# 652 Find Duplicate Subtrees

Given a binary tree, return all duplicate subtrees. For each kind of duplicate subtrees, you only need to return the root node of any one of them.
Two trees are duplicate if they have the same structure with same node values.
Example 1:
1
/ \
2 3
/ / \
4 2 4
/
4
The following are two duplicate subtrees:
2
/
4
and
4
Therefore, you need to return above trees' root in the form of a list.
The Idea: Copy all the sub-trees in the tree. In order to obtain a unique kind of identification, run a preorder traversal that accumulates the root values, as well `None`. In order to obtain a unique identification for every sub-tree, a dictionary of lists will map each unique sub-tree identifier with it's associated root. It would then follow that duplicate sub-trees will have 2 or more roots associated with a key.
Complexity: O(n) time and O(n^2) space
def findDuplicateSubtrees(self, root):
"""
:type root: TreeNode
:rtype: List[TreeNode]
"""
serials = collections.defaultdict(list)
def copyAllSubtrees(root):
if root is not None:
subtree = "%s,%s,%s" % (root.val, copyAllSubtrees(root.left), copyAllSubtrees(root.right))
serials[subtree].append(root)
return subtree
else:
return "#"
copyAllSubtrees(root)
return [roots for serial, roots in serials.items() if len(roots) > 1]