largest divisible subset

dynamic_programming/largest_divisible_subset.py

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+from __future__ import annotations
+
+
+def largest_divisible_subset(array):
+    """
+    Algorithm to find the biggest subset 
+    in the given array such that for any 
+    2 elements x and y in the subset,
+    either x divides y or y divides x
+    >>> largest_divisible_subset([1,16,7,8,4])
+    [16, 8, 4, 1]
+    >>> largest_divisible_subset([1,2,3])
+    [2, 1]
+    >>> largest_divisible_subset([1, 2, 4, 8])
+    [8, 4, 2, 1]
+    """
+    n = len(array)
+
+    # Sort the array in ascending order
+    # as the sequence does not matter 
+    # we only have to pick up a subset
+    array.sort()
+
+    # Initialize dp and hash arrays with 1s
+    dp = [1] * n
+    hash_arr = list(range(n))
+
+    # Iterate through the array
+    for i in range(n):
+        for prev_index in range(i):
+            if array[i] % array[prev_index] == 0 and 1 + dp[prev_index] > dp[i]:
+                dp[i] = 1 + dp[prev_index]
+                hash_arr[i] = prev_index
+
+    ans = -1
+    last_index = -1
+
+    # Find the maximum length and its corresponding index
+    for i in range(n):
+        if dp[i] > ans:
+            ans = dp[i]
+            last_index = i
+
+    # Reconstruct the divisible subset
+    result = [array[last_index]]
+    while hash_arr[last_index] != last_index:
+        last_index = hash_arr[last_index]
+        result.append(array[last_index])
+
+    return result
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+
+    array = [1, 16, 7, 8, 4]
+
+    ans = largest_divisible_subset(array)
+
+    print("The longest divisible subset elements are:", ans)