      if (L == 0)
        break;
      char[] road = sc.nextLine().toCharArray();
      int lastDrugStore = -1;
      int lastRestaurant = -1;
      int min = Integer.MAX_VALUE;
      for (int i = 0; i < road.length; i++) {
        if (road[i] == 'R') {
          lastRestaurant = i;
        } else if (road[i] == 'D') {
          lastDrugStore = i;
        } else if (road[i] == 'Z') {
          min = 0;
          break;
        }
        if (lastDrugStore != -1 && lastRestaurant != -1) {
          min = Math.min(Math.abs(lastDrugStore - lastRestaurant), min);
        }
      }
      out.println(min);
    }

    out.close();
    sc.close();
  }

}