LeetCode 368: Largest Divisible Subset

This repository contains a Python solution to LeetCode Problem 368 - Largest Divisible Subset.

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🔢 Problem Statement

Given a set of distinct positive integers nums, return the largest subset answer such that every pair (answer[i], answer[j]) of elements in this subset satisfies:

• answer[i] % answer[j] == 0, or
• answer[j] % answer[i] == 0

If there are multiple solutions, return any of them.

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📥 Example Inputs and Outputs

✅ Example 1:

Input: nums = [1, 2, 3]

Output: [1, 2]

Explanation: [1, 3] is also accepted.

✅ Example 2:

Input: nums = [1, 2, 4, 8]

Output: [1, 2, 4, 8]

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⚙️ Constraints

• 1 <= nums.length <= 1000
• 1 <= nums[i] <= 2 * 10^9
• All the integers in nums are unique

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🧠 Approach

This problem is solved using Dynamic Programming:

1. Sort the array to ensure proper divisibility order.
2. Use a dp[] array to keep track of the size of the largest divisible subset ending at each index.
3. Use a prev[] array to remember the previous index of the number in the subset chain.
4. Reconstruct the subset by backtracking from the largest value found.

Time Complexity: O(n^2)
Space Complexity: O(n)

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🧾 File Structure

leetcode-368-largest-divisible-subset

README.md

main.py

Python code with comments

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📌 Tags

• #DynamicProgramming
• #Subsets
• #Greedy
• #Math
• #Medium

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🔗 LeetCode Link

👉 LeetCode Problem 368 - Largest Divisible Subset

💡 Feel free to star ⭐ the repo if you find it helpful!

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