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Yes, this problem is commonly used in technical interviews at large tech companies because it tests recursion, backtracking, and state management. It also evaluates how well candidates optimize brute-force searches using symmetry and constraints.
The skip matrix encodes rules where moving between two digits requires passing through another digit. For example, moving from 1 to 3 requires that 2 is already visited. This structure allows constant-time validation of moves during backtracking.
A combination of a skip matrix and a visited tracking structure works best. The visited state can be stored using either a boolean array or a bitmask, while the skip matrix quickly checks if an intermediate key must be visited before making a move.
The optimal approach uses backtracking with a precomputed skip matrix that enforces Android’s movement constraints. By exploring valid paths and counting pattern lengths between m and n, we can generate all valid unlock sequences efficiently. Symmetry optimization further reduces repeated calculations.