Create 145_binary_tree_postorder_traversal.md

Author: Joseph Luce

leetcode/hard/145_binary_tree_postorder_traversal.md

@@ -0,0 +1,54 @@
+# 145. Binary Tree Postorder Traversal
+
+## Recursive Solution
+- Runtime: O(N)
+- Space: O(N)
+- N = Number of nodes in tree
+
+The recusive solution is fairly easy. Most of the heavy lifting is abstracted away by the recursion call.
+
+```
+class Solution:
+    def postorderTraversal(self, root: TreeNode) -> List[int]:
+        def postorder_traversal_helper(root, result):
+            if root is None:
+                return
+            postorder_traversal_helper(root.left, result)
+            postorder_traversal_helper(root.right, result)
+            result.append(root.val)
+            
+        result = list()
+        postorder_traversal_helper(root, result)
+        return result
+```
+
+## Iterative Solution
+- Runtime: O(N)
+- Space: O(N)
+- N = Number of nodes in tree
+
+The iterative solution for post order is fairly diffucult to come up with on your own.
+It requires two stacks. 
+The first stack is used to traverse the tree but in the opposite direction, going to the right side first then visiting the left nodes.
+During the traversal, the 2nd stack will place the nodes in the reverse order or post-order when they are popped off the stack.
+I recommend drawing this out, as its important to understand the relationships and responsibilities.
+
+```
+class Solution:
+    def postorderTraversal(self, root: TreeNode) -> List[int]:
+        if root is None:
+            return []
+        stack1, stack2 = list([root]), list()
+        result = list()
+        while len(stack1) > 0:
+            node = stack1.pop()
+            stack2.append(node)
+            if node.left is not None:
+                stack1.append(node.left)
+            if node.right is not None:
+                stack1.append(node.right)
+        while len(stack2) > 0:
+            node = stack2.pop()
+            result.append(node.val) # <-- Business logic goes here
+        return result
+```