Merge pull request #3 from Debaditya-Som/Debaditya-Som-patch-1-1

Added AVL Tree Insertion

Trees/AVL_Tree.cpp

@@ -0,0 +1,194 @@
+// C++ program to insert a node in AVL tree
+#include<bits/stdc++.h>
+using namespace std;
+
+// An AVL tree node
+class Node
+{
+	public:
+	int key;
+	Node *left;
+	Node *right;
+	int height;
+};
+
+// A utility function to get the
+// height of the tree
+int height(Node *N)
+{
+	if (N == NULL)
+		return 0;
+	return N->height;
+}
+
+// A utility function to get maximum
+// of two integers
+int max(int a, int b)
+{
+	return (a > b)? a : b;
+}
+
+/* Helper function that allocates a
+new node with the given key and
+NULL left and right pointers. */
+Node* newNode(int key)
+{
+	Node* node = new Node();
+	node->key = key;
+	node->left = NULL;
+	node->right = NULL;
+	node->height = 1; // new node is initially
+					// added at leaf
+	return(node);
+}
+
+// A utility function to right
+// rotate subtree rooted with y
+// See the diagram given above.
+Node *rightRotate(Node *y)
+{
+	Node *x = y->left;
+	Node *T2 = x->right;
+
+	// Perform rotation
+	x->right = y;
+	y->left = T2;
+
+	// Update heights
+	y->height = max(height(y->left),
+					height(y->right)) + 1;
+	x->height = max(height(x->left),
+					height(x->right)) + 1;
+
+	// Return new root
+	return x;
+}
+
+// A utility function to left
+// rotate subtree rooted with x
+// See the diagram given above.
+Node *leftRotate(Node *x)
+{
+	Node *y = x->right;
+	Node *T2 = y->left;
+
+	// Perform rotation
+	y->left = x;
+	x->right = T2;
+
+	// Update heights
+	x->height = max(height(x->left),
+					height(x->right)) + 1;
+	y->height = max(height(y->left),
+					height(y->right)) + 1;
+
+	// Return new root
+	return y;
+}
+
+// Get Balance factor of node N
+int getBalance(Node *N)
+{
+	if (N == NULL)
+		return 0;
+	return height(N->left) - height(N->right);
+}
+
+// Recursive function to insert a key
+// in the subtree rooted with node and
+// returns the new root of the subtree.
+Node* insert(Node* node, int key)
+{
+	/* 1. Perform the normal BST insertion */
+	if (node == NULL)
+		return(newNode(key));
+
+	if (key < node->key)
+		node->left = insert(node->left, key);
+	else if (key > node->key)
+		node->right = insert(node->right, key);
+	else // Equal keys are not allowed in BST
+		return node;
+
+	/* 2. Update height of this ancestor node */
+	node->height = 1 + max(height(node->left),
+						height(node->right));
+
+	/* 3. Get the balance factor of this ancestor
+		node to check whether this node became
+		unbalanced */
+	int balance = getBalance(node);
+
+	// If this node becomes unbalanced, then
+	// there are 4 cases
+
+	// Left Left Case
+	if (balance > 1 && key < node->left->key)
+		return rightRotate(node);
+
+	// Right Right Case
+	if (balance < -1 && key > node->right->key)
+		return leftRotate(node);
+
+	// Left Right Case
+	if (balance > 1 && key > node->left->key)
+	{
+		node->left = leftRotate(node->left);
+		return rightRotate(node);
+	}
+
+	// Right Left Case
+	if (balance < -1 && key < node->right->key)
+	{
+		node->right = rightRotate(node->right);
+		return leftRotate(node);
+	}
+
+	/* return the (unchanged) node pointer */
+	return node;
+}
+
+// A utility function to print preorder
+// traversal of the tree.
+// The function also prints height
+// of every node
+void preOrder(Node *root)
+{
+	if(root != NULL)
+	{
+		cout << root->key << " ";
+		preOrder(root->left);
+		preOrder(root->right);
+	}
+}
+
+// Driver Code
+int main()
+{
+	Node *root = NULL;
+
+	/* Constructing tree given in
+	the above figure */
+	root = insert(root, 10);
+	root = insert(root, 20);
+	root = insert(root, 30);
+	root = insert(root, 40);
+	root = insert(root, 50);
+	root = insert(root, 25);
+
+	/* The constructed AVL Tree would be
+				30
+			/ \
+			20 40
+			/ \ \
+		10 25 50
+	*/
+	cout << "Preorder traversal of the "
+			"constructed AVL tree is \n";
+	preOrder(root);
+
+	return 0;
+}
+
+// This code is contributed by
+// rathbhupendra