Open the Lock

Hard

BFS

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, 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.

This is a state-space BFS problem. Each lock state is a node, and each single-wheel rotation is an edge. BFS finds the minimum number of moves.

Example 1

Input: deadends = ["0201","0101","0102","1212","2002"], target = "0202"

Output: 6

Explanation: A sequence of valid moves: "0000" -> "1000" -> "1100" -> "1200" -> "1201" -> "1202" -> "0202". Note that "0000" -> "0001" -> "0002" -> "0102" -> "0202" won't work because "0102" is a deadend.

Example 2

Input: deadends = ["8888"], target = "0009"

Output: 1

Explanation: We can turn the last wheel in reverse to move from "0000" -> "0009".

Example 3

Input: deadends = ["8887","8889","8878","8898","8788","8988","7888","9888"], target = "8888"

Output: -1

Explanation: We cannot reach the target without getting stuck.

Constraints

•1 <= deadends.length <= 500
•deadends[i].length == 4
•target.length == 4
•target will not be in the list deadends
•target and deadends[i] consist of digits only

Show Hints (5)

Hint 1: Think of each lock state as a node in a graph.

Hint 2: From each state, you can reach 8 neighboring states (4 wheels x 2 directions).

Hint 3: Use BFS to find the shortest path from "0000" to target.

Hint 4: Use a set to track visited states and deadends to avoid revisiting.

Hint 5: Consider bidirectional BFS for optimization on larger inputs.

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