Splay Tree | Set 2 (Insert)

It is recommended to refer following post as prerequisite of this post.

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                  [20]                             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   
   /                                                          
 [20]

C++

#include <bits/stdc++.h> 
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<<root->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<stdio.h> 
#include<stdlib.h> 
  
// 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; 
} 

Output:

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

This article is compiled by Abhay Rathi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

My Personal Notes

C++

C

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