Binary Tree

Author: Parth Garg

15. Binary Tree/01 Introduction/01.cpp

@@ -0,0 +1,26 @@
+#include<bits/stdc++.h>
+using namespace std;
+
+int main()
+{
+	/*
+
+	-->Tree stores data in the form of
+	hierarchical form.
+	
+	-->Non-linear data structure.
+
+	Applications of Tree Data Structure:
+	1.used to represent hierarchical data.
+		-->organisation structure
+		-->folder structure
+		-->XML/HTML content
+		-->In OOPs(inheritance)
+	2.binary search trees
+	3.binary heap
+	4.B and B+ trees in DBMS
+	5.Spanning and shortest path trees
+	6.Parse trees, Comparison Trees in Compilers. 
+	
+	*/
+}

15. Binary Tree/01 Tree Class/01.cpp 15. Binary Tree/02 Tree Class/02.cpp

@@ -1,6 +1,12 @@
 #include<bits/stdc++.h>
 using namespace std;
 
+/*
+Binary Tree:
+Every node has almost two
+children.
+*/
+
 class Node
 {
 public:

15. Binary Tree/02 Types of Tree Traversals/02.cpp 15. Binary Tree/03 Types of Tree Traversals/03.cpp

@@ -5,12 +5,12 @@ int main()
 {
 	/*
 	
-	Traversals:
+	Tree Traversals:
+	It means printing every key of tree exactly ones.
 
 	1. Breadth First Traversal / level Order Traversal
 
 	2. Depth First Traversal
-
 		2.1 Inorder Traversal (Left Root Right)
 		2.2 Preorder Traversal (Root Left Right)
 		2.3 Postorder Traversal (Left Right Root)

15. Binary Tree/04 Preorder Traversal/04.cpp 15. Binary Tree/04 Inorder Traversal/04.cpp

@@ -17,18 +17,18 @@ class Node
 };
 
 //Time: O(N)
-//Space: O(logN)
-//Preorder: Root Left Right
-void preorder(Node* root)
+//Space: O(H)
+//Inorder: left Root Right
+void inorder(Node* root)
 {
 	if(root==NULL)
 	{
 		return ;
 	}
 
+	inorder(root->left);
 	cout<<root->data<<" ";
-	preorder(root->left);
-	preorder(root->right);
+	inorder(root->right);
 }
 
 int main()
@@ -44,7 +44,8 @@ int main()
 	root->right->left=new Node(60);
 	root->right->right=new Node(70);
 
-	preorder(root);
+	inorder(root);
+	cout<<endl;
 
 	return 0;
 }

15. Binary Tree/05 Postorder Traversal/05.cpp 15. Binary Tree/05 Preorder Traversal/05.cpp

@@ -17,18 +17,18 @@ class Node
 };
 
 //Time: O(N)
-//Space: O(logN)
-//Postorder: Left Right Root
-void postorder(Node* root)
+//Space: O(H)
+//Preorder: Root Left Right
+void preorder(Node* root)
 {
 	if(root==NULL)
 	{
 		return ;
 	}
 
-	postorder(root->left);
-	postorder(root->right);
 	cout<<root->data<<" ";
+	preorder(root->left);
+	preorder(root->right);
 }
 
 int main()
@@ -44,7 +44,8 @@ int main()
 	root->right->left=new Node(60);
 	root->right->right=new Node(70);
 
-	postorder(root);
+	preorder(root);
+	cout<<endl;
 
 	return 0;
 }

15. Binary Tree/03 Inorder Traversal/03.cpp 15. Binary Tree/06 Postorder Traversal/06.cpp

@@ -17,18 +17,18 @@ class Node
 };
 
 //Time: O(N)
-//Space: O(logN)
-//Inorder: left Root Right
-void inorder(Node* root)
+//Space: O(H)
+//Postorder: Left Right Root
+void postorder(Node* root)
 {
 	if(root==NULL)
 	{
 		return ;
 	}
 
-	inorder(root->left);
+	postorder(root->left);
+	postorder(root->right);
 	cout<<root->data<<" ";
-	inorder(root->right);
 }
 
 int main()
@@ -44,7 +44,8 @@ int main()
 	root->right->left=new Node(60);
 	root->right->right=new Node(70);
 
-	inorder(root);
+	postorder(root);
+	cout<<endl;
 
 	return 0;
 }

15. Binary Tree/06 Height of Tree/06.cpp 15. Binary Tree/07 Height of Tree/07.cpp

@@ -17,7 +17,7 @@ class Node
 };
 
 //Time: O(N)
-//Space: O(logN)
+//Space: O(H)
 int height(Node* root)
 {
 	if(root==NULL)
@@ -42,6 +42,5 @@ int main()
 	root->right->right=new Node(70);
 
 	cout<<height(root)<<endl;
-	
 	return 0;
 }

15. Binary Tree/07 Print Nodes at K Distance/07.cpp 15. Binary Tree/08 Print Nodes at K Distance/08.cpp

@@ -17,7 +17,7 @@ class Node
 };
 
 //Time: O(N)
-//Space: O(logN)
+//Space: O(H)
 //K values: [0,Height-1]
 void nodesAtKDistance(Node* root,int k)
 {
@@ -51,6 +51,7 @@ int main()
 	root->right->right=new Node(70);
 
 	nodesAtKDistance(root,2);
-	
+	cout<<endl;
+
 	return 0;
 }

15. Binary Tree/09 Level Order Traversal Line by Line/09a.cpp 15. Binary Tree/09 Level Order Traversal/09a.cpp

@@ -55,7 +55,6 @@ void levelOrder(Node* root)
 	for(int i=0;i<h;i++)
 	{
 		nodesAtKDistance(root,i);
-		cout<<endl;
 	}
 }
 
@@ -73,6 +72,7 @@ int main()
 	root->right->right=new Node(70);
 
 	levelOrder(root);
+	cout<<endl;
 
 	return 0;
 }

15. Binary Tree/09 Level Order Traversal Line by Line/09b.cpp 15. Binary Tree/09 Level Order Traversal/09b.cpp

@@ -17,8 +17,7 @@ class Node
 };
 
 //Time: O(N)
-//Space: O(N)
-//when complete level is traversed,push NULL into queue
+//Space: O(W)
 void levelOrder(Node* root)
 {
 	if(root==NULL)
@@ -28,20 +27,12 @@ void levelOrder(Node* root)
 
 	queue<Node*> q;
 	q.push(root);
-	q.push(NULL);
 
-	while(q.size()>1)
+	while(q.empty()==false)
 	{
 		Node* curr=q.front();
 		q.pop();
 
-		if(curr==NULL)
-		{
-			cout<<endl;
-			q.push(NULL);
-			continue;
-		}
-
 		cout<<curr->data<<" ";
 
 		if(curr->left)
@@ -70,6 +61,7 @@ int main()
 	root->right->right=new Node(70);
 
 	levelOrder(root);
-	
+	cout<<endl;
+
 	return 0;
 }

15. Binary Tree/08 Level Order Traversal/08a.cpp 15. Binary Tree/10 Level Order Traversal Line by Line/10a.cpp

@@ -55,6 +55,7 @@ void levelOrder(Node* root)
 	for(int i=0;i<h;i++)
 	{
 		nodesAtKDistance(root,i);
+		cout<<endl;
 	}
 }
 
@@ -72,6 +73,5 @@ int main()
 	root->right->right=new Node(70);
 
 	levelOrder(root);
-	
 	return 0;
 }

15. Binary Tree/08 Level Order Traversal/08b.cpp 15. Binary Tree/10 Level Order Traversal Line by Line/10b.cpp

@@ -17,7 +17,8 @@ class Node
 };
 
 //Time: O(N)
-//Space: O(W)
+//Space: O(N)
+//when complete level is traversed,push NULL into queue
 void levelOrder(Node* root)
 {
 	if(root==NULL)
@@ -27,12 +28,20 @@ void levelOrder(Node* root)
 
 	queue<Node*> q;
 	q.push(root);
+	q.push(NULL);
 
-	while(q.empty()==false)
+	while(q.size()>1)
 	{
 		Node* curr=q.front();
 		q.pop();
 
+		if(curr==NULL)
+		{
+			cout<<endl;
+			q.push(NULL);
+			continue;
+		}
+
 		cout<<curr->data<<" ";
 
 		if(curr->left)
@@ -61,6 +70,7 @@ int main()
 	root->right->right=new Node(70);
 
 	levelOrder(root);
-	
+	cout<<endl;
+		
 	return 0;
 }

15. Binary Tree/09 Level Order Traversal Line by Line/09c.cpp 15. Binary Tree/10 Level Order Traversal Line by Line/10c.cpp

@@ -18,14 +18,14 @@ class Node
 
 //Time: O(N)
 //Space: O(W)
-int maximum(Node* root)
+int size(Node* root)
 {
 	if(root==NULL)
 	{
 		return 0;
 	}
 
-	int max_val=INT_MIN;
+	int count=0;
 
 	queue<Node*> q;
 	q.push(root);
@@ -35,10 +35,7 @@ int maximum(Node* root)
 		Node* curr=q.front();
 		q.pop();
 
-		if(curr)
-		{
-			max_val=max(max_val,curr->data);
-		}
+		count++;
 
 		if(curr->left)
 		{
@@ -51,7 +48,7 @@ int maximum(Node* root)
 		}
 	}
 
-	return max_val;
+	return count;
 }
 
 int main()
@@ -67,7 +64,6 @@ int main()
 	root->right->left=new Node(60);
 	root->right->right=new Node(70);
 
-	cout<<maximum(root)<<endl;
-	
+	cout<<size(root)<<endl;
 	return 0;
 }

15. Binary Tree/11 Maximum in Binary Tree/11a.cpp 15. Binary Tree/11 Size of Binary Tree/11a.cpp

@@ -17,7 +17,7 @@ class Node
 };
 
 //Time: O(N)
-//Space: O(logN);
+//Space: O(H);
 int size(Node* root)
 {
 	if(root==NULL)
@@ -42,6 +42,5 @@ int main()
 	root->right->right=new Node(70);
 
 	cout<<size(root)<<endl;
-	
 	return 0;
 }