full binary tree

Author: aish21

Practice Concepts/Trees/binary-tree.py

@@ -0,0 +1,43 @@
+# Python implementation of Binary Tree
+
+class Node:
+    def __init__(self, item):
+        self.left = None
+        self.right = None
+        self.val = item
+
+    def inOrder(self):
+        if self.left:
+            self.left.inOrder()
+        print(self.val, end=' ')
+        if self.right:
+            self.right.inOrder()
+    
+    def preOrder(self):
+        print(self.val, end=' ')
+        if self.left:
+            self.left.preOrder()
+        if self.right:
+            self.right.preOrder()
+    
+    def postOrder(self):
+        if self.left:
+            self.left.postOrder()
+        if self.right:
+            self.right.postOrder()
+        print(self.val, end=' ')
+
+# Driver Code
+root = Node(1)
+root.left = Node(2)
+root.right = Node(3)
+root.left.left = Node(4)
+
+print("Pre order Traversal: ", end="")
+root.preOrder()
+print("\nIn order Traversal: ", end="")
+root.inOrder()
+print("\nPost order Traversal: ", end="")
+root.postOrder()
+        
+        

Practice Concepts/Trees/full-binary-tree.py

@@ -0,0 +1,35 @@
+# Python implementation of checking for full binary tree
+
+class Node:
+    def __init__(self, item):
+        self.leftC = None
+        self.rightC = None
+        self.item = item
+
+def isFullBinaryTree(root):
+    
+    # Empty Tree
+    if root is None:
+        return True
+    
+    if root.leftC is None and root.rightC is None:
+        return True
+    
+    if root.leftC is not None and root.rightC is not None:
+        return isFullBinaryTree(root.leftC) and isFullBinaryTree(root.rightC)
+    
+    return False
+
+# Driver Code
+root = Node(1)
+root.rightChild = Node(3)
+root.leftChild = Node(2)
+root.leftChild.leftChild = Node(4)
+root.leftChild.rightChild = Node(5)
+root.leftChild.rightChild.leftChild = Node(6)
+root.leftChild.rightChild.rightChild = Node(7)
+
+if(isFullBinaryTree(root)):
+    print("The tree is a full binary tree")
+else:
+    print("The tree is not a full binary tree")

README.md

@@ -218,19 +218,24 @@
 
     ![](https://github.com/aish21/Algorithms-and-Data-Structures/blob/main/Resources/Animations/post-order-traversal.gif)
 
-### [Binary Tree](/Practice%20Concepts/Trees/tree-traverse.py)
+### [Binary Tree](/Practice%20Concepts/Trees/binary-tree.py)
 * Tree data structure in which each parent node can have at most 2 children. Each node contains - data item, address of left child, address of right child.
-    - Full Binary Tree: 
+    - [Full Binary Tree](/Practice%20Concepts/Trees/full-binary-tree.py): 
         - Every parent/internal node has either 2 or no children nodes. 
 
         ![](https://github.com/aish21/Algorithms-and-Data-Structures/blob/main/Resources/Animations/full-binary-tree.png)
 
         - Also known as a proper binary tree
-        - Let i = number of internal nodes
-              n = total number of nodes
-              l = number of leaves
-              λ = number of levels
-        - 
+        - Let i = number of internal nodes |
+              n = total number of nodes |
+              l = number of leaves |
+              λ = number of levels 
+        - Number of leaves = i + 1
+        - n = 2i + 1
+        - l = (n + 1) / 2
+        - i = l – 1
+        - l is at most 2<sup>λ</sup> - 1
+