{"id":10426,"date":"2024-04-01T16:41:59","date_gmt":"2024-04-01T11:11:59","guid":{"rendered":"https:\/\/btechgeeks.com\/?p=10426"},"modified":"2024-04-02T11:57:27","modified_gmt":"2024-04-02T06:27:27","slug":"python-interview-questions-on-trees","status":"publish","type":"post","link":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/","title":{"rendered":"Python Interview Questions on Trees"},"content":{"rendered":"<p>We have compiled most frequently asked\u00a0<a href=\"https:\/\/btechgeeks.com\/python-interview-questions\/\">Python Interview Questions<\/a>\u00a0which will help you with different expertise levels.<\/p>\n<h2>Python Interview Questions on Trees<\/h2>\n<p>There are several types of data structures that can be used to tackle application problems. We have seen how linked lists work in a sequential manner, we have also seen how stacks and queues can be used in programming applications but they are very restricted data structures. The biggest problem while dealing with linear data structure is that if we have to conduct a search, the time taken increases linearly with the size of the data. Whereas there are some cases where linear structures can be really helpful but the fact remains that they may not be a good choice for situations that require high speed.<\/p>\n<p>So, now let\u2019s move on from the concept of linear data structures to nonlinear data structures called trees. Every tree has a distinguished node called the root. Unlike the trees that we know in real life the tree data structure branches downwards from parent to child and every node except the root is connected by a direct edge from exactly one other node.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10441\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-1.png\" alt=\"Python Interview Questions on Trees chapter 13 img 1\" width=\"325\" height=\"217\" srcset=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-1.png 325w, https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-1-300x200.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><\/p>\n<ul>\n<li><a href=\"https:\/\/btechgeeks.com\/data-structures-lecture-notes\/\">Data Structures Lecture Notes PDF | DS Lecture Notes &amp; Study Material PDF Free Download<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/advanced-data-structure-notes\/\">Advanced Data Structures and Algorithms Notes and Study Material PDF Free Download<\/a><\/li>\n<li><a href=\"https:\/\/btechgeeks.com\/search-implementations-linear-and-binary\/\">Search implementations: Linear and Binary<\/a><\/li>\n<\/ul>\n<p>Look at the figure given above:<br \/>\nA is the root and it is parent to three nodes &#8211; B, C, and D.<br \/>\nSame way B is a parent to E and C is a parent to F and G.<\/p>\n<p>Nodes like D, E, F, and G that have no children are called leaves or external nodes.<br \/>\nNodes that have at least child such as B and C are called internal nodes.<br \/>\nThe number of edges from the root to the node is called the depth or level of a<br \/>\nnode. The depth of B is 1 whereas the depth of G is 2.<br \/>\nThe height of a node is the number of edges from the node to the deepest leaf.<br \/>\nB, C, and D are siblings because they have the same parent A. Similarly, F and<br \/>\nG are also siblings because they have the same parent C.<br \/>\nChildren of one node are independent of children of another node.<br \/>\nEvery leaf node is unique.<\/p>\n<ul>\n<li>The file system that we use on our computer machines is an example of the tree structure.<\/li>\n<li>Additional information about the node is known as payload. Payload is not given much importance in algorithms but it plays a very important role in modem day computer applications.<\/li>\n<li>An edge connects two nodes to show that there is a relationship between them.<\/li>\n<li>There is only one incoming edge to every node (except the root). However, a node may have several outgoing edges.<\/li>\n<li>The root of the tree is the only node of the tree that has no incoming edges as it marks the starting point for a tree.<\/li>\n<li>Set of nodes having incoming edges from the same node are the children of that node.<\/li>\n<li>A node is a parent of all the nodes that connect to it by the outgoing edges.<\/li>\n<li>A set of nodes and edges that comprises a parent along with all its descendants are called subtrees.<\/li>\n<li>A unique path traverses from the root to each node.<\/li>\n<li>A tree that has a maximum of two children is called a binary tree.<\/li>\n<\/ul>\n<p><strong>Recursive definition of a tree<\/strong><\/p>\n<p>A tree can be empty, or it may have a root with zero or more subtree. The root of every subtree is connected to the root of a parent tree by an edge.<\/p>\n<p><strong>Simple Tree Representation<\/strong><\/p>\n<p>Have a look at the following tree. Here, we are considering the case of a binary tree.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10442\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-2.png\" alt=\"Python Interview Questions on Trees chapter 13 img 2\" width=\"343\" height=\"241\" srcset=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-2.png 343w, https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-2-300x211.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/p>\n<p>In the case of a binary tree, a node cannot have more than two children. So, for ease of understanding, we can say that the above scenario is similar to something like this:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10443\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-3.png\" alt=\"Python Interview Questions on Trees chapter 13 img 3\" width=\"515\" height=\"359\" srcset=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-3.png 515w, https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-3-300x209.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>In this diagram, left and right are references to the instances of the node that are located on the left and right of this node respectively. As you can see, every node has three values:<\/p>\n<ol>\n<li>Data<\/li>\n<li>Reference to the child on left<\/li>\n<li>Reference to the child on the right<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10444\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-4.png\" alt=\"Python Interview Questions on Trees chapter 13 img 4\" width=\"502\" height=\"339\" srcset=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-4.png 502w, https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-4-300x203.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>So, the constructor for the node class to create a Node object will be as follows:<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">class Node(object):\r\n     def_init_(self, data_value):\r\n         self.data_value = data_value\r\n         self.left = None\r\n         self.right = None<\/pre>\n<p>So, this is how a root node is created:<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Root_Node\r\nprint (\"Create Root Node\")\r\nroot = Node(\"Root_Node\")\r\nprint(\"Value of Root = \",root.data_value,\" left =\",root.left, \" right = \", root.right)<\/pre>\n<p>When we execute this block of code, the output is as follows:<br \/>\nCreate Root Node<\/p>\n<p>Value of Root = Root_Node left = None right = None<br \/>\nValue of Node = Tree Left left = None right = None<\/p>\n<p>Now, we write code for inserting values to the left or right. When a node is created, initially it&#8217;s left and right reference point to None. So, to add a child to left we just need to say:<br \/>\n<strong>self. left = child_node<\/strong><br \/>\nand a child can be added to right in a similar way:<br \/>\n<strong>self.left = child_node<\/strong><br \/>\nHowever, if the root node is already pointing to some existing child and we try to insert a child node then the existing child should be pushed down one level and the new object must take its place. So, the reference of the existing child stored in <strong>self.left<\/strong> is passed on to <strong>child.left<\/strong> and then <strong>self.help<\/strong> is assigned the reference to child. This can be achieved in the following manner:<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def insert_left (self, child):\r\n     if self.left is None :\r\n        self.left = child\r\nelse:\r\n     child.left = self.left\r\n     self.left = child\r\ndef insert_right(self, child):\r\n    if self.right is None:\r\n       self.right = child\r\nelse :\r\n    child.right = self.right\r\n    self.right = child<\/pre>\n<p><strong>Code<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">class Node(object):\r\n     def_init_(self, data__value) :\r\n        self . data_value = data_value\r\n        self.left = None\r\n        self.right = None\r\n\r\ndef insert_left(self, child):\r\n     if self.left is None:\r\n         self.left = child\r\nelse:\r\n     child.left = self.left\r\n     self.left = child\r\ndef insert_right(self, child):\r\n    if self.right is None:\r\n       self.right = child\r\nelse:\r\n    child.right = self.right\r\n    self.right = child<\/pre>\n<p><strong>Execution<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Root_Node\r\nprint (\"Create Root Node\")\r\nroot = Node(\"Root_Node\")\r\nprint(\"Value of Root = \",root.data_value,\" left = \",root.left, \" right = \", root.right)\r\n#Tree_Left\r\nprint(\"Create Tree_Left\")\r\ntree_left = Node(\"Tree_Left\")\r\nroot.insert_left(tree_left)\r\nprint (\"Value of Node = \", tree__left. data_value, \" left =\",tree_left.left, \" right = \",tree_left. right)\r\nprint(\"Value of Root = \", root,data_value,\" left = \",root.left, \" right = \", root.right)\r\n#Tree_Right\r\nprint(\"Create Tree_Right\")\r\ntree__right = Node (\"Tree_Right\")\r\nroot.insert_right(tree_right)\r\nprint(\"Value of Node = \",tree_right.data_value, \" left =\",tree_right.left, \" right = \",tree_right. right)\r\nprint(\"Value of Root = \" , root. data__value, \" left = \",root.left, \" right = \", root.right)\r\n#TreeLL\r\nprint(\"Create TreeLL\") tree11 = Node(\"TreeLL\")\r\ntree_left.insert_left(tree11)\r\nprint(\"Value of Node = \",tree11.data_value,\" left =\",tree11.left, \" right = \",tree11.right)\r\nprint(\"Value of Node = \",tree_left.data_value,\" left =\",tree_left.left, \" right = \",tree_left. right)\r\nprint(\"Value of Root = \", root.data_value,\" left =\",root.left, \" right = \", root.right)<\/pre>\n<p><strong>Output<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">Create Root Node\r\nValue of Root = Root_Node left = None right = None\r\nCreate Tree_Left\r\nValue of Node = Tree_Left left = None right = None\r\nValue of Root = Root_Node left = &lt; main .Node\r\nobject at 0x000000479EC84F60&gt; right = None Create Tree_Right\r\nValue of Node = Tree_Right left = None right = None\r\nValue of Root = Root_Node left = &lt; main .Node\r\nobject at 0x000000479EC84F60&gt; right = &lt; main\r\nNode object at 0x000000479ED05E80&gt;\r\nCreate TreeLL\r\nValue of Node = TreeLL left = None right =\r\nNone\r\nValue of Node = Tree_Left left = &lt; main .Node\r\nobject at 0x000000479ED0F160&gt; right = None\r\nValue of Root = Root_Node left = &lt; main .Node\r\nobject at 0x000000479EC84F60&gt; right = &lt; main .\r\nNode object at 0x000000479ED05E80&gt;<\/pre>\n<p>Question 1.<br \/>\nWhat is the definition of a tree?<br \/>\nAnswer.<br \/>\nA tree is a set of nodes that store elements. The nodes have a parent-child relationship such that:<\/p>\n<ul>\n<li>If the tree is not empty, it has a special node called the root of the tree. The root has no parents.<\/li>\n<li>Every node of the tree different from the root has a unique parent node.<\/li>\n<\/ul>\n<p>Question 2.<br \/>\nWrite a code to represent a tree through lists or a list of lists.<br \/>\nAnswer:<br \/>\nIn the list of lists, we shall store the value of the node as the first element. The second element will be the list that represents the left subtree and the third element represents the right subtree. The following figure shows a tree with just the root node.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10445\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-5.png\" alt=\"Python Interview Questions on Trees chapter 13 img 5\" width=\"140\" height=\"87\" \/><br \/>\nNow, suppose we add a node to the left.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-10446\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-6.png\" alt=\"Python Interview Questions on Trees chapter 13 img 6\" width=\"271\" height=\"186\" \/><br \/>\nNow, adding another subtree to the right would be equal to:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-10447\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-7.png\" alt=\"Python Interview Questions on Trees chapter 13 img 7\" width=\"316\" height=\"158\" srcset=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-7.png 316w, https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-7-300x150.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nSame way adding a node to the left of Tree Left would mean:<\/p>\n<p>Implement Trees with Lists<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10448\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-8.png\" alt=\"Python Interview Questions on Trees chapter 13 img 8\" width=\"397\" height=\"231\" srcset=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-8.png 397w, https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-8-300x175.png 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><\/p>\n<p>Here you can see that the tree can be defined as follows:<br \/>\nbinary_tree = [ &#8216;Root_Node&#8217; , [ &#8216;Tree_Left&#8217; ,[ &#8216;TreeLL&#8217;,[ ],[ ] ],[ ] ], [ &#8216;Tree_Right&#8217;,[ ],[ ] ] ]<\/p>\n<p>Here, the root is <strong>Root_Node<\/strong> which is located at <strong>binary_tree[0]<\/strong>.<br \/>\nLeft subtree is at <strong>binary_tree[1]<\/strong>.<br \/>\nThe right subtree is at <strong>binary_tree[2]<\/strong>.<br \/>\nNow let\u2019s write the code for this.<\/p>\n<p><strong>Step 1:<\/strong><\/p>\n<p><strong>Define Class<\/strong><\/p>\n<pre>class Tree:<\/pre>\n<p><strong>Step 2:<\/strong><\/p>\n<p><strong>Create Constructor<\/strong><\/p>\n<p>Now let\u2019s write the code for the constructor. Here, when we create an object we pass a value. The constructor creates a list where the value is placed at index 0 and at index 1 and 2 we have two empty lists. If we have to add subtree at the left side we will do so at index 1 and for the right subtree, we will insert values in the list at index 2.<\/p>\n<pre>def_init_(self, data):\r\nself.tree = [data, [ ],[ ] ]<\/pre>\n<p><strong>Step 3:<\/strong><\/p>\n<p><strong>Define a function to insert left and right subtree<\/strong><\/p>\n<p>If you have to insert a value in the left subtree then pop the element at index 1 and insert the new list at that place. Similarly, if you have to insert a child on the right-hand side, pop the value at index 2 and insert the new list.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def left_subtree(self,branch):\r\n        left_list = self . tree.pop(1)\r\n        self.tree.insert(1,branch.tree)\r\n\r\ndef right_subtree(self,branch):\r\n    right_list = self.tree.pop(2)\r\n    self.tree.insert(2,branch.tree)<\/pre>\n<p>Now, let\u2019s execute the code:<\/p>\n<p><strong>Code<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">class Tree:\r\n     def_init_(self,data):\r\n         self.tree = [data, [ ],[ ] ]\r\n\r\ndef left_subtree(self,branch):\r\n    left_list = self.tree.pop(1)\r\n    self.tree.insert(1,branch.tree)\r\n\r\ndef right_subtree(self,branch):\r\n    right_list = self.tree.pop(2)\r\n     self.tree.insert(2,branch.tree)<\/pre>\n<p><strong>Execution<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">print(\"Create Root Node\")\r\nroot = Tree(\"Root_node\")\r\nprint(\"Value of Root = \", root.tree)\r\nprint(\"Create Left Tree\")\r\ntree_left = Tree(\"Tree_Left\")\r\nroot.left_subtree(tree_left)\r\nprint(\"Value of Tree_Left = \", root.tree)\r\nprint(\"Create Right Tree\")\r\ntree_right = Tree(\"Tree_Right\")\r\nroot.right_subtree(tree_right)\r\nprint(\"Value of Tree_Right = \", root.tree)\r\nCreate Root Node\r\nValue of Root = ['Root_node', [ ], [ ] ]\r\nCreate Left Tree\r\nValue of Tree_Left = ['Root_node', ['Tree_Left', [ ] ]\/ [ ] ]\r\nCreate Right Tree\r\nValue of Tree_Right = ['Root_node', [ 'Tree_Left', [ ], [ ] ], ['Tree_Right', [ ], [ ] ] ]\r\nCreate Terrell\r\nValue of Tree_Left = ['Root_node', ['Tree_Left', [ 'TreeLL', [ ], [ ] ], [ ] ], ['Tree_Right', [ ], [ ] ] ]\r\n&gt;&gt;&gt;<\/pre>\n<p>There is however one thing ignored in this code. What if we want to insert a child somewhere in between? Here, in this case the child will be inserted at the given location and the subtree existing at that place will be pushed down.<\/p>\n<p>For this we make changes in the insert functions.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def left_subtree(self,branch):\r\n    left_list = self.tree.pop(1)\r\n    if len(left_list) &gt; 1:\r\n        branch.tree[1]=left_list\r\n        self.tree.insert (1,branch.tree)\r\n  else:\r\n        self.tree.insert(1,branch.tree)<\/pre>\n<p>If we have to insert a child in the left then first we pop the element at index 1. If the length of element at index 1 is 0 then, we simply insert the list. However, if the length is not zero then we push the element to the left of the new child. The same happens in case of right subtree.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def right_subtree(self,branch):\r\n       right_list = self.tree.pop (2)\r\n       if len(right_list) &gt; 1:\r\n          branch.tree[2]=right_list\r\n          self.tree.insert(2,branch.tree)\r\n    else:\r\n         self.tree.insert(2,branch.tree)\r\nprint (\"Create TreeLL\")\r\ntree11 = Tree(\"TreeLL\")\r\ntree_left.left_subtree(tree11)\r\nprint(\"Value of Tree_Left = \", root.tree)<\/pre>\n<p><strong>Code<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">class Tree:\r\n   def_init_(self,data) :\r\n      self.tree = [data, [ ], [ ] ]\r\n\r\ndef left_subtree(self,branch):\r\n    left_list = self.tree.pop(1)\r\n    if len(left_list) &gt; 1:\r\n       branch.tree[1]=left_list\r\n       self.tree.insert (1,branch.tree)\r\n  else:\r\n       self.tree.insert(1,branch.tree)\r\n\r\ndef right_subtree(self,branch):\r\n    right_list = self.tree.pop(2)\r\n    if len(right_list) &gt; 1:\r\n        branch.tree[2]=right_list\r\n        self.tree.insert(2,branch.tree)\r\n   else:\r\n      self.tree.insert(2,branch.tree)<\/pre>\n<p><strong>Execution<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">print (\"Create Root Node\")\r\nroot = Tree(\"Root_node\")\r\nprint(\"Value of Root = \", root.tree)\r\nprint(\"Create Left Tree\")\r\ntree_left = Tree(\"Tree_Left\")\r\nroot.left_subtree(tree_left)\r\nprint(\"Value of Tree_Left = \", root.tree)\r\nprint(\"Create Right Tree\")\r\ntree_right = Tree(\"Tree_Right\")\r\nroot.right_subtree(tree_right)\r\nprint(\"Value of Tree_Right = \", root.tree)\r\nprint(\"Create Left Inbetween\")\r\ntree_inbtw = Tree(\"Tree left in between\")\r\nroot.left_subtree(tree_inbtw)\r\nprint(\"Value of Tree_Left = \", root.tree)\r\nprint(\"Create TreeLL\")\r\ntreell = Tree(\"TreeLL\")\r\ntree_left.left_subtree(tree11)\r\nprint(\"Value of TREE = \", root.tree)<\/pre>\n<p><strong>Output<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">Create Root Node\r\nValue of Root = ['Root node', [ ], [ ] ]\r\nCreate Left Tree\r\nValue of Tree Left = [ 'Root node', [ 'Tree Left', [ ], [ ] ], [ ] ]\r\nCreate Right Tree\r\nValue of Tree Right = [ 'Root node' , [ 'Tree Left', [ ] , [lie 1 'Tree Right', [], [ ] ] ]\r\nCreate Left Inbetween\r\nValue of Tree Left = [ 'Root node' , [ 'Tree left in between' , [ 'Tree Left', [ ] , [ ] ] , [ ] ] ,\r\n['Tree_Right', [ ], [ ] ] ]\r\nCreate TreeLL\r\nValue of TREE = [ 'Root node', [ 'Tree left in between' , ['Tree Left' , [ 'TreeLL', [ ], [ ] ], [ ]], ['Tree_Right', [ ], [ ] ] ]\r\n&gt;&gt;&gt;<\/pre>\n<p>Question 3.<br \/>\nWhat is a binary tree? What are the properties of a binary tree?<br \/>\nAnswer:<br \/>\nA data structure is said to be a binary tree if each of its nodes can have at most two children. The children of the binary tree are referred to as the left child and the right child.<\/p>\n<p>Question 4.<br \/>\nWhat are tree traversal methods?<br \/>\nAnswer:<br \/>\nTraversals<br \/>\nPreorder Traversal: First visit the root node, then visit all nodes on the left followed by all nodes on the right.<\/p>\n<p><strong>Code<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">class Node(object) :\r\n     def_init_(self, data_value):\r\n         self.data_value = data_value\r\n         self.left = None\r\n         self.right = None\r\ndef insert_left(self, child):\r\n     if self.left is None:\r\n        self.left = child\r\nelse:\r\n      child.left = self.left\r\n      self.left = child\r\ndef insert_right(self, child):\r\n      if self.right is None:\r\n         self.right = child\r\nelse:\r\n     child.right = self.right\r\n     self.right = child\r\ndef preorder(self, node):\r\n\r\nres= [ ]\r\nif node:\r\n      res.append(node.data_value)\r\n      res = res + self.preorder(node.left)\r\n      res = res + self.preorder(node.right) \r\n   return res<\/pre>\n<p><strong>Execution<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Root_Node\r\nprint(\"Create Root Node\")\r\nroot = Node(\"Root_Node\")\r\n#Tree_Left\r\nprint (\"Create Tree_Left\")\r\ntree_left = Node(\"Tree_Left\")\r\nroot.insert_left(tree_left)\r\n#Tree_Right\r\nprint(\"Create Tree_Right\")\r\ntree_right = Node(\"Tree_Right\")\r\nroot.insert_right(tree_right)\r\n#TreeLL\r\nprint (\"Create TreeLL\")\r\ntreell = Node(\"TreeLL\")\r\ntree_left.insert_left(treell)\r\nprint(\"*****Preorder Traversal*****\")\r\nprint(root.preorder(root))<\/pre>\n<p><strong>Output<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">Create Root Node\r\nCreate Tree_Left\r\nCreate Tree_Right\r\nCreate TreeLL\r\n*****Preorder Traversal*****\r\n['Root_Node', 'Tree_Left', 'TreeLL', 'Tree_ Right']\r\n&gt;&gt;&gt;<\/pre>\n<p>In Order Traversal :First visit all nodes on the left then the root node and then all nodes on the right..<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">class Node(object):\r\n     def_init_(self, data_value):\r\n          self.data_value = data_value\r\n          self.left = None\r\n          self.right = None\r\n   def insert_left(self, child):\r\n       if self.left is None:\r\n          self.left = child\r\n   else:\r\n      child.left = self.left\r\n       self.left = child\r\ndef insert_right(self, child):\r\n    if self.right is None:\r\n       self.right = child\r\nelse:\r\n     child.right = self.right\r\n     self.right = child\r\ndef inorder(self, node):\r\n  res=[ ]\r\n  if node:\r\n       res = self.inorder(node.left)\r\n       res.append(node.data_value)\r\n        res = res + self.inorder(node.right)\r\n  return res\r\n# Root_Node\r\nprint(\"Create Root Node\")\r\nroot = Node(\"Root_Node\")\r\n#Tree_Left\r\nprint (\"Create Tree_Left\")\r\ntree_left = Node(\"Tree_Left\")\r\nroot.insert_left(tree_left)\r\n#Tree_Right\r\nprint(\"Create Tree_Right\")\r\ntree_right = Node(\"Tree_Right\")\r\nroot.insert_right(tree_right)\r\n#TreeLL\r\nprint(\"Create TreeLL\")\r\ntreell = Node (\"TreeLL\")\r\ntree_left.insert_left (treell)\r\nprint(\"*****Inorder Traversal*****)\r\nprint(root.inorder(root))<\/pre>\n<p><strong>Output<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">Create Root Node\r\nCreate Tree_Left\r\nCreate Tree_Right\r\nCreate TreeLL\r\n*****Inorder Traversal*****\r\n*****Inorder Traversal*****\r\n*****Inorder Traversal*****\r\n*****Inorder Traversal*****\r\n*****Inorder Traversal*****\r\n*****Inorder Traversal*****\r\n*****Inorder Traversal*****\r\n*****Inorder Traversal*****\r\n*****Inorder Traversal*****\r\n[\"TreeLL' , 'Tree_Left' , 'Root_Node' , 'Tree_Right']\r\n&gt;&gt;&gt;<\/pre>\n<p><strong>Post order Traversal:<\/strong> Visit all nodes on the left, then visit all nodes on the right , then visit the root node.<\/p>\n<p><strong>code<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">class Node(object):\r\n     def_init_(self, data_value):\r\n        self.data_value = data_value\r\n        self.left = None\r\n        self.right = None\r\n    def insert_left (self, child):\r\n        if self.left is None:\r\n           self.left = child\r\nelse:\r\n     child.right = self.right\r\n     self.right = child\r\ndef postorder (self, node):\r\nres = [ ]\r\nif node:\r\n    res = self.postorder (node.left)\r\n    res = res + self.postorder (node.right)\r\n    res.append (node.data_value)\r\n\r\n   return res<\/pre>\n<p><strong>Execution<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">#Root_Node\r\nprint(\"Create Root Node\")\r\nroot = Node (\"Root_Node\")\r\n#Tree_Left\r\nprint(\"Create Tree_Left\")\r\ntree_left = Node(\"Tree_Left\")\r\nroot.insert_left(tree_left)\r\n#Tree_Right\r\nprint(\"Create Tree_Right\")\r\ntree_right = Node(\"Tree_Right\")\r\n\r\nroot . insert_right(tree_right)\r\n#TreeLL\r\nprint (\"Create TreeLL\")\r\ntree11 = Node (\"TreeLL\")\r\ntree_left . insert_left(tree11)\r\nprint(\"*****postorder Traversal *****\")\r\nprint (root.postorder (root))\r\nOUTPUT\r\nCreate Root Node\r\nCreate Tree_Left\r\nCreate Tree_Right\r\nCreate TreeLL\r\n*****Postorder Traversal*****\r\n['TreeLL' , 'Tree_Left' , 'Tree_Right' , \"Root_Node']<\/pre>\n<p>A binary heap is a binary tree. It is a complete tree, which means that all levels are completely filled except possibly the last level. It also means that the tree is balanced<br \/>\nAs every new item is inserted next to the available space. A Binary heap can be stored in an array.<\/p>\n<p>A binary heap can be of two types: Min Heap or Max Heap. In case of Min Heap binary heap, the root node is the minimum of all the nodes in the binary heap,all parent nodes are smaller than their children. On the other hand in case of Max Heap the root is the maximum among all the keys present in the heap and and all nodes are bigger than their children.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10449\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-9.png\" alt=\"Python Interview Questions on Trees chapter 13 img 9\" width=\"498\" height=\"183\" srcset=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-9.png 498w, https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-9-300x110.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/p>\n<p>Heap has two important properties:<br \/>\n1. It is complete and is constructed from left to right across each row and the last row may not be completely full. Each row should be filled<br \/>\nup sequentially. So, the order of inserting values should be from left to right, row by row sequentially as shown in the following figure:<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10450\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-10.png\" alt=\"Python Interview Questions on Trees chapter 13 img 10\" width=\"245\" height=\"184\" \/><\/p>\n<p>2. The parent must be larger (Max Heap)\/smaller(Min Heap) than the children.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10451\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-11.png\" alt=\"Python Interview Questions on Trees chapter 13 img 11\" width=\"256\" height=\"192\" \/><\/p>\n<p>Look at the figure shown above, it is a case of Maximum heap because all parents are greater than their children.<br \/>\nThe binary heap can be represented in an array as follows:<br \/>\n0 1 2 3 4 5<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10452\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-12.png\" alt=\"Python Interview Questions on Trees chapter 13 img 12\" width=\"423\" height=\"113\" srcset=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-12.png 423w, https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-12-300x80.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/p>\n<p>If you look at the array carefully you will realize that if a parent exists at location n then the left child is at 2n+l and the right child is at 2n + 2. &#8221;<br \/>\nn= 0<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10453\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-13.png\" alt=\"Python Interview Questions on Trees chapter 13 img 13\" width=\"392\" height=\"254\" srcset=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-13.png 392w, https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-13-300x194.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>So, if we know the location of the parent child we can easily find out the location of the left and right child.<br \/>\nNow suppose we have to build up a Max Heap using following values: 20,4, 90, 1, 125<\/p>\n<p><strong>Step 1:<\/strong><br \/>\nInsert 20<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10454\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-14.png\" alt=\"Python Interview Questions on Trees chapter 13 img 14\" width=\"128\" height=\"66\" \/><\/p>\n<p><strong>Step 2:<\/strong><br \/>\nInsert 4 -&gt; Left to Right-&gt; First element in second row<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10455\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-15.png\" alt=\"Python Interview Questions on Trees chapter 13 img 15\" width=\"164\" height=\"127\" \/><\/p>\n<p>Since the parent is greater than the child, this is fine.<\/p>\n<p><strong>Step 3:<\/strong><br \/>\nInsert 90 -&gt; Left to Right -&gt; Second element in second row<br \/>\nHowever when we insert 90 as the right child, it violates the rule of the max heap because the parent has a key value of 20. So, in order to resolve this problem it is better to swap places as shown in the following figure:<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10456\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-16.png\" alt=\"Python Interview Questions on Trees chapter 13 img 16\" width=\"257\" height=\"132\" \/><\/p>\n<p>After swapping, the heap would look something like this:<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10457\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-17.png\" alt=\"Python Interview Questions on Trees chapter 13 img 17\" width=\"218\" height=\"128\" \/><\/p>\n<p><strong>Step 4:<\/strong><br \/>\nInsert 1 -&gt; left to right -&gt; first element third row<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10458\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-18.png\" alt=\"Python Interview Questions on Trees chapter 13 img 18\" width=\"202\" height=\"166\" \/><\/p>\n<p>Since 1 is smaller than the parent node, this is fine.<br \/>\n<strong>Step 5:<\/strong><br \/>\nInsert 125<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10459\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-19.png\" alt=\"Python Interview Questions on Trees chapter 13 img 19\" width=\"236\" height=\"185\" \/><\/p>\n<p>This violated the rule of Max Heap Swap 4 and 125<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10460\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-20.png\" alt=\"Python Interview Questions on Trees chapter 13 img 20\" width=\"259\" height=\"202\" \/><\/p>\n<p>Not a heap still Swap 125 and 90<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10461\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-21.png\" alt=\"Python Interview Questions on Trees chapter 13 img 21\" width=\"229\" height=\"172\" \/><\/p>\n<p>We now have a Max Heap.<\/p>\n<p>Question 5.<br \/>\nWrite python code to implement Max Heap. How would you insert a value so that the root node has the maximum value and all parents are greater than their children.<br \/>\nAnswer:<br \/>\nHere we will write The code to implement Maxheap class. The class will have two functions:<br \/>\n<strong>Push( ) :<\/strong> To insert value.<br \/>\n<strong>FIoat_up( ):<\/strong> To place the value where it belongs.<\/p>\n<p><strong>Step 1<\/strong><\/p>\n<p><strong>Define the class<\/strong><\/p>\n<pre>class MaxHeap:<\/pre>\n<p><strong>Step 2<\/strong><\/p>\n<p><strong>Define The Constructor<\/strong><\/p>\n<pre>def init (self):\r\nself.heap = [ ]<\/pre>\n<p><strong>Step 3<\/strong><\/p>\n<p><strong>Define the push( ) function<\/strong><\/p>\n<p>The push function does two jobs:<\/p>\n<ol>\n<li>Appends the value at the end of the list. (We have seen earlier that the value has to be inserted first at the available location)<\/li>\n<li>After appending the value, the push() function will call the float_ up(index) function. The pushQ function passes the index of the last element to the float_up() function so that the float_up() function can analyse the values and do the needful as described in the next step.<\/li>\n<\/ol>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def push(self,value):\r\n                 self.heap.append(value)\r\n                 self .floatj_up (len (self . heap) -1)<\/pre>\n<p><strong>Step 4<\/strong><br \/>\nDefine the float_up function<br \/>\n1. The <strong>float_up( )<\/strong>function takes index value as parameter.<\/p>\n<pre>def float_up (self, index) :<\/pre>\n<p>2. The push( ) function passes the index value of the last element in the heap. The first thing that the float function does is that it checks if the element is at index 0 or not. If yes, then it is the root node. Root node has no parents and since it\u2019s the last element of the heap it has no children either. So, we can return the value.<\/p>\n<pre>if index==0:\r\nreturn<\/pre>\n<p>3. If the index is greater than 0 then we can proceed further. Look the following figure once again:<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-10462\" src=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-22.png\" alt=\"Python Interview Questions on Trees chapter 13 img 22\" width=\"270\" height=\"199\" \/><\/p>\n<p>For programming, you need to understand few things:<\/p>\n<p>The index 0 has two children at position 1 and 2. If I have an element at 1 then I can find the parent by calculating value of (1\/\/2). Similarly for element at index 2, the parent\u2019s index value can be found out by calculating value of (2\/\/2 -1). So, we can say that if an element has an index value index and it is odd then it\u2019s parent\u2019s index value, parent_ ofindex = index\/\/2. However, if index is even parentofindex will be (index\/\/2)-1. This becomes the outer frame for the float_up function. The right child has an even number as index and the left child has an odd number as index.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">if index==0:\r\n         return\r\n   else:\r\n      if index%2==0:\r\n         parent_of_index = (index\/\/2)-l\r\n         ----------write code----------\r\n  else:\r\n         parent_of_index = index\/\/2\r\n         ----------write code--------<\/pre>\n<p>4. Now, we compare the values of the child and the parent. If the child is greater than the parent, swap the elements.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def float_up (self, index) :\r\n        if index==0:\r\n              return\r\n      else:\r\n        if index%2==0:\r\n           parent_of_index = (index\/\/2)-1\r\n           if self.heap[index]&gt; self, heap[parent_of_index]:\r\n          self.swap(index, parent_of_index)\r\n     else:\r\n          parent_of_index = index\/\/2\r\n          if self.heap[index]&gt; self, heap[parent_of_index]:\r\n         self.swap(index, parent_of_index)\r\n         self.float_up (parent_of_index)<\/pre>\n<p><strong>Step 5<\/strong><\/p>\n<p><strong>Define the swap function<\/strong><\/p>\n<p>The swap( ) function helps in swapping the values of the parent and the child, the code for this is given as follows:<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def swap(self,indexl, index2):\r\n      temp = self.heap[index1]\r\n      self.heap[index1] = self.heap[index2]\r\n      self.heap[index2] = temp<\/pre>\n<p><strong>Code<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">class MaxHeap:\r\n      def_init_(self):\r\n          self.heap = [ ]\r\n     def push(self,value):\r\n          self.heap.append(value)\r\n          self .float_up (len (self .heap) -1)\r\n    def float_up (self, index) :\r\n         if index==0:\r\n return\r\n    else:\r\n            if index%2==0:\r\n             parent_of_index = (index\/\/2)-1\r\n             if self.heap[index]&gt; self, heap[parent_of_index]:\r\n          self.swap(index, parent_of_ index)\r\n  else:\r\n            parent_of_index = index\/\/2\r\n            if self.heap[index]&gt; self, heap[parent_of_index]:\r\n            self.swap(index, parent_of_index)\r\n           self .float_up (parent_of_index)\r\ndef peek(self):\r\n      print(self.heap[0])\r\ndef pop(self):\r\n        if len(self.heap)&gt;=2:\r\n           temp = self.heap[0]\r\n             self.heap[0]=self.heap[len(self.heap)-1]\r\n              self.heap[len(self.heap)-1]\r\n             self.heap.pop( )\r\n             self.down_adj( )\r\n      elif len(self.heap)==1:\r\n            self.heap.pop( )\r\n  else:\r\n            print(\"Nothing to pop\")\r\n def swap(self,indexl, index2):\r\n            temp = self.heap[index1]\r\n            self.heap[indexl] = self.heap[index2]\r\n            self.heap[index2] = temp<\/pre>\n<p><strong>Execution<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">H = MaxHeap( )\r\nprint(\"*****pushing values***********\")\r\nprint(\"pushing 165\")\r\nH.push(165)\r\nprint(H.heap)\r\nprint(\"pushing 60\")\r\nH.push (60)\r\nprint(H.heap)\r\nprint(\"pushing 179\")\r\nH.push(179)\r\nprint(H.heap)\r\nprint(\"pushing 400\")\r\nH.push(400)\r\nprint(H.heap)\r\nprint(\"pushing 6\")\r\nH.push(6)\r\nprint(H.heap)\r\nprint(\"pushing 275\")\r\nH.push(275)\r\nprint(H.heap)<\/pre>\n<p><strong>Output<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">*****pushing values***********\r\npushing 165\r\n[165]\r\npushing 60\r\n[165, 60]\r\npushing 179\r\n[179, 60, 165]\r\npushing 400\r\n[400, 179, 165, 60]\r\npushing 6\r\n[400, 179, 165, 60, 6]\r\npushing 275\r\n[400, 179, 275, 60, 6, 165]\r\n&gt;&gt;&gt;<\/pre>\n<p>Question 6.<br \/>\nWrite code to find out the maximum value in the Max heap.<br \/>\nAnswer:<br \/>\nIt is easy to find the max value in the max heap as the maximum value is available at the root node which is index 0 of the heap.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def peek(self):\r\nprint(self.heap[0])<\/pre>\n<p>Question 7.<br \/>\nWrite the code to pop the maximum value from Max Heap.<br \/>\nAnswer:<br \/>\nThere are two steps involved:<\/p>\n<ol>\n<li>Swap the root with the last element in the array and pop the value.<\/li>\n<li>The root node now does have the maximum value. So, now we need to move downwards, comparing the parent with their left and right child to ensure that the children are smaller than the parent. If not we will have to swap places again.<\/li>\n<\/ol>\n<p><strong>Step 1<\/strong><\/p>\n<p><strong>Define pop( ) function.<\/strong><\/p>\n<p>The pop( ) function which swaps the values of the root node with the last element in the list and pops the value. The function then calls the down_ adj( ) function which moves downwards and adjusts the values. The pop() function first checks the size of the heap. If the length of the heap is 1 then that means that it only contains one element that\u2019s the root and there is no need to swap further.<\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def pop(self):\r\n          if len(self.heap)&gt;2:\r\n              temp = self.heap[0]\r\n              self.heap[0]=self.heap[len(self.heap)\u20141]\r\n              self.heap[len(self.heap)-1]\r\n              self.heap.pop ( )\r\n              print(\"heap after popping largest value =\", self.heap)\r\n             self.down_adj( )\r\n        elif len(self.heap)==1:\r\n            self.heap.pop( )\r\n     else:\r\n          print(\"Nothing to pop\")<\/pre>\n<p><strong>Step 2:<\/strong><\/p>\n<p><strong>Define downadj( ) function<\/strong><\/p>\n<p>Set Index Value To 0.<br \/>\nIndex of left child = left_child = index*2+1 Index of right child = right child = index*2+2<br \/>\nThen we go through loop where we check the value of the parent with both left and right child. If the parent is smaller than the left child then we swap the value. We then compare the parent value with the right child, if it is less then we swap again.<br \/>\nThis can be done as follows:<\/p>\n<ul>\n<li>Check if parent is less than left child:<\/li>\n<li>If yes, check if left child is less than the right child<\/li>\n<li>if yes, then swap the parent with the right child<\/li>\n<li>Change the value of index to value of right_child for further assessment<\/li>\n<li>If no the just swap the parent with the left child<\/li>\n<li>Set the value of index to value of left_child for further assessment<\/li>\n<li>If the parent is not less than left child but only less than the right child then swap values with the right child<\/li>\n<li>Change the value of index to right_child<\/li>\n<\/ul>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">def down_adj(self):\r\nindex = 0\r\nfor i in range(len(self.heap)\/\/2):\r\nleft_child = index*2+1 .\r\nif left_child &gt; len (self.heap) :\r\nreturn\r\nprint(\"left child = \", left_child)\r\nright_child = index*2+2\r\nif right_child &gt; len (self.heap) :\r\nreturn\r\nprint(\"right child = \", right_child)\r\nif self.heap[index]&lt;self.heap[left_child]:\r\ntemp = self.heap[index]\r\nself.heap[index] = self.heap[left_child]\r\nself.heap[left_child] = temp\r\nindex = left_child\r\nif self.heap[index]&lt;self.heap[right_child]:\r\ntemp = self.heap[index]\r\nself.heap[index] = self.heap[right_child]\r\nself.heap[right_child] = temp\r\nindex = right_child<\/pre>\n<p><strong>Code<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">class MaxHeap:\r\n      def_init_(self):\r\n         self.heap = [ ]\r\n    def push(self,value):\r\n         self.heap.append(value)\r\n         self .float_up (len (self, heap) -1)\r\ndef float_up (self, index) :\r\n     if index==0:\r\n           return\r\n    else:\r\n         if index%2==0:\r\n               parent_of_index = (index\/\/2)-1\r\n               if self.heap[index]&gt; self, heap[parent_of_index]:\r\n                            temp = self.heap[parent_of_index]\r\n                           self.heap[parent_of_index] =self.heap[index]\r\n                              self.heap[index] = temp\r\n         else:\r\n               parent_of_index = index\/\/2\r\n               if self.heap[index]&gt; self, heap[parent_of_index]:\r\n                           temp = self.heap[parent_of_index]\r\n                           self.heap[parent_of_index] = self.heap[index]\r\n                           self.heap[index] = temp self.float_up (parent_of_index)\r\n     def peek(self):\r\n              print(self.heap [0])\r\n     def pop(self):\r\n           if len(self.heap)&gt;=2:\r\n                    temp = self.heap[0]\r\n                    self.heap[0]=self.heap[len(self.heap)-1]\r\n                    self.heap[len(self.heap)-1]\r\n                    self.heap.pop( )\r\n                    self.down_adj( )\r\n                elif len(self.heap)==1:\r\n                    self.heap.pop ( )\r\n        else:\r\n                 print (\"Nothing to pop\")\r\ndef swap(self,indexl, index2):\r\n                temp = self.heap[index1]\r\n                self.heap[indexl] = self.heap[index2]\r\n                self.heap[index2] = temp\r\n\r\ndef down_adj(self):\r\n       index = 0\r\n       for i in range(len(self.heap)\/\/2):\r\n            left_child = index*2+1\r\n            if left_child &gt; len(self.heap)-1:\r\n                 print(self.heap)\r\n                 print(\"End Point\")\r\n                 print(\"Heap value after pop( ) =\",self.heap)\r\n     return\r\n            right_child = index*2+2\r\n            if right_child &gt; len(self.heap)-1:\r\n                   print (\"right child does not exist\")\r\n                     if self.heap[index]&lt;self.heap[left_child]:\r\n                 self.swap(index,left_child)\r\n                     index = left_child\r\n                print(\"Heap value after pop( ) =\", self.heap)\r\n   return\r\n                 if self.heap[index]&lt;self.heap[left_child]:\r\n                if self.heap[left_child]&lt;self. heap[right_child]:\r\n               self.swap(index,right_child) index = right_child \r\n      else:\r\n                 self.swap(index,left_child) index = left_child\r\n                  elif self.heap[index]&lt;self.heap[right_child]:\r\n           self.swap(index,right_child) index = right_child\r\n   else:\r\n           print(\"No change required\" )\r\n          print(\"Heap value after pop() = \", self.heap)<\/pre>\n<p>&nbsp;<\/p>\n<p><strong>Execution<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">H = MaxHeap( )\r\nprint(\"*****pushing values***********\")\r\nH.push (165)\r\nprint(H.heap)\r\nH.push(60)\r\nprint(H.heap)\r\nH.push(179)\r\nprint(H.heap)\r\nH.push(400)\r\nprint(H.heap)\r\nH.push(6)\r\nprint(H.heap)\r\nH.push(275)\r\nprint(H.heap)\r\nprint(\"*********popping values*******\")\r\nH.pop ( )\r\nH.pop( )\r\nH.pop ( )\r\nH.pop ( )\r\nH.pop ( )\r\nH.pop ( )\r\nH.pop ( )<\/pre>\n<p><strong>Output<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">pushing values\r\n[165]\r\n[165, 60]\r\n[179, 60, 165]\r\n[400, 179, 165, 60]\r\n[400, 179, 165, 60, 6]\r\n[400, 179, 275, 60, 6, 165]\r\n*********popping values*******\r\n[275, 179, 165, 60, 6]\r\nEnd Point\r\nHeap value after pop( ) = [275, 179, 165, 60, 6]\r\nright child does not'exist\r\nHeap value after pop() = [179, 60, 165, 6]\r\nHeap value after pop() = [165, 60, 6]\r\nright child does not exist\r\nHeap value after pop() = [60, 6]\r\nHeap value after pop () = [6]\r\nNothing to pop\r\n&gt;&gt;&gt;<\/pre>\n<p>Question 8.<br \/>\nTime complexity for max heap:<br \/>\nAnswer:<\/p>\n<ul>\n<li>Insert: 0(log n)<\/li>\n<li>Get Max: 0(1) because the maximum value is always the root at &#8216; index( )<\/li>\n<li>Remove Max: 0(log n)<\/li>\n<\/ul>\n<p>The implementation of Min Heap is similar to Max Heap just that in this case the root has the lowest value and the value of parent is less than the left and right child.<\/p>\n<p><strong>Code<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">class MinHeap:\r\ndef_init_(self):\r\n     self.heap = [ ]\r\ndef push(self,value):\r\n      self.heap.append(value)\r\n      self .float_up (len (self .heap) -1)\r\ndef float_up (self, index) :\r\n   if index==0:\r\n        return\r\nelse:\r\n   if index%2==0:\r\n        parent_of_index = (index\/\/2)-1\r\n        if self.heap[index]&lt; self, heap[parent_of_index]:\r\n        self.swap(index, parent_of_index)\r\nelse:\r\n       parent_of_index = index\/\/2\r\n      if self.heap[index]&lt; self, heap[parent_of_index]:\r\n     self.swap(index, parent_of_index)\r\n     self .floatyup (parent_of_index)\r\ndef peek(self) :\r\n      print(self.heap [0])\r\ndef pop (self) :\r\n     if len(self.heap)&gt;=2:\r\n     temp = self.heap[0]\r\n     self.heap[0]=seIf.heap[len(self.heap)-1]\r\n     self.heap[len(self.heap)-1]\r\n     self.heap.pop ( )\r\n     self.down_adj( )\r\n  elif len(self.heap)==1:\r\n     self.heap.pop()\r\nelse:\r\n     print(\"Nothing to pop\")\r\ndef swap(self,indexl, index2):\r\n     temp = self.heap[index1]\r\n     self.heap[indexl] = self.heap[index2]\r\n     self.heap[index2] = temp<\/pre>\n<p><strong>Execution<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">H = MinHeap( )\r\nprint(\"*****pushing values***********\")\r\nprint(\"pushing 165\")\r\nH.push (165)\r\nprint(H.heap)\r\nprint(\"pushing 60\")\r\nH.push(60)\r\nprint(H.heap)\r\nprint(\"pushing 179\")\r\nH.push(179)\r\nprint(H.heap)\r\nprint(\"pushing 400\")\r\nH.push(400)\r\nprint(H.heap)\r\nprint(\"pushing 6\")\r\nH.push (6)\r\nprint(H.heap)\r\nprint(\"pushing 275\")\r\nH.push(275) '\r\nprint(H.heap)<\/pre>\n<p><strong>Output<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\">*****pushing values***********\r\npushing 165 [165]\r\npushing 60\r\n[60, 165]\r\npushing 179\r\n[60, 165, 179]\r\npushing 400\r\n[60, 165, 179, 400]\r\npushing 6\r\n[6, 60, 179, 400, 165]\r\npushing 275\r\n[6, 60, 179, 400, 165, 275]\r\n&gt;&gt;&gt;<\/pre>\n<p>Question 9.<br \/>\nWhat are the applications of binary heap?<br \/>\nAnswer:<\/p>\n<ul>\n<li>Dijkstra Algorithm<\/li>\n<li>Prims Algorithm<\/li>\n<li>Priority Queue<\/li>\n<li>Can be used to solve problems such as:<\/li>\n<li>K\u2019th Largest Element in an array<\/li>\n<li>Sort an almost sorted array<\/li>\n<li>Merge K Sorted Array<\/li>\n<\/ul>\n<p>Question 10.<br \/>\nWhat is a priority queue and how can it be implemented?<br \/>\nAnswer:<br \/>\nPriority queue is like a queue but it is more advanced. It has methods same as a queue. However, the main difference is that it keeps the value of higher priority at front and the value of lowest priority at the back. Items are added from the rear and removed from the front. In priority queue elements are added in order. So, basically there is a priority associated with every element. Element of highest priority is removed first. Elements of equal priority are treated ass per their order in queue.<\/p>\n<p>Binary heap is the most preferred way of implementing priority queue as they can retrieve the element of highest priority in 0(1) time. Insert and delete can take O(logn) time. Besides that since, the binary heap use lists or arrays, it is easy to locate elements and the processes involved are definitely quite cache friendly. Binary heaps do not demand extra space for pointers and are much easier to insert.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We have compiled most frequently asked\u00a0Python Interview Questions\u00a0which will help you with different expertise levels. Python Interview Questions on Trees There are several types of data structures that can be used to tackle application problems. We have seen how linked lists work in a sequential manner, we have also seen how stacks and queues can &#8230; <a title=\"Python Interview Questions on Trees\" class=\"read-more\" href=\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/\" aria-label=\"More on Python Interview Questions on Trees\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python Interview Questions on Trees - BTech Geeks<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python Interview Questions on Trees - BTech Geeks\" \/>\n<meta property=\"og:description\" content=\"We have compiled most frequently asked\u00a0Python Interview Questions\u00a0which will help you with different expertise levels. Python Interview Questions on Trees There are several types of data structures that can be used to tackle application problems. We have seen how linked lists work in a sequential manner, we have also seen how stacks and queues can ... Read more\" \/>\n<meta property=\"og:url\" content=\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/\" \/>\n<meta property=\"og:site_name\" content=\"BTech Geeks\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/btechgeeks\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-01T11:11:59+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-04-02T06:27:27+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-1.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@btech_geeks\" \/>\n<meta name=\"twitter:site\" content=\"@btech_geeks\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"26 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/btechgeeks.com\/#organization\",\"name\":\"BTech Geeks\",\"url\":\"https:\/\/btechgeeks.com\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/btechgeeks\",\"https:\/\/www.instagram.com\/btechgeeks\/\",\"https:\/\/www.linkedin.com\/in\/btechgeeks\",\"https:\/\/www.youtube.com\/channel\/UC9MlCqdJ3lKqz2p5114SDIg\",\"https:\/\/in.pinterest.com\/btechgeek\/\",\"https:\/\/twitter.com\/btech_geeks\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/btechgeeks.com\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2020\/11\/BTechGeeks.png\",\"contentUrl\":\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2020\/11\/BTechGeeks.png\",\"width\":350,\"height\":70,\"caption\":\"BTech Geeks\"},\"image\":{\"@id\":\"https:\/\/btechgeeks.com\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/btechgeeks.com\/#website\",\"url\":\"https:\/\/btechgeeks.com\/\",\"name\":\"BTech Geeks\",\"description\":\"Lecture Notes for BTech, BSc Students\",\"publisher\":{\"@id\":\"https:\/\/btechgeeks.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/btechgeeks.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-1.png\",\"contentUrl\":\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-1.png\",\"width\":325,\"height\":217,\"caption\":\"Python Interview Questions on Trees chapter 13 img 1\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#webpage\",\"url\":\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/\",\"name\":\"Python Interview Questions on Trees - BTech Geeks\",\"isPartOf\":{\"@id\":\"https:\/\/btechgeeks.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#primaryimage\"},\"datePublished\":\"2024-04-01T11:11:59+00:00\",\"dateModified\":\"2024-04-02T06:27:27+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/btechgeeks.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Python Interview Questions on Trees\"}]},{\"@type\":\"Article\",\"@id\":\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#webpage\"},\"author\":{\"@id\":\"https:\/\/btechgeeks.com\/#\/schema\/person\/ea8ce699662f0d7e248e52fe080b85bb\"},\"headline\":\"Python Interview Questions on Trees\",\"datePublished\":\"2024-04-01T11:11:59+00:00\",\"dateModified\":\"2024-04-02T06:27:27+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#webpage\"},\"wordCount\":3032,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/btechgeeks.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-1.png\",\"articleSection\":[\"Python\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#respond\"]}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/btechgeeks.com\/#\/schema\/person\/ea8ce699662f0d7e248e52fe080b85bb\",\"name\":\"Prasanna\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/btechgeeks.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"caption\":\"Prasanna\"},\"url\":\"https:\/\/btechgeeks.com\/author\/prasanna\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Python Interview Questions on Trees - BTech Geeks","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/","og_locale":"en_US","og_type":"article","og_title":"Python Interview Questions on Trees - BTech Geeks","og_description":"We have compiled most frequently asked\u00a0Python Interview Questions\u00a0which will help you with different expertise levels. Python Interview Questions on Trees There are several types of data structures that can be used to tackle application problems. We have seen how linked lists work in a sequential manner, we have also seen how stacks and queues can ... Read more","og_url":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/","og_site_name":"BTech Geeks","article_publisher":"https:\/\/www.facebook.com\/btechgeeks","article_published_time":"2024-04-01T11:11:59+00:00","article_modified_time":"2024-04-02T06:27:27+00:00","og_image":[{"url":"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-1.png"}],"twitter_card":"summary_large_image","twitter_creator":"@btech_geeks","twitter_site":"@btech_geeks","twitter_misc":{"Written by":"Prasanna","Est. reading time":"26 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/btechgeeks.com\/#organization","name":"BTech Geeks","url":"https:\/\/btechgeeks.com\/","sameAs":["https:\/\/www.facebook.com\/btechgeeks","https:\/\/www.instagram.com\/btechgeeks\/","https:\/\/www.linkedin.com\/in\/btechgeeks","https:\/\/www.youtube.com\/channel\/UC9MlCqdJ3lKqz2p5114SDIg","https:\/\/in.pinterest.com\/btechgeek\/","https:\/\/twitter.com\/btech_geeks"],"logo":{"@type":"ImageObject","@id":"https:\/\/btechgeeks.com\/#logo","inLanguage":"en-US","url":"https:\/\/btechgeeks.com\/wp-content\/uploads\/2020\/11\/BTechGeeks.png","contentUrl":"https:\/\/btechgeeks.com\/wp-content\/uploads\/2020\/11\/BTechGeeks.png","width":350,"height":70,"caption":"BTech Geeks"},"image":{"@id":"https:\/\/btechgeeks.com\/#logo"}},{"@type":"WebSite","@id":"https:\/\/btechgeeks.com\/#website","url":"https:\/\/btechgeeks.com\/","name":"BTech Geeks","description":"Lecture Notes for BTech, BSc Students","publisher":{"@id":"https:\/\/btechgeeks.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/btechgeeks.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#primaryimage","inLanguage":"en-US","url":"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-1.png","contentUrl":"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-1.png","width":325,"height":217,"caption":"Python Interview Questions on Trees chapter 13 img 1"},{"@type":"WebPage","@id":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#webpage","url":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/","name":"Python Interview Questions on Trees - BTech Geeks","isPartOf":{"@id":"https:\/\/btechgeeks.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#primaryimage"},"datePublished":"2024-04-01T11:11:59+00:00","dateModified":"2024-04-02T06:27:27+00:00","breadcrumb":{"@id":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/btechgeeks.com\/"},{"@type":"ListItem","position":2,"name":"Python Interview Questions on Trees"}]},{"@type":"Article","@id":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#article","isPartOf":{"@id":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#webpage"},"author":{"@id":"https:\/\/btechgeeks.com\/#\/schema\/person\/ea8ce699662f0d7e248e52fe080b85bb"},"headline":"Python Interview Questions on Trees","datePublished":"2024-04-01T11:11:59+00:00","dateModified":"2024-04-02T06:27:27+00:00","mainEntityOfPage":{"@id":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#webpage"},"wordCount":3032,"commentCount":0,"publisher":{"@id":"https:\/\/btechgeeks.com\/#organization"},"image":{"@id":"https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#primaryimage"},"thumbnailUrl":"https:\/\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Python-Interview-Questions-on-Trees-chapter-13-img-1.png","articleSection":["Python"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/btechgeeks.com\/python-interview-questions-on-trees\/#respond"]}]},{"@type":"Person","@id":"https:\/\/btechgeeks.com\/#\/schema\/person\/ea8ce699662f0d7e248e52fe080b85bb","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/btechgeeks.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/btechgeeks.com\/author\/prasanna\/"}]}},"jetpack_featured_media_url":"","jetpack-related-posts":[{"id":291,"url":"https:\/\/btechgeeks.com\/data-structures-question-bank-with-answers\/","url_meta":{"origin":10426,"position":0},"title":"Data Structures Question Bank With Answers PDF Free Download","date":"November 27, 2022","format":false,"excerpt":"Data Structures Question Bank With Answers PDF: Are you a student and facing trouble in finding the right questions for your preparation for data structures exam? Students can overcome this problem just by downloading the data structures question bank with answers PDF, and it will eliminate all the troubles. It\u2026","rel":"","context":"In &quot;Lecture Notes&quot;","img":{"alt_text":"data-structures-question-bank-with-answers-pdf","src":"https:\/\/i1.wp.com\/btechgeeks.com\/wp-content\/uploads\/2020\/11\/data-structures-question-bank-with-answers-pdf.jpeg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":256,"url":"https:\/\/btechgeeks.com\/data-structures-and-algorithms-lecture-notes\/","url_meta":{"origin":10426,"position":1},"title":"Java data structures and algorithms pdf - Data Structures and Algorithms Lecture Notes & Study Material PDF Free Download","date":"December 6, 2022","format":false,"excerpt":"Data Structures And Algorithms Notes PDF Download:\u00a0Data structure is used to store & organize data. Data structure helps in organizing data in an ordered manner so that it can be used in the future for different reasons. The algorithm is the procedure that provides a set of instructions that should\u2026","rel":"","context":"In &quot;Lecture Notes&quot;","img":{"alt_text":"data-structures-and-algorithms-lecture-notes","src":"https:\/\/i0.wp.com\/btechgeeks.com\/wp-content\/uploads\/2020\/11\/data-structures-and-algorithms-lecture-notes.jpeg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":286,"url":"https:\/\/btechgeeks.com\/data-structures-notes\/","url_meta":{"origin":10426,"position":2},"title":"Data Structures Notes and Study Material PDF Free Download","date":"February 13, 2023","format":false,"excerpt":"Data Structures Notes: Anything that can store data is called Data Structure. There are two types of data structures. One is a primitive data structure, and another is an abstract data structure. Data structures help us to perform various operations on data. Data structures store the ordered data so that\u2026","rel":"","context":"In &quot;Lecture Notes&quot;","img":{"alt_text":"data-structures-notes","src":"https:\/\/i1.wp.com\/btechgeeks.com\/wp-content\/uploads\/2020\/11\/data-structures-notes.jpeg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":3522,"url":"https:\/\/btechgeeks.com\/python-programming-data-structures\/","url_meta":{"origin":10426,"position":3},"title":"Python Programming - Data Structures","date":"June 21, 2022","format":false,"excerpt":"In this Page, We are Providing Python Programming - Data Structures. Students can visit for more Detail and Explanation of Python Handwritten Notes\u00a0Pdf. Python Programming - Data Structures A data structure is a group of data elements grouped together under one name. Python's data structures are very intuitive from a\u2026","rel":"","context":"In &quot;Python&quot;","img":{"alt_text":"TreeStructure-Data-Structures-in-Python","src":"https:\/\/i0.wp.com\/btechgeeks.com\/wp-content\/uploads\/2021\/04\/TreeStructure-Data-Structures-in-Python.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":1474,"url":"https:\/\/btechgeeks.com\/data-structure-through-c-lecture-notes\/","url_meta":{"origin":10426,"position":4},"title":"Data Structure through C++ Lecture Notes | Syllabus, Reference Books and Important Questions","date":"February 23, 2023","format":false,"excerpt":"Data Structure through C++ Lecture Notes: Aspirants looking to get hold of the Data Structure through C++ Study Material and Notes can access the best notes for their preparation process or to have a revision of essential concepts. Students can refer to the Big Data Lecture Notes For CSE as\u2026","rel":"","context":"In &quot;Lecture Notes&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":8361,"url":"https:\/\/btechgeeks.com\/program-to-reverse-a-string-using-a-stack-data-structure-in-c-and-python\/","url_meta":{"origin":10426,"position":5},"title":"Program to Reverse a String using a Stack Data Structure in C++ and Python","date":"June 17, 2022","format":false,"excerpt":"Strings: A string data type is used in most computer languages for data values that are made up of ordered sequences of characters, such as \"hello world.\" A string can include any visible or unseen series of characters, and characters can be repeated. The length of a string is the\u2026","rel":"","context":"In &quot;CPP Programming&quot;","img":{"alt_text":"Program to Reverse a String using a Stack Data Structure in C++ and Python","src":"https:\/\/i1.wp.com\/btechgeeks.com\/wp-content\/uploads\/2021\/06\/Program-to-Reverse-a-String-using-a-Stack-Data-Structure-in-C-and-Python.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]}],"_links":{"self":[{"href":"https:\/\/btechgeeks.com\/wp-json\/wp\/v2\/posts\/10426"}],"collection":[{"href":"https:\/\/btechgeeks.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/btechgeeks.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/btechgeeks.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/btechgeeks.com\/wp-json\/wp\/v2\/comments?post=10426"}],"version-history":[{"count":1,"href":"https:\/\/btechgeeks.com\/wp-json\/wp\/v2\/posts\/10426\/revisions"}],"predecessor-version":[{"id":34931,"href":"https:\/\/btechgeeks.com\/wp-json\/wp\/v2\/posts\/10426\/revisions\/34931"}],"wp:attachment":[{"href":"https:\/\/btechgeeks.com\/wp-json\/wp\/v2\/media?parent=10426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/btechgeeks.com\/wp-json\/wp\/v2\/categories?post=10426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/btechgeeks.com\/wp-json\/wp\/v2\/tags?post=10426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}