Merge pull request #197 from sailok/master

Adding Leetcode Problem 368. Largest Divisible Subset.

Author: larissalages

leetcode/python/Dynamic Programming/Largest_Divisible_Subset.py

@@ -0,0 +1,50 @@
+# Given a set of distinct positive integers, find the largest subset such that every pair (Si, Sj) of elements in this subset satisfies:
+
+# Si % Sj = 0 or Sj % Si = 0.
+
+# If there are multiple solutions, return any subset is fine.
+
+# Example 1:
+
+# Input: [1,2,3]
+
+# Output: [1,2] (of course, [1,3] will also be ok)
+
+# Example 2:
+
+# Input: [1,2,4,8]
+
+# Output: [1,2,4,8]
+class Solution:
+    def largestDivisibleSubset(self, nums: List[int]) -> List[int]:
+        if len(nums) < 2:
+            return nums
+        
+        #creating a monotonic sequence of list
+        nums.sort()
+        
+        dp = [1]*len(nums)
+        max_ind = 0
+        
+        #dp pass using the following condition
+        for i in range(1, len(nums)):
+            for j in range(i):
+                if nums[i]%nums[j] == 0:
+                    dp[i] = max(dp[i], dp[j] + 1)
+                if dp[max_ind] < dp[i]:
+                    max_ind = i
+        
+        res = []
+        res.append(nums[max_ind])
+        
+        prev = nums[max_ind]
+
+        #reconstructing the sequence by iterating backwards
+        for i in range(max_ind - 1, -1, -1):
+            if dp[i] > 0 and dp[max_ind]-1 == dp[i] and prev%nums[i] == 0:
+                res.append(nums[i])
+                prev = nums[i]
+                max_ind = i
+                
+        res.reverse()
+        return res