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:
2, 4, ...).1, 3, ...).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 <= 10000 <= presses <= 1000The brute force method involves simulating all possible presses and tracking unique bulb statuses. Given the four button types, the problem can quickly become computationally expensive with high values of n and presses. However, for small values, especially considering n's repetitive behavior beyond 3, this approach is feasible.
This Python function handles different cases for presses:
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Time Complexity: O(1) - Constant time due to direct evaluation based on provided conditions.
Space Complexity: O(1) - Uses fixed space.
By analyzing the problem and the stated button functionalities, we can deduce that the bulb statuses form repeatable patterns for n > 3. Consequently, the approach deduces patterns up to n = 3 directly, which encompasses every unique possible state combination for larger n due to periodic overlap.
The function deduces the count of unique configurations depending on presses limitations and n value, considerably reducing computational effort by recognizing recurring patterns from n=3 onwards.
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Java
C++
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JavaScript
Time Complexity: O(1) - Executes in constant time.
Space Complexity: O(1) - Minimal variable usage.
| Approach | Complexity |
|---|---|
| Brute Force Simulation | Time Complexity: O(1) - Constant time due to direct evaluation based on provided conditions. |
| Analytical Pattern Recognition | Time Complexity: O(1) - Executes in constant time. |
LeetCode 319. Bulb Switcher - Math Trick Fully Explained [Coding Interview Question] • Shiran Afergan • 8,487 views views
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