Bulb Switcher II
medium · verified · 50% accepted · 196 likes · top 38%
math · bit manipulation · depth-first search · breadth-first search
Description
There is a room with n bulbs labeled from 1 to n that all are turned on initially, and four buttons on the wall. Each of the four buttons has a different functionality where:
- Button 1: Flips the status of all the bulbs.
- Button 2: Flips the status of all the bulbs with even labels (i.e., 2, 4, ...).
- Button 3: Flips the status of all the bulbs with odd labels (i.e., 1, 3, ...).
- Button 4: Flips the status of all the bulbs with a label j = 3k + 1 where k = 0, 1, 2, ... (i.e., 1, 4, 7, 10, ...).
You must make exactly presses button presses in total. For each press, you may pick any of the four buttons to press.
Given the two integers n and presses, return the number of different possible statuses after performing all presses button presses.
Example 1:
Example 2:
Example 3:
Solution