Microsoft interview coding question: Lock wheel string transformation

Problem Statement Determine the minimum number of operations required to transform a starting string "000" into a specific destination string (e.g., "222") given a list of "deadend" strings (e.g.,

Problem Statement Determine the minimum number of operations required to transform a starting string "000" into a specific destination string (e.g., "222") given a list of "deadend" strings (e.g., {"111", "101"}). *

Mechanism: The string represents lock wheels where each digit (0-9) can be rotated. *

Movement: Rotations are bidirectional (e.g., 0 to 1 or 0 to 9) and wrap around. *

Cost: Each rotation of one wheel counts as 1 operation. *

Constraints: If the string matches a "deadend," no further moves are possible from that state. *

Output:

Return the minimum operation count, or -1 if the destination is impossible to reach.

Example *

Input: Start: "000", Destination: "222" *

Valid Shortest Path: 000 → 100 → 200 → 210 → 220 → 221 → 222 *

Result: 6 operations.

Analysis of Failed Approach The attempted solution used Backtracking (Depth-First Search). This approach is generally unsuitable for finding the shortest path in an unweighted graph because: 1. DFS explores deep paths first, often finding valid but non-optimal (longer) paths before finding the shortest one. 2. It requires exhaustive search to ensure the minimum is found, leading to Time Limit Exceeded (TLE) errors on large state spaces.

Correct Approach: Breadth-First Search (BFS) Since the edge weight between states is uniform (1 move), BFS guarantees finding the shortest path first.

Algorithm: 1.

Initialization: Create a queue and add the starting string "000" with a distance of 0. Create a visited set containing all deadends and "000" to prevent cycles and invalid moves. 2.

Processing: * Dequeue the current string. * If the current string equals the destination,

return the current distance. * Generate all possible next states (for each of the 3 wheels, calculate the +1 and -1 digit wrapping 0-9). 3.

Validation: If a generated state is not in the visited set: * Mark it as visited. * Enqueue it with current_distance + 1. 4.

Termination: If the queue empties without reaching the destination,

return -1. Note: This is a classic graph theory problem often titled "Open the Lock" (LeetCode 752).