752. Open The Lock

/**

 * 752. Open the Lock

 * You have a lock in front of you with 4 circular wheels.

 * Each wheel has 10 slots: ‘0’, ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, ‘6’, ‘7’, ‘8’, ‘9’.

 * The wheels can rotate freely and wrap around: for example we can turn ‘9’ to be ‘0’, or ‘0’ to be ‘9’.

 * Each move consists of turning one wheel one slot.

 * The lock initially starts at ‘0000’, a string representing the state of the 4 wheels.

 * You are given a list of deadends dead ends, meaning if the lock displays any of these codes,

 * the wheels of the lock will stop turning and you will be unable to open it.

 * Given a target representing the value of the wheels that will unlock the lock,

 * return the minimum total number of turns required to open the lock, or -1 if it is impossible.

 * Example 1:

 * Input: deadends = [“0201″,”0101″,”0102″,”1212″,”2002”], target = “0202”

 * Output: 6

 * Explanation:

 * A sequence of valid moves would be “0000” -> “1000” -> “1100” -> “1200” -> “1201” -> “1202” -> “0202”.

 * Note that a sequence like “0000” -> “0001” -> “0002” -> “0102” -> “0202” would be invalid,

 * because the wheels of the lock become stuck after the display becomes the dead end “0102”.  

* /

See the solution to the problem on github here: https://github.com/zcoderz/leetcode/blob/main/src/main/java/queue/bfs/OpenTheLock.java

The solution to the question is based on BFS where the approach can be applied to other problems as well.

The algorithm is as below:

1. Run a BFS based search using a queue
2. Add markers in queue identifying end of a level so that we can easily calculate the depth in queue so far traversed
3. For each element in the queue
   1. If you reach one of the dead-end elements, skip it
   1. Create all possible transforms that haven’t been so far visited
   1. Add them to queue
   1. Once you reach the target value return the depth so far traversed

Here is the code:

public int openLock(String[] deadends, String target) {
    String start = "0000";
    Queue<String> queue = new LinkedList<>();
    String level = "L";
    queue.add(start);
    queue.add(level);
    Set<String> deads = new HashSet<>();
    Collections.addAll(deads, deadends);
    int passes = 0;
    while (!queue.isEmpty()) {
        String str = queue.poll();
        if (str.equals(level)) {
            passes++;
            if (!queue.isEmpty()) {
                queue.add(level);
            }
            continue;
        }
        if (str.equals(target)) {
            return passes;
        }
        if (deads.contains(str)) {
            continue;
        }
        List<String> possibleTransforms = transform(str);
        queue.addAll(possibleTransforms);
    }
    return -1;
}