insertion in AVL trees in c++

Data_Structures/AVL_Tree/c++/Insertion_in_AVL_Trees.cpp

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+// 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 maximum
+// of two integers
+int max(int a, int b);
+
+// 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;
+}