How do you solve Maximum Running Time of N Computers on LeetCode?

Maximum Running Time of N Computers (LeetCode #2141) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log(sum(batteries))) time complexity and O(1) space complexity. Key insight: Binary search allows us to efficiently find the maximum running time.

What is the brute force solution for Maximum Running Time of N Computers?

The brute force approach for Maximum Running Time of N Computers is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves checking every possible time duration to see if we can run all computers for that long using the available batteries. This method is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log(sum(batteries))).

What algorithm or data structure is used to solve Maximum Running Time of N Computers?

Maximum Running Time of N Computers uses the following concepts: Array, Binary Search, Greedy, Sorting. The recommended patterns to study are: Binary Search, Greedy.

What are the interview tips for Maximum Running Time of N Computers?

Explain your thought process clearly when discussing your approach. Be prepared to optimize your solution if asked. Practice binary search problems to become comfortable with the technique.

What are common mistakes when solving Maximum Running Time of N Computers?

Forgetting to consider the total power available when checking feasibility. Not handling edge cases where batteries might be fewer than computers.

#2141

Maximum Running Time of N Computers

Hard

ArrayBinary SearchGreedySortingBinary SearchGreedy

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log(sum(batteries)))
Space	O(1)	O(1)

💡

Intuition

Time O(n log(sum(batteries)))Space O(1)

The optimal solution uses binary search to efficiently find the maximum running time. Instead of checking every possible time, we can narrow down our search space based on whether a certain time is feasible or not.

⚙️

Algorithm

4 steps

1Step 1: Set low = 0 and high = sum of batteries.
2Step 2: While low < high, calculate mid = (low + high + 1) // 2.
3Step 3: Check if it's possible to run all n computers for 'mid' minutes. If yes, set low = mid; otherwise, set high = mid - 1.
4Step 4: Return low as the maximum running time.

solution.py16 lines

1# Full working Python code
2
3def canRunForTime(n, batteries, time):
4    totalPower = sum(min(battery, time) for battery in batteries)
5    return totalPower >= n * time
6
7
8def maxRunTime(n, batteries):
9    low, high = 0, sum(batteries)
10    while low < high:
11        mid = (low + high + 1) // 2
12        if canRunForTime(n, batteries, mid):
13            low = mid
14        else:
15            high = mid - 1
16    return low

ℹ

Complexity note: The time complexity is O(n log(sum(batteries))) because we perform a binary search over the range of possible times, and for each mid value, we check if it's feasible by summing the batteries, which takes O(n).

1Binary search allows us to efficiently find the maximum running time.
2The feasibility check for a given time is crucial for narrowing down the search space.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.