Is Bulb Switcher II easy or hard?

Bulb Switcher II is classified as a Medium difficulty problem. The implementation itself is short, but recognizing the repeating bulb patterns and reducing the state space to three bulbs requires mathematical insight.

Bulb Switcher II Python/Java solution

The Python or Java implementation for the optimal solution usually consists of a few conditional checks based on n and presses. Since the number of states is fixed, the code directly returns values such as 2, 3, 4, 7, or 8 depending on the case.

How to solve Bulb Switcher II in O(1)?

Reduce the problem to the first three bulbs since the switch patterns repeat for larger indices. Enumerate the maximum number of unique configurations achievable for different values of presses. For n ≥ 3: presses=1 gives 4 states, presses=2 gives 7 states, and presses ≥ 3 gives 8 states.

What is the best approach for Bulb Switcher II?

The optimal approach uses analytical pattern recognition. By observing that bulb states repeat after the first three positions, the problem reduces to analyzing a small fixed set of patterns. This leads to an O(1) time and O(1) space solution instead of simulating all switch presses.

Is Bulb Switcher II asked at Google/Amazon/Meta?

Bulb Switcher II represents the type of reasoning-heavy math and bit manipulation problems commonly asked in top tech interviews. Variants of switch toggling and state reduction problems appear in interviews at companies like Google, Amazon, and Meta.

What data structure is used in Bulb Switcher II?

Brute force solutions typically use a set or hash set to track unique bulb configurations while exploring states with BFS or DFS. The optimal solution mainly relies on mathematical reasoning and bit manipulation rather than complex data structures.

What is the time complexity of Bulb Switcher II?

The optimal analytical solution runs in O(1) time because the number of possible bulb states is bounded (maximum of 8). A brute force simulation using BFS or DFS can take up to O(2^p * n) time depending on how many press combinations are explored.

Description Solution Video 8:58

672. Bulb Switcher II

Medium51.2% acceptance1 company

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:

Input: n = 1, presses = 1
Output: 2
Explanation: Status can be:
- [off] by pressing button 1
- [on] by pressing button 2

Example 2:

Input: n = 2, presses = 1
Output: 3
Explanation: Status can be:
- [off, off] by pressing button 1
- [on, off] by pressing button 2
- [off, on] by pressing button 3

Example 3:

Input: n = 3, presses = 1
Output: 4
Explanation: Status can be:
- [off, off, off] by pressing button 1
- [off, on, off] by pressing button 2
- [on, off, on] by pressing button 3
- [off, on, on] by pressing button 4

Constraints:

1 <= n <= 1000
0 <= presses <= 1000

Asked at 1 company

Microsoft

Topics

8:58

Still stuck?Read 3 approaches, or watch a walkthrough.

Open solution

672. Bulb Switcher II

Asked at 1 company

Topics

Similar problems