Minimum Number of Switches to Turn On All Bulbs

Problem: Find the minimum number of switch presses required to turn on all bulbs in a given configuration, where each switch may control multiple bulbs (or toggle behavior varies per the specific puzzle setup described by the interviewer).

Constraints: The exact switch-to-bulb mapping and toggle rules are typically clarified interactively with the interviewer as part of the puzzle.

Approach: Model switches and bulbs as a bipartite toggle relationship (e.g., each switch flips a specific subset of bulbs). For small instances, brute-force over all 2^k switch combinations (k = number of switches) and check which combination results in all bulbs on, tracking the minimum popcount. For structured variants (e.g., each switch toggles a contiguous range), use difference-array/prefix-XOR techniques to solve more efficiently.