Create all-possible-full-binary-trees.py

Author: kamyu104

Python/all-possible-full-binary-trees.py

@@ -0,0 +1,55 @@
+# Time:  O(n * 4^n / n^(3/2)) ~= Catalan numbers
+# Space: O(n * 4^n / n^(3/2)) ~= Catalan numbers
+
+# A full binary tree is a binary tree where each node has exactly 0 or 2 children.
+#
+# Return a list of all possible full binary trees with N nodes.
+# Each element of the answer is the root node of one possible tree.
+#
+# Each node of each tree in the answer must have node.val = 0.
+#
+# You may return the final list of trees in any order.
+#
+# Example 1:
+#
+# Input: 7
+# Output: [[0,0,0,null,null,0,0,null,null,0,0],[0,0,0,null,null,0,0,0,0],
+#          [0,0,0,0,0,0,0],[0,0,0,0,0,null,null,null,null,0,0],[0,0,0,0,0,null,null,0,0]]
+# Explanation:
+#
+# Note:
+# - 1 <= N <= 20
+
+# Definition for a binary tree node.
+class TreeNode(object):
+    def __init__(self, x):
+        self.val = x
+        self.left = None
+        self.right = None
+
+
+class Solution(object):
+    def __init__(self):
+        self.__memo = {1: [TreeNode(0)]}
+    
+    def allPossibleFBT(self, N):
+        """
+        :type N: int
+        :rtype: List[TreeNode]
+        """
+        if N % 2 == 0:
+            return []
+
+        if N not in self.__memo:
+            result = []
+            for i in xrange(N):
+                for left in self.allPossibleFBT(i):
+                    for right in self.allPossibleFBT(N-1-i):
+                        node = TreeNode(0)
+                        node.left = left
+                        node.right = right
+                        result.append(node)
+            self.__memo[N] = result
+
+        return self.__memo[N]
+