What is the time complexity of Earliest Possible Day of Full Bloom?

The optimal solution has a time complexity of O(n log n).

What data structures are used to solve Earliest Possible Day of Full Bloom?

This problem uses Array, Greedy, Sorting. Understanding these concepts is essential for solving this Hard problem efficiently.

What are the key insights for solving Earliest Possible Day of Full Bloom?

Insight 1: The key insight is that the order in which we plant the seeds significantly affects the final bloom time. Seeds with longer grow times should be planted earlier to minimize the overall time. Insight 2: We can use a greedy approach by sorting the seeds in descending order of their `growTime`. This ensures that seeds with longer growth periods are planted first.

Which companies ask LeetCode 2136. Earliest Possible Day of Full Bloom in interviews?

This problem is frequently asked at Visa.

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Earliest Possible Day of Full Bloom - LeetCode 2136 Solution

Earliest Possible Day of Full Bloom - Complete Solution Guide

Earliest Possible Day of Full Bloom is LeetCode problem 2136, a Hard level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

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

Detailed Explanation

The problem asks us to find the earliest possible day when all given flower seeds are blooming. We are given two arrays: `plantTime` and `growTime`. `plantTime[i]` is the number of days it takes to plant the i-th seed, and `growTime[i]` is the number of days it takes for the i-th seed to grow after it is planted. We can plant the seeds in any order, and we can only plant one seed each day. The goal is to minimize the maximum bloom time among all seeds.

Solution Approach

The solution employs a greedy approach combined with sorting. We sort the seeds based on their `growTime` in descending order. Then, we iterate through the sorted seeds, keeping track of the current planting time and the maximum bloom time. For each seed, we add its `plantTime` to the current planting time and calculate its bloom time (current planting time + `growTime`). The maximum bloom time is updated to be the maximum of the current maximum bloom time and the bloom time of the current seed.

Step-by-Step Algorithm

Step 1: Create an array of pairs (or a similar data structure) to store the `growTime` and `plantTime` for each seed.
Step 2: Sort this array of pairs in descending order based on the `growTime`.
Step 3: Initialize `current_plant_time` to 0 and `max_bloom_time` to 0.
Step 4: Iterate through the sorted array of seeds.
Step 5: For each seed, update `current_plant_time` by adding the `plantTime` of the current seed.
Step 6: Calculate the bloom time of the current seed by adding `current_plant_time` and the `growTime` of the current seed.
Step 7: Update `max_bloom_time` to be the maximum of `max_bloom_time` and the bloom time of the current seed.
Step 8: After iterating through all the seeds, return `max_bloom_time`.

Key Insights

Insight 1: The key insight is that the order in which we plant the seeds significantly affects the final bloom time. Seeds with longer grow times should be planted earlier to minimize the overall time.
Insight 2: We can use a greedy approach by sorting the seeds in descending order of their `growTime`. This ensures that seeds with longer growth periods are planted first.
Insight 3: The earliest bloom day is the maximum of the bloom days of each seed. The bloom day of a seed is the sum of the total plant time up to that seed and the grow time of that specific seed.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(n)

Topics

This problem involves: Array, Greedy, Sorting.

Companies

Asked at: Visa.

Earliest Possible Day of Full Bloom | LeetCode 2136

Hard

Array Greedy Sorting

Time: O(n log n)Space: O(n)

Solution Code

Available in:

import java.util.Arrays;
import java.util.Comparator;

class Solution {
    public int earliestFullBloom(int[] plantTime, int[] growTime) {
        int n = plantTime.length;
        Integer[] indices = new Integer[n];
        for (int i = 0; i < n; i++) {
            indices[i] = i;
        }

        Arrays.sort(indices, Comparator.comparingInt(i -> growTime[i]).reversed());

        int current_plant_time = 0;
        int max_bloom_time = 0;

        for (int i = 0; i < n; i++) {
            int index = indices[i];
            current_plant_time += plantTime[index];
            max_bloom_time = Math.max(max_bloom_time, current_plant_time + growTime[index]);
        }

        return max_bloom_time;
    }
}

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Problem Info

Description

Problem 2136: Earliest Possible Day of Full Bloom - Detailed explanation and solution approaches.

Topics

Array Greedy Sorting

Companies

Visa

Stats

Difficulty:Hard

Languages:4

Companies:1

Problem #:2136

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

8 steps

1
Step 1: Create an array of pairs (or a similar data structure) to store the `growTime` and `plantTime` for each seed.
2
Step 2: Sort this array of pairs in descending order based on the `growTime`.
3
Step 3: Initialize `current_plant_time` to 0 and `max_bloom_time` to 0.
4
Step 4: Iterate through the sorted array of seeds.
5
Step 5: For each seed, update `current_plant_time` by adding the `plantTime` of the current seed.
6
Step 6: Calculate the bloom time of the current seed by adding `current_plant_time` and the `growTime` of the current seed.
7
Step 7: Update `max_bloom_time` to be the maximum of `max_bloom_time` and the bloom time of the current seed.
8
Step 8: After iterating through all the seeds, return `max_bloom_time`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is determined by the sorting algorithm used, which is typically O(n log n) for efficient sorting algorithms like merge sort or quicksort. The space complexity is mainly due to the storage of the pairs (growTime, plantTime) to perform the sorting without altering the original input arrays, requiring O(n) space.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Brute Force

Try all possible permutations of the planting order and calculate the earliest bloom time for each permutation. Select the minimum of all bloom times.

Time: O(n! * n), where n is the number of seeds. Generating all permutations takes O(n!) time, and calculating the bloom time for each permutation takes O(n) time.Space: O(n), for storing a permutation.

Trade-offs: This approach is only feasible for very small values of n (e.g., n <= 10) due to the factorial time complexity. It's not practical for the given constraint of n <= 10^5. The greedy approach is much more efficient.

✨

Key Insights

1Insight 1: The key insight is that the order in which we plant the seeds significantly affects the final bloom time. Seeds with longer grow times should be planted earlier to minimize the overall time.
2Insight 2: We can use a greedy approach by sorting the seeds in descending order of their `growTime`. This ensures that seeds with longer growth periods are planted first.
3Insight 3: The earliest bloom day is the maximum of the bloom days of each seed. The bloom day of a seed is the sum of the total plant time up to that seed and the grow time of that specific seed.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Greedy Algorithm

Making the best choice at each step without looking ahead.

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: When there's only one seed (n=1), the algorithm correctly calculates the bloom time as `plantTime[0] + growTime[0]`.
Edge case 2: When all `growTime` values are the same, the order of planting doesn't matter, and the algorithm will still produce the correct result. The sorting will still happen, but the final `max_bloom_time` will remain the same regardless of the order.
Edge case 3: If plantTime or growTime contains very large numbers, integer overflow could be an issue. The provided solutions might not explicitly address this, and in some languages, using larger data types (e.g., long in Java/C++) might be needed.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not sorting the seeds based on `growTime`. Planting seeds in an arbitrary order will likely result in a suboptimal bloom time.

✗Common mistake 2: Incorrectly calculating the bloom time. The bloom time for each seed is calculated based on the cumulative planting time up to that seed plus the seed's `growTime`, and the earliest full bloom day is the maximum of all bloom times, not the sum of them.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Task scheduling: Optimizing the order of tasks to minimize the overall completion time, considering the time required to prepare for a task (plantTime) and the duration of the task itself (growTime).

🏦Real-world scenario 2: Manufacturing process: Determining the sequence of operations to minimize the total production time, where each operation has a setup time (plantTime) and a processing time (growTime).

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Hard problems often combine multiple techniques. Break the problem into sub-problems.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: November 4, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 13

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

How do I verify if a greedy approach is correct?

Prove the greedy choice property: the locally optimal choice leads to globally optimal solution. Use exchange argument: show that swapping any element with the greedy choice doesn't improve the solution. If you can't prove it, test extensively or consider DP.

How do I approach hard algorithm problems?

Hard problems often require: 1) Breaking down into subproblems, 2) Combining multiple advanced techniques, 3) Careful optimization of brute force. Start with a working solution (even O(n²) or worse), then optimize. Draw examples, identify patterns, and think about what makes this problem unique.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Earliest Possible Day of Full Bloom"?

For this hard-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether greedy techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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