Remove all leaf nodes from the binary search tree

We have given a binary search tree and we want to delete the leaf nodes from the binary search tree. 

Examples:

Input : 20 10 5 15 30 25 35
Output : Inorder before Deleting the leaf node
         5 10 15 20 25 30 35
         Inorder after Deleting the leaf node
         10 20 30

        This is the binary search tree where we
        want to delete the leaf node.
              20
           /     \
          10      30
         /  \    /  \
       5     15 25   35 

      After deleting the leaf node the binary 
      search tree looks like
              20
           /     \
          10      30
     

We traverse given Binary Search Tree in inorder way. During traversal, we check if current node is leaf, if yes, we delete it. Else we recur for left and right children. An important thing to remember is, we must assign new left and right children if there is any modification in roots of subtrees. 

Implementation:

C++

// C++ program to delete leaf Node from
// binary search tree.
#include <bits/stdc++.h>
using namespace std;

struct Node {
    int data;
    struct Node* left;
    struct Node* right;
};

// Create a newNode in binary search tree.
struct Node* newNode(int data)
{
    struct Node* temp = new Node;
    temp->data = data;
    temp->left = temp->right = NULL;
    return temp;
}

// Insert a Node in binary search tree.
struct Node* insert(struct Node* root, int data)
{
    if (root == NULL)
        return newNode(data);
    if (data < root->data)
        root->left = insert(root->left, data);
    else if (data > root->data)
        root->right = insert(root->right, data);
    return root;
}

// Function for inorder traversal in a BST.
void inorder(struct Node* root)
{
    if (root != NULL) {
        inorder(root->left);
        cout << root->data << " ";
        inorder(root->right);
    }
}

// Delete leaf nodes from binary search tree.
struct Node* leafDelete(struct Node* root)
{
    if (root == NULL)
        return NULL;
    if (root->left == NULL && root->right == NULL) {
        free(root);
        return NULL;
    }

    // Else recursively delete in left and right
    // subtrees.
    root->left = leafDelete(root->left);
    root->right = leafDelete(root->right);

    return root;
}

// Driver code
int main()
{
    struct Node* root = NULL;
    root = insert(root, 20);
    insert(root, 10);
    insert(root, 5);
    insert(root, 15);
    insert(root, 30);
    insert(root, 25);
    insert(root, 35);
    cout << "Inorder before Deleting the leaf Node." << endl;
    inorder(root);
    cout << endl;
    leafDelete(root);
    cout << "INorder after Deleting the leaf Node." << endl;
    inorder(root);
    return 0;
}

Java

// Java program to delete leaf Node from
// binary search tree.
class GfG {

    static class Node {
        int data;
        Node left;
        Node right;
    }

    // Create a newNode in binary search tree.
    static Node newNode(int data)
    {
        Node temp = new Node();
        temp.data = data;
        temp.left = null;
        temp.right = null;
        return temp;
    }

    // Insert a Node in binary search tree.
    static Node insert(Node root, int data)
    {
        if (root == null)
            return newNode(data);
        if (data < root.data)
            root.left = insert(root.left, data);
        else if (data > root.data)
            root.right = insert(root.right, data);
        return root;
    }

    // Function for inorder traversal in a BST.
    static void inorder(Node root)
    {
        if (root != null) {
            inorder(root.left);
            System.out.print(root.data + " ");
            inorder(root.right);
        }
    }

    // Delete leaf nodes from binary search tree.
    static Node leafDelete(Node root)
    {
        if (root == null) {
            return null;
        }
        if (root.left == null && root.right == null) {
            return null;
        }

        // Else recursively delete in left and right
        // subtrees.
        root.left = leafDelete(root.left);
        root.right = leafDelete(root.right);

        return root;
    }

    // Driver code
    public static void main(String[] args)
    {
        Node root = null;
        root = insert(root, 20);
        insert(root, 10);
        insert(root, 5);
        insert(root, 15);
        insert(root, 30);
        insert(root, 25);
        insert(root, 35);
        System.out.println("Inorder before Deleting the leaf Node. ");
        inorder(root);
        System.out.println();
        leafDelete(root);
        System.out.println("INorder after Deleting the leaf Node. ");
        inorder(root);
    }
}
// This code is contributed by Prerna saini

Python3

# Python 3 program to delete leaf
# Node from binary search tree.

# Create a newNode in binary search tree.
class newNode:

    # Constructor to create a new node
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

# Insert a Node in binary search tree.
def insert(root, data):
    if root == None:
        return newNode(data)
    if data < root.data:
        root.left = insert(root.left, data)
    else if data > root.data:
        root.right = insert(root.right, data)
    return root

# Function for inorder traversal in a BST.
def inorder(root):
    if root != None:
        inorder(root.left)
        print(root.data, end = " ")
        inorder(root.right)

# Delete leaf nodes from binary search tree.
def leafDelete(root):
    if root == None:
        return None
    if root.left == None and root.right == None:
        return None

    # Else recursively delete in left
    # and right subtrees.
    root.left = leafDelete(root.left)
    root.right = leafDelete(root.right)

    return root

# Driver code
if __name__ == '__main__':
    root = None
    root = insert(root, 20)
    insert(root, 10)
    insert(root, 5)
    insert(root, 15)
    insert(root, 30)
    insert(root, 25)
    insert(root, 35)
    print("Inorder before Deleting the leaf Node.")
    inorder(root)
    leafDelete(root)
    print()
    print("INorder after Deleting the leaf Node.")
    inorder(root)

# This code is contributed by PranchalK

C#

// C# program to delete leaf Node from
// binary search tree.
using System;

class GfG {

    class Node {
        public int data;
        public Node left;
        public Node right;
    }

    // Create a newNode in binary search tree.
    static Node newNode(int data)
    {
        Node temp = new Node();
        temp.data = data;
        temp.left = null;
        temp.right = null;
        return temp;
    }

    // Insert a Node in binary search tree.
    static Node insert(Node root, int data)
    {
        if (root == null)
            return newNode(data);
        if (data < root.data)
            root.left = insert(root.left, data);
        else if (data > root.data)
            root.right = insert(root.right, data);
        return root;
    }

    // Function for inorder traversal in a BST.
    static void inorder(Node root)
    {
        if (root != null) {
            inorder(root.left);
            Console.Write(root.data + " ");
            inorder(root.right);
        }
    }

    // Delete leaf nodes from binary search tree.
    static Node leafDelete(Node root)
    {
        if (root == null) {
            return null;
        }
        if (root.left == null && root.right == null) {
            return null;
        }

        // Else recursively delete in
        // left and right subtrees.
        root.left = leafDelete(root.left);
        root.right = leafDelete(root.right);

        return root;
    }

    // Driver code
    public static void Main(String[] args)
    {
        Node root = null;
        root = insert(root, 20);
        insert(root, 10);
        insert(root, 5);
        insert(root, 15);
        insert(root, 30);
        insert(root, 25);
        insert(root, 35);
        Console.WriteLine("Inorder before Deleting"
                          + "the leaf Node. ");
        inorder(root);
        Console.WriteLine();
        leafDelete(root);
        Console.WriteLine("INorder after Deleting"
                          + "the leaf Node. ");
        inorder(root);
    }
}

// This code has been contributed
// by PrinciRaj1992

Javascript

<script>

// JavaScript program to delete leaf Node from
// binary search tree.
class Node {
    constructor() {
        this.data = 0;
        this.left = null;
        this.right = null;
    }
}

    // Create a newNode in binary search tree.
    function newNode(data) {
        var temp = new Node();
        temp.data = data;
        temp.left = null;
        temp.right = null;
        return temp;
    }

    // Insert a Node in binary search tree.
    function insert(root , data) {
        if (root == null)
            return newNode(data);
        if (data < root.data)
            root.left = insert(root.left, data);
        else if (data > root.data)
            root.right = insert(root.right, data);
        return root;
    }

    // Function for inorder traversal in a BST.
    function inorder(root) {
        if (root != null) {
            inorder(root.left);
            document.write(root.data + " ");
            inorder(root.right);
        }
    }

    // Delete leaf nodes from binary search tree.
    function leafDelete(root) {
        if (root == null) {
            return null;
        }
        if (root.left == null && root.right == null) {
            return null;
        }

        // Else recursively delete in left and right
        // subtrees.
        root.left = leafDelete(root.left);
        root.right = leafDelete(root.right);

        return root;
    }

    // Driver code

        var root = null;
        root = insert(root, 20);
        insert(root, 10);
        insert(root, 5);
        insert(root, 15);
        insert(root, 30);
        insert(root, 25);
        insert(root, 35);
        document.write(
        "Inorder before Deleting the leaf Node. <br/>"
        );
        inorder(root);
        document.write("<br/>");
        leafDelete(root);
        document.write(
        "INorder after Deleting the leaf Node. <br/>"
        );
        inorder(root);

// This code is contributed by todaysgaurav

</script>

Output

Inorder before Deleting the leaf Node.
5 10 15 20 25 30 35 
INorder after Deleting the leaf Node.
10 20 30 

Time Complexity: O(n), As we are visiting every node just once. Here n is the number of nodes in the tree.
Auxiliary Space: O(h), Here h is the height of the tree and the extra space is used in the recursion call stack.

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