#2136

Hard

auto_awesomeGreedy choice plus invariant validation

LeetCode Problem Workspace

Earliest Possible Day of Full Bloom

Find the earliest day where all flower seeds are blooming based on their planting and growth times, using a greedy strategy.

array greedy sorting

Problem Statement

You have n flower seeds. Each seed must be planted before it begins to grow, and the growth takes time. You are given two arrays: plantTime and growTime, both of size n. The planting of a seed takes time, and so does its growth. You need to determine the earliest day when all the seeds are blooming, considering the time required for both planting and growing.

You can plant the seeds in any order starting from day 0. After planting, each seed will grow for a certain number of days before blooming. The goal is to optimize the planting sequence to minimize the total time needed for all seeds to bloom. Return the earliest day where every seed is 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 0th seed. The seed grows for 2 full days and blooms on day 3. On days 1, 2, 3, and 4, plant the 1st seed. The seed grows for 3 full days and blooms on day 8. On days 5, 6, and 7, plant the 2nd 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 0th seed. The seed grows for 2 full days and blooms on day 4. On days 0 and 3, plant the 1st seed. The seed grows for 1 full day and blooms on day 5. On days 2, 4, and 5, plant the 2nd seed. The seed grows for 2 full days and blooms on day 8. On days 6 and 7, plant the 3rd 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 0th 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 <= 105
1 <= plantTime[i], growTime[i] <= 104

Solution Approach

Greedy Strategy for Planting Seeds

Sort the seeds in descending order of their grow time. By planting seeds with the longest growth time first, you allow the plants that take longer to grow to bloom sooner, maximizing the time available for the shorter ones.

Simulating the Planting Process

Iterate through the sorted seeds, keeping track of the current day. For each seed, plant it and calculate the bloom day based on the plantTime and growTime. The earliest bloom day is determined by the sum of the plantTime and growTime for the last planted seed.

Efficient Bloom Day Calculation

For each seed, calculate its bloom day by accumulating its plantTime before starting its growTime. After processing all seeds, the maximum bloom day will give the answer to the problem.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity is O(n log n) due to the sorting of the seeds, where n is the number of seeds. The space complexity is O(n) due to the storage of the plantTime and growTime arrays, as well as the additional variables used for calculating bloom days.

What Interviewers Usually Probe

Candidate shows understanding of greedy strategies and can apply sorting based on custom criteria.
Candidate demonstrates the ability to simulate the plant-grow-bloom sequence and compute the final result efficiently.
Candidate struggles with determining the right plant order and the impact of plantTime and growTime on bloom day.

Common Pitfalls or Variants

Common pitfalls

Not sorting the seeds correctly by growTime, which results in a suboptimal planting order and delays bloom times.
Misunderstanding the relationship between plantTime, growTime, and the overall timeline, leading to incorrect calculations.
Failing to handle edge cases, such as when all seeds have the same plantTime or growTime, which may require careful handling in the sorting step.

Follow-up variants

What if there are different constraints on the maximum values for plantTime and growTime?
How does this problem change when considering additional constraints, like limited planting space or simultaneous blooming?
Can the solution be optimized further for cases where n is very large (e.g., n > 10^5)?

FAQ

How do I solve the Earliest Possible Day of Full Bloom problem?

Use a greedy approach by sorting the seeds based on their grow times in descending order. Then, simulate the planting process to calculate the final bloom day.

What is the time complexity of the solution for this problem?

The time complexity is O(n log n) due to the sorting step, where n is the number of seeds.

What is the primary pattern used in this problem?

The problem uses a greedy approach, where the goal is to minimize the total bloom day by choosing an optimal planting order.

How do the plantTime and growTime arrays affect the solution?

The plantTime array determines how long it takes to plant each seed, and the growTime array determines how long each seed needs to grow before blooming. Both are critical in determining the optimal planting order.

Can I solve this problem without sorting the seeds?

Sorting the seeds is essential for this problem. A greedy approach that doesn't prioritize seeds with the longest grow time first would lead to a suboptimal solution.

terminal

Solution

Solution 1: Greedy + Sorting

According to the problem description, we know that only one seed can be planted per day. Therefore, regardless of the planting order, the sum of the planting times for all seeds is always equal to $\sum_{i=0}^{n-1} plantTime[i]$. To make all seeds bloom as soon as possible, we should prioritize planting the seeds with the longest growth time. Hence, we can sort all seeds by their growth time in descending order and then plant them in sequence.

class Solution:
    def earliestFullBloom(self, plantTime: List[int], growTime: List[int]) -> int:
        ans = t = 0
        for pt, gt in sorted(zip(plantTime, growTime), key=lambda x: -x[1]):
            t += pt
            ans = max(ans, t + gt)
        return ans

Continue Practicing

#2141 maximum running time of n computers #2144 minimum cost of buying candies with discount #2126 destroying asteroids