Cartesian Tree

Max Tree.py

@@ -0,0 +1,62 @@
+"""
+Given an integer array with no duplicates. A max tree building on this array is defined as follow:
+
+The root is the maximum number in the array
+The left subtree and right subtree are the max trees of the subarray divided by the root number.
+Construct the max tree by the given array.
+Example
+Given [2, 5, 6, 0, 3, 1], the max tree is
+
+              6
+
+            /    \
+
+         5       3
+
+       /        /   \
+
+     2        0     1
+
+
+Challenge
+O(n) time complexity
+"""
+__author__ = 'Danyang'
+class TreeNode:
+    def __init__(self, val):
+        self.val = val
+        self.left, self.right = None, None
+
+class Solution:
+    def maxTree(self, A):
+        """
+        Cartesian Tree, Heap-ordered, treap, stack O(n)
+        http://en.wikipedia.org/wiki/Cartesian_tree
+
+        using stack
+        1. construct left tree and maintain the Cartesian tree
+        2. connect right tree
+        O(n) since each node on the tree is pushed and popped out from stack once 
+
+
+        :param A: Given an integer array with no duplicates.
+        :return: The root of max tree.
+        """
+        stk = []
+        for num in A:
+            cur = TreeNode(num)
+            while stk and stk[-1].val<=cur.val:
+                left_neighbor = stk.pop()
+                left_neighbor.right = cur.left
+                cur.left = left_neighbor
+            stk.append(cur)
+
+        pre = None
+        while stk:
+            cur = stk.pop()
+            cur.right = pre
+            pre = cur
+
+        return pre
+
+    # TODO, alternative methods