Added diameter_of_binary_tree.py

Author: MTrajK

Diff for: Trees/diameter_of_binary_tree.py

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+'''
+Diameter of Binary Tree
+
+Given a binary tree, you need to compute the length of the diameter of the tree.
+The diameter of a binary tree is the length of the longest path between any two nodes in a tree.
+This path may or may not pass through the root.
+Note: The length of path between two nodes is represented by the number of nodes.
+
+Input: 3
+      / \
+     1   4
+      \   \
+       2   5
+      /
+     7
+Output: 6
+Output Explanation: [7, 2, 1, 3, 4, 5] is the diameter of the binary tree.
+
+Input: 5
+      / \
+     3   6
+    / \
+   2   4
+  /     \
+ 1       8
+Output: 5
+Output Explanation: [1, 2, 3, 4, 8] is the diameter of the binary tree.
+
+=========================================
+Traverse the tree and keep/return information about the longest/max branch and longest/max diameter.
+    Time Complexity:    O(N)
+    Space Complexity:   O(N)        , because of the recursion stack (but this is if the tree is one branch), O(LogN) if the tree is balanced.
+'''
+
+
+############
+# Solution #
+############
+
+# import TreeNode class from tree_helpers.py
+from tree_helpers import TreeNode
+
+def diameter(root):
+  	return find_diameter(root)[1]
+
+def find_diameter(root):
+    ''' returns (max branch length, max diameter) '''
+    if not root:
+        return 0, 0
+
+    # traverse left and right subtrees
+    left, right = find_diameter(root.left), find_diameter(root.right)
+
+    # return the max branch from the left and right subtrees plus the current node
+    # and find the max diameter till now (using the current node and the max left and right subtree branches)
+    return max(left[0], right[0]) + 1, max(left[1], right[1], left[0] + right[0] + 1)
+
+
+###########
+# Testing #
+###########
+
+# Test 1
+# Correct result => 6
+tree = TreeNode(3, TreeNode(1, None, TreeNode(2, TreeNode(7))), TreeNode(4, None, TreeNode(5)))
+print(diameter(tree))
+
+# Test 2
+# Correct result => 5
+tree = TreeNode(5, TreeNode(3, TreeNode(2, TreeNode(1)), TreeNode(4, None, TreeNode(8))), TreeNode(6))
+print(diameter(tree))