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

<ul>
	<li><code>answer[i] % answer[j] == 0</code>, or</li>
	<li><code>answer[j] % answer[i] == 0</code></li>
</ul>

<p>If there are multiple solutions, return any of them.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3]
<strong>Output:</strong> [1,2]
<strong>Explanation:</strong> [1,3] is also accepted.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,4,8]
<strong>Output:</strong> [1,2,4,8]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 2 * 10<sup>9</sup></code></li>
	<li>All the integers in <code>nums</code> are <strong>unique</strong>.</li>
</ul>

def findLargestSubset(nums, prev_index, current_index, dp):
    if current_index == len(nums):
        return []
    
    if dp[prev_index + 1][current_index] != None:
        return dp[prev_index + 1][current_index]
    
    # Exclude the current element
    exclude = findLargestSubset(nums, prev_index, current_index + 1, dp)
    
    # Include the current element if it's divisible by the previous element in the subset
    include = []
    if prev_index == -1 or nums[current_index] % nums[prev_index] == 0:
        include = [nums[current_index]] + findLargestSubset(nums, current_index, current_index + 1, dp)
    
    # Store the result in DP array and return the larger subset
    dp[prev_index + 1][current_index] = max(include, exclude, key=len)
    return dp[prev_index + 1][current_index]

class Solution:
    def largestDivisibleSubset(self, nums: List[int]) -> List[int]:
        nums.sort()
        n = len(nums)
        dp = [[None] * n for _ in range(n + 1)]
        return findLargestSubset(nums, -1, 0, dp)


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