AVL Tree added

Author: neha030

Data Structures/Trees/AVL_Tree_or_not.cpp

@@ -0,0 +1,125 @@
+/*
+Given a Binary Search Tree ,Check if its a AVL Tree or not
+A BST is said to be a AVL Tree 
+
+AVL Tree can be defined as height balanced binary search tree in which each node is associated with a balance factor
+which is calculated by subtracting the height of its right sub-tree from that of its left sub-tree.
+Tree is said to be balanced if balance factor of each node is in between -1 to 1, otherwise, 
+the tree will be unbalanced and need to be balanced.
+
+Balance Factor (k) = height (left(k)) - height (right(k))
+*/
+
+#include <bits/stdc++.h> 
+using namespace std;
+
+//Define Node as structure
+struct Node 
+{
+    int key;
+    Node* left;
+    Node* right;
+};
+ 
+/* Function to create a node with 'value' as the data stored in it. 
+ Both the children of this new Node are initially null. */
+struct Node* newNode(int value)
+{
+    Node* n = new Node;
+    n->key = value;
+    n->left = NULL;
+    n->right = NULL;
+    return n;
+}
+
+// Function to insert a node with given value to the root
+struct Node* insert(struct Node* root,int element) 
+{
+    /*If the root is NULL , create a node with given element and assign it to root
+    else if the root itself is the node with given data , return 
+    else recursively insert it in one of the subtrees accordingly */
+    if(root==NULL)
+        root = newNode(element);
+    else if(root->key < element)
+        root->right = insert(root->right,element);
+    else if(root->key > element)
+        root->left = insert(root->left,element);
+    
+    return root;
+}
+
+// Function to calculate height of a given Tree recursively
+int Height(struct Node* root)
+{
+    /* If root is a NULL node return 0
+    else recursively calculate heights of subtrees and get height of the root */
+    if(root==NULL)
+      return 0;
+    else
+      return 1 + max( Height(root->left) , Height(root->right) );
+}
+
+//Function to determine whether given Tree is AVL Tree or not
+bool IsAVLTree(struct Node* root)
+{
+    /* If heights of subtrees differ atmost by 1 , return True
+     else return False */
+    if(abs( Height(root->left) - Height(root->right) ) <= 1)
+      return true;
+    else
+      return false;
+}
+
+// Driver code
+int main()
+{
+    int n;
+    cout<<"Enter total no.of nodes of the input Tree ( including NULL nodes ) : ";
+    cin>>n;
+
+    //create a null node  and initialise it as a NULL node
+    struct Node* root;
+    root=NULL;
+    
+    cout<<"Enter value of each node of the Tree , with head as the first value ( if a node is NULL , enter -1 ) with spaces"<<endl;
+    for(int i=0;i<n;i++)
+    {
+        int data;
+        cin>>data; 
+        //take input of data of each node and insert it in the root
+        root = insert(root,data);
+    }
+
+    //Call the function and print the result
+    if(IsAVLTree(root))
+        cout<<"Hence given BST is a AVL Tree";
+    else
+        cout<<"Hence given BST is not a AVL Tree";
+
+    return 0; 
+}
+    
+/*
+While entering node values of the tree , 
+value of the head of the tree should be enetered first
+ 
+Input Binary Tree:                    
+            11                                                             
+          /     \                                             
+         2      20                                      
+        / \                              
+       1   5                                
+           /
+          4
+Input: 
+Enter total no.of nodes of the input Tree ( including NULL nodes ) : 6
+Enter value of each node of the Tree , with head as the first value ( if a node is NULL , enter -1 ) with spaces
+11 2 20 1 5 4
+Output:
+Hence given BST is not a AVL Tree
+
+Time Complexity : O(n) 
+   Where n is the no.of nodes ofthe tree
+Space Complexity : O(h) 
+   Where h is the height of the tree
+*/