1 files changed, 179 insertions, 0 deletions
diff --git a/data_structures_and_algorithms/second-largest-item-bst.py b/data_structures_and_algorithms/second-largest-item-bst.py
new file mode 100644
index 000000000000..bc167d975a7b
--- /dev/null
+++ b/data_structures_and_algorithms/second-largest-item-bst.py
@@ -0,0 +1,179 @@
+import unittest
+from collections import deque
+
+
+################################################################################
+# Implementation
+################################################################################
+def is_leaf(node):
+    return node.left is None and node.right is None
+
+
+def find_largest(node):
+    current = node
+    while current.right is not None:
+        current = current.right
+    return current.value
+
+
+def find_second_largest(node):
+    history = deque()
+    current = node
+
+    while current.right:
+        history.append(current)
+        current = current.right
+
+    if current.left:
+        return find_largest(current.left)
+    elif history:
+        return history.pop().value
+    else:
+        raise TypeError
+
+
+def find_second_largest_backup(node):
+    history = deque()
+    current = node
+
+    # traverse -> largest
+    while current.right:
+        history.append(current)
+        current = current.right
+
+    if current.left:
+        return find_largest(current.left)
+    elif history:
+        return history.pop().value
+    else:
+        raise ArgumentError
+
+
+# Write a iterative version to avoid consuming memory with the call stack.
+# Commenting out the recursive code for now.
+def find_second_largest_backup(node):
+    if node.left is None and node.right is None:
+        raise ArgumentError
+
+    elif node.right is None and is_leaf(node.left):
+        return node.left.value
+
+    # recursion
+    # elif node.right is None:
+    #     return find_largest(node.left)
+
+    # iterative version
+    elif node.right is None:
+        current = node.left
+        while current.right is not None:
+            current = current.right
+        return current.value
+
+    # recursion
+    # TODO: Remove recursion from here.
+    elif not is_leaf(node.right):
+        return find_second_largest(node.right)
+
+    # could do an else here, but let's be more assertive.
+    elif is_leaf(node.right):
+        return node.value
+
+    else:
+        raise ArgumentError
+
+
+################################################################################
+# Tests
+################################################################################
+class Test(unittest.TestCase):
+    class BinaryTreeNode(object):
+        def __init__(self, value):
+            self.value = value
+            self.left = None
+            self.right = None
+
+        def insert_left(self, value):
+            self.left = Test.BinaryTreeNode(value)
+            return self.left
+
+        def insert_right(self, value):
+            self.right = Test.BinaryTreeNode(value)
+            return self.right
+
+    def test_full_tree(self):
+        tree = Test.BinaryTreeNode(50)
+        left = tree.insert_left(30)
+        right = tree.insert_right(70)
+        left.insert_left(10)
+        left.insert_right(40)
+        right.insert_left(60)
+        right.insert_right(80)
+        actual = find_second_largest(tree)
+        expected = 70
+        self.assertEqual(actual, expected)
+
+    def test_largest_has_a_left_child(self):
+        tree = Test.BinaryTreeNode(50)
+        left = tree.insert_left(30)
+        right = tree.insert_right(70)
+        left.insert_left(10)
+        left.insert_right(40)
+        right.insert_left(60)
+        actual = find_second_largest(tree)
+        expected = 60
+        self.assertEqual(actual, expected)
+
+    def test_largest_has_a_left_subtree(self):
+        tree = Test.BinaryTreeNode(50)
+        left = tree.insert_left(30)
+        right = tree.insert_right(70)
+        left.insert_left(10)
+        left.insert_right(40)
+        right_left = right.insert_left(60)
+        right_left_left = right_left.insert_left(55)
+        right_left.insert_right(65)
+        right_left_left.insert_right(58)
+        actual = find_second_largest(tree)
+        expected = 65
+        self.assertEqual(actual, expected)
+
+    def test_second_largest_is_root_node(self):
+        tree = Test.BinaryTreeNode(50)
+        left = tree.insert_left(30)
+        tree.insert_right(70)
+        left.insert_left(10)
+        left.insert_right(40)
+        actual = find_second_largest(tree)
+        expected = 50
+        self.assertEqual(actual, expected)
+
+    def test_descending_linked_list(self):
+        tree = Test.BinaryTreeNode(50)
+        left = tree.insert_left(40)
+        left_left = left.insert_left(30)
+        left_left_left = left_left.insert_left(20)
+        left_left_left.insert_left(10)
+        actual = find_second_largest(tree)
+        expected = 40
+        self.assertEqual(actual, expected)
+
+    def test_ascending_linked_list(self):
+        tree = Test.BinaryTreeNode(50)
+        right = tree.insert_right(60)
+        right_right = right.insert_right(70)
+        right_right.insert_right(80)
+        actual = find_second_largest(tree)
+        expected = 70
+        self.assertEqual(actual, expected)
+
+    def test_error_when_tree_has_one_node(self):
+        tree = Test.BinaryTreeNode(50)
+        with self.assertRaises(Exception):
+            find_second_largest(tree)
+
+    def test_error_when_tree_is_empty(self):
+        with self.assertRaises(Exception):
+            find_second_largest(None)
+
+
+unittest.main(verbosity=2)