Earliest Possible Day of Full Bloom

arraygreedysorting

Problem Statement

You have n flower seeds. Every seed must be planted first before it can begin to grow, then bloom. Planting a seed takes time and so does the growth of a seed. You are given two 0-indexed integer arrays plantTime and growTime , of length n each:

plantTime[i] is the number of full days it takes you to plant the i ^th seed. Every day, you can work on planting exactly one seed. You do not have to work on planting the same seed on consecutive days, but the planting of a seed is not complete until you have worked plantTime[i] days on planting it in total.

growTime[i] is the number of full days it takes the i ^th seed to grow after being completely planted. After the last day of its growth, the flower blooms and stays bloomed forever.

From the beginning of day 0 , you can plant the seeds in any order.

Return the earliest possible day where all seeds are blooming .

Examples

Example 1

Input: plantTime = [1,4,3], growTime = [2,3,1]
Output: 9
The grayed out pots represent planting days, colored pots represent growing days, and the flower represents the day it blooms.
One optimal way is:
On day 0, plant the 0 ^th seed. The seed grows for 2 full days and blooms on day 3.
On days 1, 2, 3, and 4, plant the 1 ^st seed. The seed grows for 3 full days and blooms on day 8.
On days 5, 6, and 7, plant the 2 ^nd seed. The seed grows for 1 full day and blooms on day 9.
Thus, on day 9, all the seeds are blooming.

Example 2

Input: plantTime = [1,2,3,2], growTime = [2,1,2,1]
Output: 9
The grayed out pots represent planting days, colored pots represent growing days, and the flower represents the day it blooms.
One optimal way is:
On day 1, plant the 0 ^th seed. The seed grows for 2 full days and blooms on day 4.
On days 0 and 3, plant the 1 ^st seed. The seed grows for 1 full day and blooms on day 5.
On days 2, 4, and 5, plant the 2 ^nd seed. The seed grows for 2 full days and blooms on day 8.
On days 6 and 7, plant the 3 ^rd seed. The seed grows for 1 full day and blooms on day 9.
Thus, on day 9, all the seeds are blooming.

Example 3

Input: plantTime = [1], growTime = [1]
Output: 2
On day 0, plant the 0 ^th seed. The seed grows for 1 full day and blooms on day 2.
Thus, on day 2, all the seeds are blooming.

Constraints

n == plantTime.length == growTime.length

1 <= n <= 10 ^5

1 <= plantTime[i], growTime[i] <= 10 ^4

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicGreedy