Related Articles

# Splay Tree | Set 2 (Insert)

• Difficulty Level : Medium
• Last Updated : 02 Jun, 2021

It is recommended to refer following post as prerequisite of this post.
Splay Tree | Set 1 (Search)
As discussed in the previous post, Splay tree is a self-balancing data structure where the last accessed key is always at root. The insert operation is similar to Binary Search Tree insert with additional steps to make sure that the newly inserted key becomes the new root.
Following are different cases to insert a key k in splay tree.
1) Root is NULL: We simply allocate a new node and return it as root.
2) Splay the given key k. If k is already present, then it becomes the new root. If not present, then last accessed leaf node becomes the new root.
3) If new root’s key is same as k, don’t do anything as k is already present.
4) Else allocate memory for new node and compare root’s key with k.
…….4.a) If k is smaller than root’s key, make root as right child of new node, copy left child of root as left child of new node and make left child of root as NULL.
…….4.b) If k is greater than root’s key, make root as left child of new node, copy right child of root as right child of new node and make right child of root as NULL.
5) Return new node as new root of tree.
Example:

```
100                                               25
/  \                   \                             /  \
50   200                  50                          20   50
/          insert(25)     /  \        insert(25)           /  \
40          ======>      30   100      ========>           30  100
/          1. Splay(25)    \     \      2. insert 25         \    \
30                          40    200                         40   200
/
 ```

## C++

 `#include ``using` `namespace` `std;` `// An AVL tree node``class` `node``{``    ``public``:``    ``int` `key;``    ``node *left, *right;``};` `/* 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 = Node->right = NULL;``    ``return` `(Node);``}` `// A utility function to right``// rotate subtree rooted with y``// See the diagram given above.``node *rightRotate(node *x)``{``    ``node *y = x->left;``    ``x->left = y->right;``    ``y->right = x;``    ``return` `y;``}` `// A utility function to left``// rotate subtree rooted with x``// See the diagram given above.``node *leftRotate(node *x)``{``    ``node *y = x->right;``    ``x->right = y->left;``    ``y->left = x;``    ``return` `y;``}` `// This function brings the key at``// root if key is present in tree.``// If key is not present, then it``// brings the last accessed item at``// root. This function modifies the``// tree and returns the new root``node *splay(node *root, ``int` `key)``{``    ``// Base cases: root is NULL or``    ``// key is present at root``    ``if` `(root == NULL || root->key == key)``        ``return` `root;` `    ``// Key lies in left subtree``    ``if` `(root->key > key)``    ``{``        ``// Key is not in tree, we are done``        ``if` `(root->left == NULL) ``return` `root;` `        ``// Zig-Zig (Left Left)``        ``if` `(root->left->key > key)``        ``{``            ``// First recursively bring the``            ``// key as root of left-left``            ``root->left->left = splay(root->left->left, key);` `            ``// Do first rotation for root,``            ``// second rotation is done after else``            ``root = rightRotate(root);``        ``}``        ``else` `if` `(root->left->key < key) ``// Zig-Zag (Left Right)``        ``{``            ``// First recursively bring``            ``// the key as root of left-right``            ``root->left->right = splay(root->left->right, key);` `            ``// Do first rotation for root->left``            ``if` `(root->left->right != NULL)``                ``root->left = leftRotate(root->left);``        ``}` `        ``// Do second rotation for root``        ``return` `(root->left == NULL)? root: rightRotate(root);``    ``}``    ``else` `// Key lies in right subtree``    ``{``        ``// Key is not in tree, we are done``        ``if` `(root->right == NULL) ``return` `root;` `        ``// Zig-Zag (Right Left)``        ``if` `(root->right->key > key)``        ``{``            ``// Bring the key as root of right-left``            ``root->right->left = splay(root->right->left, key);` `            ``// Do first rotation for root->right``            ``if` `(root->right->left != NULL)``                ``root->right = rightRotate(root->right);``        ``}``        ``else` `if` `(root->right->key < key)``// Zag-Zag (Right Right)``        ``{``            ``// Bring the key as root of``            ``// right-right and do first rotation``            ``root->right->right = splay(root->right->right, key);``            ``root = leftRotate(root);``        ``}` `        ``// Do second rotation for root``        ``return` `(root->right == NULL)? root: leftRotate(root);``    ``}``}` `// Function to insert a new key k``// in splay tree with given root``node *insert(node *root, ``int` `k)``{``    ``// Simple Case: If tree is empty``    ``if` `(root == NULL) ``return` `newNode(k);` `    ``// Bring the closest leaf node to root``    ``root = splay(root, k);` `    ``// If key is already present, then return``    ``if` `(root->key == k) ``return` `root;` `    ``// Otherwise allocate memory for new node``    ``node *newnode = newNode(k);` `    ``// If root's key is greater, make``    ``// root as right child of newnode``    ``// and copy the left child of root to newnode``    ``if` `(root->key > k)``    ``{``        ``newnode->right = root;``        ``newnode->left = root->left;``        ``root->left = NULL;``    ``}` `    ``// If root's key is smaller, make``    ``// root as left child of newnode``    ``// and copy the right child of root to newnode``    ``else``    ``{``        ``newnode->left = root;``        ``newnode->right = root->right;``        ``root->right = NULL;``    ``}` `    ``return` `newnode; ``// newnode becomes new root``}` `// 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<key<<``" "``;``        ``preOrder(root->left);``        ``preOrder(root->right);``    ``}``}` `/* Driver code*/``int` `main()``{``    ``node *root = newNode(100);``    ``root->left = newNode(50);``    ``root->right = newNode(200);``    ``root->left->left = newNode(40);``    ``root->left->left->left = newNode(30);``    ``root->left->left->left->left = newNode(20);``    ``root = insert(root, 25);``    ``cout<<``"Preorder traversal of the modified Splay tree is \n"``;``    ``preOrder(root);``    ``return` `0;``}` `// This code is contributed by rathbhupendra`

## C

 `// This code is adopted from http://algs4.cs.princeton.edu/33balanced/SplayBST.java.html``#include``#include` `// An AVL tree node``struct` `node``{``    ``int` `key;``    ``struct` `node *left, *right;``};` `/* Helper function that allocates a new node with the given key and``    ``NULL left and right pointers. */``struct` `node* newNode(``int` `key)``{``    ``struct` `node* node = (``struct` `node*)``malloc``(``sizeof``(``struct` `node));``    ``node->key   = key;``    ``node->left  = node->right  = NULL;``    ``return` `(node);``}` `// A utility function to right rotate subtree rooted with y``// See the diagram given above.``struct` `node *rightRotate(``struct` `node *x)``{``    ``struct` `node *y = x->left;``    ``x->left = y->right;``    ``y->right = x;``    ``return` `y;``}` `// A utility function to left rotate subtree rooted with x``// See the diagram given above.``struct` `node *leftRotate(``struct` `node *x)``{``    ``struct` `node *y = x->right;``    ``x->right = y->left;``    ``y->left = x;``    ``return` `y;``}` `// This function brings the key at root if key is present in tree.``// If key is not present, then it brings the last accessed item at``// root.  This function modifies the tree and returns the new root``struct` `node *splay(``struct` `node *root, ``int` `key)``{``    ``// Base cases: root is NULL or key is present at root``    ``if` `(root == NULL || root->key == key)``        ``return` `root;` `    ``// Key lies in left subtree``    ``if` `(root->key > key)``    ``{``        ``// Key is not in tree, we are done``        ``if` `(root->left == NULL) ``return` `root;` `        ``// Zig-Zig (Left Left)``        ``if` `(root->left->key > key)``        ``{``            ``// First recursively bring the key as root of left-left``            ``root->left->left = splay(root->left->left, key);` `            ``// Do first rotation for root, second rotation is done after else``            ``root = rightRotate(root);``        ``}``        ``else` `if` `(root->left->key < key) ``// Zig-Zag (Left Right)``        ``{``            ``// First recursively bring the key as root of left-right``            ``root->left->right = splay(root->left->right, key);` `            ``// Do first rotation for root->left``            ``if` `(root->left->right != NULL)``                ``root->left = leftRotate(root->left);``        ``}` `        ``// Do second rotation for root``        ``return` `(root->left == NULL)? root: rightRotate(root);``    ``}``    ``else` `// Key lies in right subtree``    ``{``        ``// Key is not in tree, we are done``        ``if` `(root->right == NULL) ``return` `root;` `        ``// Zig-Zag (Right Left)``        ``if` `(root->right->key > key)``        ``{``            ``// Bring the key as root of right-left``            ``root->right->left = splay(root->right->left, key);` `            ``// Do first rotation for root->right``            ``if` `(root->right->left != NULL)``                ``root->right = rightRotate(root->right);``        ``}``        ``else` `if` `(root->right->key < key)``// Zag-Zag (Right Right)``        ``{``            ``// Bring the key as root of right-right and do first rotation``            ``root->right->right = splay(root->right->right, key);``            ``root = leftRotate(root);``        ``}` `        ``// Do second rotation for root``        ``return` `(root->right == NULL)? root: leftRotate(root);``    ``}``}` `// Function to insert a new key k in splay tree with given root``struct` `node *insert(``struct` `node *root, ``int` `k)``{``    ``// Simple Case: If tree is empty``    ``if` `(root == NULL) ``return` `newNode(k);` `    ``// Bring the closest leaf node to root``    ``root = splay(root, k);` `    ``// If key is already present, then return``    ``if` `(root->key == k) ``return` `root;` `    ``// Otherwise allocate memory for new node``    ``struct` `node *newnode  = newNode(k);` `    ``// If root's key is greater, make root as right child``    ``// of newnode and copy the left child of root to newnode``    ``if` `(root->key > k)``    ``{``        ``newnode->right = root;``        ``newnode->left = root->left;``        ``root->left = NULL;``    ``}` `    ``// If root's key is smaller, make root as left child``    ``// of newnode and copy the right child of root to newnode``    ``else``    ``{``        ``newnode->left = root;``        ``newnode->right = root->right;``        ``root->right = NULL;``    ``}` `    ``return` `newnode; ``// newnode becomes new root``}` `// A utility function to print preorder traversal of the tree.``// The function also prints height of every node``void` `preOrder(``struct` `node *root)``{``    ``if` `(root != NULL)``    ``{``        ``printf``(``"%d "``, root->key);``        ``preOrder(root->left);``        ``preOrder(root->right);``    ``}``}` `/* Driver program to test above function*/``int` `main()``{``    ``struct` `node *root = newNode(100);``    ``root->left = newNode(50);``    ``root->right = newNode(200);``    ``root->left->left = newNode(40);``    ``root->left->left->left = newNode(30);``    ``root->left->left->left->left = newNode(20);``    ``root = insert(root, 25);``    ``printf``(``"Preorder traversal of the modified Splay tree is \n"``);``    ``preOrder(root);``    ``return` `0;``}`

## Java

 `import` `java.util.*;` `class` `GFG{` `// An AVL tree node``static` `class` `node``{` `    ``int` `key;``    ``node left, right;``};` `/* Helper function that allocates``a new node with the given key and``    ``null left and right pointers. */``static` `node newNode(``int` `key)``{``    ``node Node = ``new` `node();``    ``Node.key = key;``    ``Node.left = Node.right = ``null``;``    ``return` `(Node);``}` `// A utility function to right``// rotate subtree rooted with y``// See the diagram given above.``static` `node rightRotate(node x)``{``    ``node y = x.left;``    ``x.left = y.right;``    ``y.right = x;``    ``return` `y;``}` `// A utility function to left``// rotate subtree rooted with x``// See the diagram given above.``static` `node leftRotate(node x)``{``    ``node y = x.right;``    ``x.right = y.left;``    ``y.left = x;``    ``return` `y;``}` `// This function brings the key at``// root if key is present in tree.``// If key is not present, then it``// brings the last accessed item at``// root. This function modifies the``// tree and returns the new root``static` `node splay(node root, ``int` `key)``{``    ``// Base cases: root is null or``    ``// key is present at root``    ``if` `(root == ``null` `|| root.key == key)``        ``return` `root;` `    ``// Key lies in left subtree``    ``if` `(root.key > key)``    ``{``        ``// Key is not in tree, we are done``        ``if` `(root.left == ``null``) ``return` `root;` `        ``// Zig-Zig (Left Left)``        ``if` `(root.left.key > key)``        ``{``            ``// First recursively bring the``            ``// key as root of left-left``            ``root.left.left = splay(root.left.left, key);` `            ``// Do first rotation for root,``            ``// second rotation is done after else``            ``root = rightRotate(root);``        ``}``        ``else` `if` `(root.left.key < key) ``// Zig-Zag (Left Right)``        ``{``            ``// First recursively bring``            ``// the key as root of left-right``            ``root.left.right = splay(root.left.right, key);` `            ``// Do first rotation for root.left``            ``if` `(root.left.right != ``null``)``                ``root.left = leftRotate(root.left);``        ``}` `        ``// Do second rotation for root``        ``return` `(root.left == ``null``)? root: rightRotate(root);``    ``}``    ``else` `// Key lies in right subtree``    ``{``        ``// Key is not in tree, we are done``        ``if` `(root.right == ``null``) ``return` `root;` `        ``// Zig-Zag (Right Left)``        ``if` `(root.right.key > key)``        ``{``            ``// Bring the key as root of right-left``            ``root.right.left = splay(root.right.left, key);` `            ``// Do first rotation for root.right``            ``if` `(root.right.left != ``null``)``                ``root.right = rightRotate(root.right);``        ``}``        ``else` `if` `(root.right.key < key)``// Zag-Zag (Right Right)``        ``{``            ``// Bring the key as root of``            ``// right-right and do first rotation``            ``root.right.right = splay(root.right.right, key);``            ``root = leftRotate(root);``        ``}` `        ``// Do second rotation for root``        ``return` `(root.right == ``null``)? root: leftRotate(root);``    ``}``}` `// Function to insert a new key k``// in splay tree with given root``static` `node insert(node root, ``int` `k)``{``    ``// Simple Case: If tree is empty``    ``if` `(root == ``null``) ``return` `newNode(k);` `    ``// Bring the closest leaf node to root``    ``root = splay(root, k);` `    ``// If key is already present, then return``    ``if` `(root.key == k) ``return` `root;` `    ``// Otherwise allocate memory for new node``    ``node newnode = newNode(k);` `    ``// If root's key is greater, make``    ``// root as right child of newnode``    ``// and copy the left child of root to newnode``    ``if` `(root.key > k)``    ``{``        ``newnode.right = root;``        ``newnode.left = root.left;``        ``root.left = ``null``;``    ``}` `    ``// If root's key is smaller, make``    ``// root as left child of newnode``    ``// and copy the right child of root to newnode``    ``else``    ``{``        ``newnode.left = root;``        ``newnode.right = root.right;``        ``root.right = ``null``;``    ``}` `    ``return` `newnode; ``// newnode becomes new root``}` `// A utility function to print``// preorder traversal of the tree.``// The function also prints height of every node``static` `void` `preOrder(node root)``{``    ``if` `(root != ``null``)``    ``{``        ``System.out.print(root.key+``" "``);``        ``preOrder(root.left);``        ``preOrder(root.right);``    ``}``}` `/* Driver code*/``public` `static` `void` `main(String[] args)``{``    ``node root = newNode(``100``);``    ``root.left = newNode(``50``);``    ``root.right =  newNode(``200``);``    ``root.left.left =  newNode(``40``);``    ``root.left.left.left =  newNode(``30``);``    ``root.left.left.left.left =  newNode(``20``);``    ``root = insert(root, ``25``);``    ``System.out.print(``"Preorder traversal of the modified Splay tree is \n"``);``    ``preOrder(root);``}``}`  `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output:

```Preorder traversal of the modified Splay tree is
25 20 50 30 40 100 200```