Program to find length of the largest subset where one element in every pair is divisible by other in Python

Suppose we have a list of unique numbers called nums, so we have to find the largest subset such that every pair of elements in the subset like (i, j) satisfies either i % j = 0 or j % i = 0. So we have to find the size of this subset.

So, if the input is like nums = [3, 6, 12, 24, 26, 39], then the output will be 4, as the largest valid subset is [3, 6, 12, 24].

To solve this, we will follow these steps −

• dp := a list of size nums and fill with 1
• sort the list nums
• n := size of nums
• if n <= 1, then
  • return n
• ans := 0
• for i in range 1 to n, do
  • for j in range 0 to i, do
    • if nums[i] is divisible by nums[j], then
      • dp[i] := maximum of dp[i] and dp[j] + 1
  • ans := maximum of ans and dp[i]
• return ans

Example (Python)

Let us see the following implementation to get better understanding −

class Solution:
   def solve(self, nums):
      dp = [1] * len(nums)
      nums.sort()
      n = len(nums)
      if n <= 1:
         return n
      ans = 0
      for i in range(1, n):
         for j in range(0, i):
            if nums[i] % nums[j] == 0:
            dp[i] = max(dp[i], dp[j] + 1)
         ans = max(ans, dp[i])
      return ans
ob = Solution()
nums = [3, 6, 12, 24, 26, 39]
print(ob.solve(nums))

Input

[3, 6, 12, 24, 26, 39]

Output

4