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The 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.
Time Complexity: O(1) - Constant time due to direct evaluation based on provided conditions.
Space Complexity: O(1) - Uses fixed space.
1def flipLights(n, presses):
2 if presses == 0:
3 return 1
4 if n == 1:
5 return 2 if presses > 0 else 1
6 if n == 2:
7 return 3 if presses == 1 else 4
8 return 4 if presses == 1 else 7 if presses == 2 else 8
9This Python function handles different cases for presses:
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.
Time Complexity: O(1) - Executes in constant time.
Space Complexity: O(1) - Minimal variable usage.
1A Java solution recognizing the sequencing pattern of bulb operations, thus optimizing performance by reducing needless computations for n > 3.