Maximum Total Beauty of the Gardens

arraytwo pointersbinary search

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 i ^th 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.

Examples

Example 1

Input: flowers = [1,3,1,1], newFlowers = 7, target = 6, full = 12, partial = 1
Output: 14
Alice can plant
- 2 flowers in the 0 ^th garden
- 3 flowers in the 1 ^st garden
- 1 flower in the 2 ^nd garden
- 1 flower in the 3 ^rd 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
Alice can plant
- 3 flowers in the 0 ^th garden
- 0 flowers in the 1 ^st garden
- 0 flowers in the 2 ^nd garden
- 2 flowers in the 3 ^rd 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 <= 10 ^5

1 <= flowers[i], target <= 10 ^5

1 <= newFlowers <= 10 ^10

1 <= full, partial <= 10 ^5

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicTwo Pointers