How do you solve Maximum Total Beauty of the Gardens on LeetCode?

Maximum Total Beauty of the Gardens (LeetCode #2234) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Greedy strategies often yield optimal results in resource allocation problems.

What is the time complexity of Maximum Total Beauty of the Gardens?

The optimal solution for Maximum Total Beauty of the Gardens runs in O(n log n) time and uses O(1) space. The time complexity is O(n log n) due to the sorting step, and the space complexity is O(1) since we are using a constant amount of extra space.

What is the brute force solution for Maximum Total Beauty of the Gardens?

The brute force approach for Maximum Total Beauty of the Gardens is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach tries every possible combination of gardens to determine which ones can be made complete with the available flowers. This method is simple but inefficient as it checks all combinations. The optimal Optimal Solution approach improves this to O(n log n).

What are the interview tips for Maximum Total Beauty of the Gardens?

Always clarify the problem and constraints before diving into the solution. Think about edge cases, such as all gardens already being complete. Discuss your thought process out loud to engage with the interviewer.

What are common mistakes when solving Maximum Total Beauty of the Gardens?

Failing to account for remaining flowers after completing gardens. Not considering the minimum flowers in incomplete gardens correctly.

#2234

Maximum Total Beauty of the Gardens

Hard

ArrayTwo PointersBinary SearchGreedySortingEnumerationPrefix SumGreedySortingTwo Pointers

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

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

The optimal approach uses a greedy strategy to maximize the number of complete gardens first, then calculates the beauty based on the remaining flowers. This is efficient and leverages sorting to prioritize gardens.

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Algorithm

4 steps

1Step 1: Sort the gardens based on the number of flowers already planted.
2Step 2: Iterate through the sorted list, attempting to make as many gardens complete as possible with the available newFlowers.
3Step 3: For each garden made complete, subtract the required flowers from newFlowers and update the count of complete gardens.
4Step 4: Calculate the minimum number of flowers in incomplete gardens and compute the total beauty.

solution.py16 lines

1def maxBeautyOptimal(flowers, newFlowers, target, full, partial):
2    flowers.sort()
3    complete_gardens = 0
4    n = len(flowers)
5    for i in range(n):
6        if flowers[i] < target:
7            needed = target - flowers[i]
8            if newFlowers >= needed:
9                newFlowers -= needed
10                complete_gardens += 1
11            else:
12                flowers[i] += newFlowers
13                break
14    incomplete_min = min((flowers[i] for i in range(n) if flowers[i] < target), default=0)
15    beauty = complete_gardens * full + (incomplete_min * partial if complete_gardens < n else 0)
16    return beauty

ℹ

Complexity note: The time complexity is O(n log n) due to the sorting step, and the space complexity is O(1) since we are using a constant amount of extra space.

1Greedy strategies often yield optimal results in resource allocation problems.
2Sorting helps prioritize which gardens to complete first.

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