Is Minimum Energy to Maintain Brightness easy or hard?

The problem is generally considered Medium difficulty. The challenge lies in recognizing that the time-based simulation can be converted into a direct deficit calculation, reducing the complexity from O(n * t) to O(n).

Minimum Energy to Maintain Brightness Python/Java solution

Implement a single pass through the brightness array. For each lamp, compute max(0, t - brightness[i]) and accumulate the result. This logic translates directly into Python, Java, or C++ with a simple loop and integer arithmetic.

How to solve Minimum Energy to Maintain Brightness in O(n)?

Iterate through each lamp's brightness value and compare it with the required duration t. If brightness[i] is less than t, add the difference (t − brightness[i]) to the energy cost. Summing these deficits across the array yields the minimum energy needed in linear time.

What is the best approach for Minimum Energy to Maintain Brightness?

The most efficient approach is a greedy deficit calculation. Each lamp must have at least t brightness to survive t minutes if brightness decreases by 1 per minute. The minimum energy is the sum of max(0, t − brightness[i]) across all lamps. This runs in O(n) time and O(1) space.

Is Minimum Energy to Maintain Brightness asked at Google/Amazon/Meta?

Problems with greedy deficit calculations and resource maintenance frequently appear in interviews at companies like Google, Amazon, and Meta. While the exact problem title may vary, the underlying pattern of minimizing adjustments to meet constraints is common.

What data structure is used in Minimum Energy to Maintain Brightness?

The optimal solution typically uses only an array traversal with constant extra space. Some variations use a priority queue (min-heap) to always recharge the lamp closest to depletion when decisions must be made dynamically.

What is the time complexity of Minimum Energy to Maintain Brightness?

The optimal greedy solution runs in O(n) time because you only scan the brightness array once and compute deficits. Space complexity is O(1) since only a running total of required energy is maintained.

Description Hints 4 Solution Video 18:36

3951. Minimum Energy to Maintain Brightness

Medium53.4% acceptance

You are given an integer n, representing n light bulbs arranged in a line and indexed from 0 to n - 1.

You are also given an integer brightness and a 2D integer array intervals, where intervals[i] = [start_i, end_i] represents an inclusive time interval during which the lighting requirement must be satisfied.

At each time unit, every bulb can independently be either on or off. A bulb that is on illuminates its own position and its adjacent positions, if they exist.

The total illumination at a time unit is the number of illuminated positions. Each position is counted at most once.

For every integer time unit covered by at least one interval in intervals, the total illumination must be at least brightness. At time units not covered by any interval, all bulbs may remain off. Each bulb that is on consumes 1 unit of energy for that time unit.

Return an integer denoting the minimum total energy required.

Example 1:

Input: n = 5, brightness = 5, intervals = [[6,12]]

Output: 14

Explanation:

Turn on the light bulbs at positions 1 and 4.
Current state of line: 0 1 0 0 1.
All 5 positions are illuminated, so the required brightness is reached.
The active interval has length 12 - 6 + 1 = 7, so the total energy is 2 * 7 = 14.

Example 2:

Input: n = 2, brightness = 1, intervals = [[0,0],[2,2]]

Output: 2

Explanation:

Turn on one light bulb during each active interval.
Each interval has length 1, so the total active time is 1 + 1 = 2.
The total energy is 1 * 2 = 2.

Example 3:

Input: n = 4, brightness = 2, intervals = [[1,3],[2,4]]

Output: 4

Explanation:

Turn on one light bulb. It can illuminate at least 2 positions.
The active intervals overlap, so the total active time is the length of [1,4], which is 4.
The total energy is 1 * 4 = 4.

Constraints:

1 <= n <= 10⁶
1 <= brightness <= n
1 <= intervals.length <= 10⁵
intervals[i] == [start_i, end_i]
0 <= start_i <= end_i <= 10⁹

Topics

Array Sorting

Hints open one at a time

Hint 1

The actual bulb configuration does not depend on the time unit, only on the required brightness.

Hint 2

First compute the minimum number of bulbs needed to illuminate at least brightness positions on a line of length n.

Hint 3

One bulb can illuminate at most 3 positions, except near the boundaries. So the answer is essentially ceil(brightness / 3).

Hint 4

Merge all overlapping intervals to compute the total number of active time units.

18:36

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1class Solution:
2    def minEnergy(self, n: int, brightness: int, intervals: list[list[int]]) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

5
5
[[6,12]]

Input

2
1
[[0,0],[2,2]]

Input

4
2
[[1,3],[2,4]]

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