Introduction

In this blog post, we will explore how to solve the LeetCode problem "2234" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

Alice is a caretaker of n gardens and she wants to plant flowers to maximize the total beauty of all her gardens. You are given a 0-indexed integer array flowers of size n, where flowers[i] is the number of flowers already planted in the ith garden. Flowers that are already planted cannot be removed. You are then given another integer newFlowers, which is the maximum number of flowers that Alice can additionally plant. You are also given the integers target, full, and partial. A garden is considered complete if it has at least target flowers. The total beauty of the gardens is then determined as the sum of the following: The number of complete gardens multiplied by full. The minimum number of flowers in any of the incomplete gardens multiplied by partial. If there are no incomplete gardens, then this value will be 0. Return the maximum total beauty that Alice can obtain after planting at most newFlowers flowers. Example 1: Input: flowers = [1,3,1,1], newFlowers = 7, target = 6, full = 12, partial = 1 Output: 14 Explanation: Alice can plant - 2 flowers in the 0th garden - 3 flowers in the 1st garden - 1 flower in the 2nd garden - 1 flower in the 3rd garden The gardens will then be [3,6,2,2]. She planted a total of 2 + 3 + 1 + 1 = 7 flowers. There is 1 garden that is complete. The minimum number of flowers in the incomplete gardens is 2. Thus, the total beauty is 1 12 + 2 1 = 12 + 2 = 14. No other way of planting flowers can obtain a total beauty higher than 14. Example 2: Input: flowers = [2,4,5,3], newFlowers = 10, target = 5, full = 2, partial = 6 Output: 30 Explanation: Alice can plant - 3 flowers in the 0th garden - 0 flowers in the 1st garden - 0 flowers in the 2nd garden - 2 flowers in the 3rd garden The gardens will then be [5,4,5,5]. She planted a total of 3 + 0 + 0 + 2 = 5 flowers. There are 3 gardens that are complete. The minimum number of flowers in the incomplete gardens is 4. Thus, the total beauty is 3 2 + 4 6 = 6 + 24 = 30. No other way of planting flowers can obtain a total beauty higher than 30. Note that Alice could make all the gardens complete but in this case, she would obtain a lower total beauty. Constraints: 1 <= flowers.length <= 105 1 <= flowers[i], target <= 105 1 <= newFlowers <= 1010 1 <= full, partial <= 105

Explanation

Here's the breakdown of the approach and the Python code:

• High-Level Approach:

  • Optimize for 'full' gardens: Iterate through the possible number of fully completed gardens. For each number, calculate the flowers needed to achieve that count.
  • Maximize 'partial' beauty: For the remaining incomplete gardens, use binary search to find the optimal minimum flower count to maximize the partial beauty, given the remaining flowers.
  • Calculate and compare: Calculate the total beauty for each combination of full and partial gardens and keep track of the maximum.

• Complexity:

  • Runtime: O(n log n) due to sorting and binary search within the loop.
  • Storage: O(n) for the sorted flowers array and prefix sum array.

Code

    def maximumBeauty(flowers, newFlowers, target, full, partial):
    n = len(flowers)
    flowers.sort()

    prefix_sum = [0] * (n + 1)
    for i in range(n):
        prefix_sum[i + 1] = prefix_sum[i] + flowers[i]

    max_beauty = 0
    for num_full in range(n + 1):
        needed_flowers = 0
        if num_full > 0:
            needed_flowers = 0
            for i in range(n - num_full, n):
                needed_flowers += max(0, target - flowers[i])

        if needed_flowers > newFlowers:
            continue

        num_incomplete = n - num_full
        remaining_flowers = newFlowers - needed_flowers

        if num_incomplete == 0:
            max_beauty = max(max_beauty, num_full * full)
            continue

        low = 0
        high = target - 1
        best_min = 0

        while low <= high:
            mid = (low + high) // 2
            needed = 0
            l, r = 0, num_incomplete - 1
            idx = -1
            while l <= r:
                m = (l + r) // 2
                if flowers[m] >= mid:
                    idx = m
                    r = m - 1
                else:
                    l = m + 1

            if idx == -1:
                needed = mid * num_incomplete - prefix_sum[num_incomplete]
            else:
                needed = mid * idx - prefix_sum[idx]
                needed += prefix_sum[num_incomplete] - prefix_sum[idx] - (num_incomplete - idx) * mid


            if needed <= remaining_flowers:
                best_min = mid
                low = mid + 1
            else:
                high = mid - 1

        max_beauty = max(max_beauty, num_full * full + best_min * partial)

    return max_beauty