Check whether a given binary tree is skewed binary tree or not?

Last Updated : 08 Sep, 2022

Given a Binary Tree check whether it is skewed binary tree or not. A skewed tree is a tree where each node has only one child node or none.

Examples:

Input :         5
             /   
            4
              \
               3
             /
           2
Output : Yes

Input :       5
            /
           4
            \
             3
           /  \
          2    4
Output : No

The idea is to check if a node has two children. If node has two children return false, else recursively compute whether subtree with one child is skewed tree. If node is leaf node return true.

Below is the implementation of above approach:

C++

// C++ program to Check whether a given 
// binary tree is skewed binary tree or not?
 
#include <bits/stdc++.h>
using namespace std;
 
// A Tree node
struct Node {
    int key;
    struct Node *left, *right;
};
 
// Utility function to create a new node
Node* newNode(int key)
{
    Node* temp = new Node;
    temp->key = key;
    temp->left = temp->right = NULL;
    return (temp);
}
 
bool isSkewedBT(Node* root)
{
    // check if node is NULL or is a leaf node
    if (root == NULL || (root->left == NULL && 
                        root->right == NULL))
        return true;
 
    // check if node has two children if
    // yes, return false
    if (root->left && root->right) 
        return false;
    if (root->left)
        return isSkewedBT(root->left);
    return isSkewedBT(root->right);
}
 
// Driver program
int main()
{
    /*   10
       /     \
     12       13
           /     \
         14       15    
        /   \     /  \
       21   22   23   24           
    Let us create Binary Tree shown in above example */
    Node* root = newNode(10);
    root->left = newNode(12);
    root->left->right = newNode(15);
    cout << isSkewedBT(root) << endl;
 
    root = newNode(5);
    root->right = newNode(4);
    root->right->left = newNode(3);
    root->right->left->right = newNode(2);
    cout << isSkewedBT(root) << endl;
 
    root = newNode(5);
    root->left = newNode(4);
    root->left->right = newNode(3);
    root->left->right->left = newNode(2);
    root->left->right->right = newNode(4);
    cout << isSkewedBT(root) << endl;
}

Java

// Java program to Check whether a given 
// binary tree is skewed binary tree or not?
 
class Solution
{
// A Tree node 
 static class Node { 
    int key; 
     Node left, right; 
}
 
// Utility function to create a new node 
static Node newNode(int key) 
{ 
    Node temp = new Node(); 
    temp.key = key; 
    temp.left = temp.right = null; 
    return (temp); 
} 
 
static boolean isSkewedBT(Node root) 
{ 
    // check if node is null or is a leaf node 
    if (root == null || (root.left == null && 
                        root.right == null)) 
        return true; 
 
    // check if node has two children if 
    // yes, return false 
    if (root.left!=null && root.right!=null) 
        return false; 
    if (root.left!=null) 
        return isSkewedBT(root.left); 
    return isSkewedBT(root.right); 
} 
 
// Driver program 
public static void main(String args[])
{ 
    /* 10 
    /     \ 
    12     13 
        /     \ 
        14     15     
        / \     / \ 
    21 22 23 24         
    Let us create Binary Tree shown in above example */
    Node root = newNode(10); 
    root.left = newNode(12); 
    root.left.right = newNode(15); 
    System.out.println( isSkewedBT(root)?1:0 ); 
 
    root = newNode(5); 
    root.right = newNode(4); 
    root.right.left = newNode(3); 
    root.right.left.right = newNode(2); 
    System.out.println( isSkewedBT(root)?1:0 ); 
 
    root = newNode(5); 
    root.left = newNode(4); 
    root.left.right = newNode(3); 
    root.left.right.left = newNode(2); 
    root.left.right.right = newNode(4); 
    System.out.println(  isSkewedBT(root)?1:0 ); 
} 
}
//contributed by Arnab Kundu

Python3

# Python3 program to Check whether a given 
# binary tree is skewed binary tree or not? 
 
# Binary Tree Node 
""" utility that allocates a newNode 
with the given key """
class newNode: 
 
    # Construct to create a newNode 
    def __init__(self, key): 
        self.data = key
        self.left = None
        self.right = None
 
def isSkewedBT(root): 
 
    # check if node is None or is a leaf node 
    if (root == None or (root.left == None and
                         root.right == None)): 
        return 1
 
    # check if node has two children if 
    # yes, return false 
    if (root.left and root.right): 
        return 0
    if (root.left) :
        return isSkewedBT(root.left) 
    return isSkewedBT(root.right) 
 
# Driver Code 
if __name__ == '__main__':
 
    """ 10 
    /     \ 
    12     13 
        /     \ 
        14     15     
        / \     / \ 
    21 22 23 24         
    Let us create Binary Tree shown in above example """
    root = newNode(10) 
    root.left = newNode(12) 
    root.left.right = newNode(15) 
    print(isSkewedBT(root))
 
    root = newNode(5) 
    root.right = newNode(4) 
    root.right.left = newNode(3) 
    root.right.left.right = newNode(2) 
    print(isSkewedBT(root))
 
    root = newNode(5) 
    root.left = newNode(4) 
    root.left.right = newNode(3) 
    root.left.right.left = newNode(2) 
    root.left.right.right = newNode(4) 
    print(isSkewedBT(root))
 
# This code is contributed by
# Shubham Singh(SHUBHAMSINGH10)

C#

// C# program to Check whether a given 
// binary tree is skewed binary tree or not? 
using System;
 
public class GFG 
{ 
     
// A Tree node 
class Node 
{ 
    public int key; 
    public Node left, right; 
} 
 
// Utility function to create a new node 
static Node newNode(int key) 
{ 
    Node temp = new Node(); 
    temp.key = key; 
    temp.left = temp.right = null; 
    return (temp); 
} 
 
static bool isSkewedBT(Node root) 
{ 
    // check if node is null or is a leaf node 
    if (root == null || (root.left == null && 
                        root.right == null)) 
        return true; 
 
    // check if node has two children if 
    // yes, return false 
    if (root.left!=null && root.right!=null) 
        return false; 
    if (root.left!=null) 
        return isSkewedBT(root.left); 
    return isSkewedBT(root.right); 
} 
 
// Driver code 
public static void Main() 
{ 
    /* 10 
    / \ 
    12 13 
        / \ 
        14 15 
        / \ / \ 
    21 22 23 24 
    Let us create Binary Tree shown in above example */
    Node root = newNode(10); 
    root.left = newNode(12); 
    root.left.right = newNode(15); 
    Console.WriteLine( isSkewedBT(root)?1:0 ); 
 
    root = newNode(5); 
    root.right = newNode(4); 
    root.right.left = newNode(3); 
    root.right.left.right = newNode(2); 
    Console.WriteLine( isSkewedBT(root)?1:0 ); 
 
    root = newNode(5); 
    root.left = newNode(4); 
    root.left.right = newNode(3); 
    root.left.right.left = newNode(2); 
    root.left.right.right = newNode(4); 
    Console.WriteLine( isSkewedBT(root)?1:0 ); 
} 
} 
 
/* This code is contributed by Rajput-Ji*/

Javascript

<script>
    // Javascript program to Check whether a given 
    // binary tree is skewed binary tree or not?
     
    // Binary tree node
    class Node
    {
        constructor(key) {
           this.left = null;
           this.right = null;
           this.data = key;
        }
    }
     
    // Utility function to create a new node 
    function newNode(key) 
    { 
        let temp = new Node(key); 
        return (temp); 
    } 
 
    function isSkewedBT(root) 
    { 
        // check if node is null or is a leaf node 
        if (root == null || (root.left == null && 
                            root.right == null)) 
            return true; 
 
        // check if node has two children if 
        // yes, return false 
        if (root.left!=null && root.right!=null) 
            return false; 
        if (root.left!=null) 
            return isSkewedBT(root.left); 
        return isSkewedBT(root.right); 
    }
     
    /* 10 
    /     \ 
    12     13 
        /     \ 
        14     15     
        / \     / \ 
    21 22 23 24         
    Let us create Binary Tree shown in above example */
    let root = newNode(10); 
    root.left = newNode(12); 
    root.left.right = newNode(15); 
    document.write(isSkewedBT(root)?1 + "</br>":0 + "</br>"); 
   
    root = newNode(5); 
    root.right = newNode(4); 
    root.right.left = newNode(3); 
    root.right.left.right = newNode(2); 
    document.write(isSkewedBT(root)?1 + "</br>":0 + "</br>"); 
   
    root = newNode(5); 
    root.left = newNode(4); 
    root.left.right = newNode(3); 
    root.left.right.left = newNode(2); 
    root.left.right.right = newNode(4); 
    document.write(isSkewedBT(root)?1 + "</br>":0 + "</br>"); 
  
 // This code is contributed by decode2207.
</script>

Output

1
1
0

Complexity Analysis:

Time complexity:
- Best case : O(1) when root has two children.
- Worst case : O(h) when tree is skewed tree.
Auxiliary Space: O(h)
- Here h is the height of the tree

Another approach:(iterative method)

We can also check if a tree is skewed or not by iterative method using above approach.

Implementation:

C++

// C++ program to Check whether a given
// binary tree is skewed binary tree or not using iterative
// method
 
#include <bits/stdc++.h>
using namespace std;
 
// A Tree node
struct Node {
    int key;
    struct Node *left, *right;
};
 
// Utility function to create a new node
Node* newNode(int key)
{
    Node* temp = new Node;
    temp->key = key;
    temp->left = temp->right = NULL;
    return (temp);
}
 
bool isSkewedBT(Node* root)
{
 
    while (root != NULL) {
        // check if the node is a leaf node
        if (root->left == NULL && root->right == NULL)
            return true;
        // check if node has two children if
        // yes, return false
        if (root->left != NULL && root->right != NULL)
            return false;
        // move towards left if it has a left child
        if (root->left != NULL)
            root = root->left;
        // or move towards right if it has a right child
        else
            root = root->right;
    }
    return true;
}
 
// Driver program
int main()
{
    /*   10
       /     \
     12       13
           /     \
         14       15
        /   \     /  \
       21   22   23   24
    Let us create Binary Tree shown in above example */
    Node* root = newNode(10);
    root->left = newNode(12);
    root->left->right = newNode(15);
    cout << isSkewedBT(root) << endl;
 
    root = newNode(5);
    root->right = newNode(4);
    root->right->left = newNode(3);
    root->right->left->right = newNode(2);
    cout << isSkewedBT(root) << endl;
 
    root = newNode(5);
    root->left = newNode(4);
    root->left->right = newNode(3);
    root->left->right->left = newNode(2);
    root->left->right->right = newNode(4);
    cout << isSkewedBT(root) << endl;
}
 
// This code is contributed by Abhijeet Kumar(abhijeet19403)

Java

// Java program to Check whether a given
// binary tree is skewed binary tree or not using iterative method
 
class Solution {
    // A Tree node
    static class Node {
        int key;
        Node left, right;
    }
 
    // Utility function to create a new node
    static Node newNode(int key)
    {
        Node temp = new Node();
        temp.key = key;
        temp.left = temp.right = null;
        return (temp);
    }
 
    static boolean isSkewedBT(Node root)
    {
        while (root != null) {
            // check if the node is a leaf node
            if (root.left == null && root.right == null)
                return true;
            // check if node has two children if
            // yes, return false
            if (root.left!=null && root.right!=null)
                return false;
              // move towards left if it has a left child 
            if (root.left != null)
                root = root.left;
              // or move towards right if it has a right child
            else
                root = root.right;
        }
        return true;
    }
 
    // Driver program
    public static void main(String args[])
    {
        /* 10
        /     \
        12     13
            /     \
            14     15
            / \     / \
        21 22 23 24
        Let us create Binary Tree shown in above example */
        Node root = newNode(10);
        root.left = newNode(12);
        root.left.right = newNode(15);
        System.out.println(isSkewedBT(root) ? 1 : 0);
 
        root = newNode(5);
        root.right = newNode(4);
        root.right.left = newNode(3);
        root.right.left.right = newNode(2);
        System.out.println(isSkewedBT(root) ? 1 : 0);
 
        root = newNode(5);
        root.left = newNode(4);
        root.left.right = newNode(3);
        root.left.right.left = newNode(2);
        root.left.right.right = newNode(4);
        System.out.println(isSkewedBT(root) ? 1 : 0);
    }
}
// This code is contributed by Abhijeet Kumar(abhijeet19403)

Python3

# Python3 program to Check whether a given
# binary tree is skewed binary tree or not using iterative method
 
# Binary Tree Node
""" utility that allocates a newNode
with the given key """
 
 
class newNode:
 
    # Construct to create a newNode
    def __init__(self, key):
        self.data = key
        self.left = None
        self.right = None
 
 
def isSkewedBT(root):
 
    while (root != None):
            # check if the node is a leaf node
            if (root.left == None and root.right == None):
                return 1
            # check if node has two children if
            # yes, return false
            if (root.left != None and root.right != None):
                return 0
              # move towards left if it has a left child
            if (root.left != None):
                root = root.left
              # or move towards right if it has a right child
            else:
                root = root.right
 
    return 1
 
# Driver Code 
if __name__ == '__main__':
 
    """ 10 
    /     \ 
    12     13 
        /     \ 
        14     15     
        / \     / \ 
    21 22 23 24         
    Let us create Binary Tree shown in above example """
    root = newNode(10) 
    root.left = newNode(12) 
    root.left.right = newNode(15) 
    print(isSkewedBT(root))
 
    root = newNode(5) 
    root.right = newNode(4) 
    root.right.left = newNode(3) 
    root.right.left.right = newNode(2) 
    print(isSkewedBT(root))
 
    root = newNode(5) 
    root.left = newNode(4) 
    root.left.right = newNode(3) 
    root.left.right.left = newNode(2) 
    root.left.right.right = newNode(4) 
    print(isSkewedBT(root))
 
# This code is contributed by
# Abhijeet Kumar(abhijeet19403)

C#

// C# program to Check whether a given
// binary tree is skewed binary tree or not using iterative method
using System;
 
public class GFG {
 
    // A Tree node
    class Node {
        public int key;
        public Node left, right;
    }
 
    // Utility function to create a new node
    static Node newNode(int key)
    {
        Node temp = new Node();
        temp.key = key;
        temp.left = temp.right = null;
        return (temp);
    }
 
    static bool isSkewedBT(Node root)
    {
        while (root != null) {
            // check if the node is a leaf node
            if (root.left == null && root.right == null)
                return true;
            // check if node has two children if
            // yes, return false
            if (root.left != null && root.right != null)
                return false;
            // move towards left if it has a left child
            if (root.left != null)
                root = root.left;
            // or move towards right if it has a right child
            else
                root = root.right;
        }
        return true;
    }
 
    // Driver code
    public static void Main()
    {
        /* 10
        / \
        12 13
            / \
            14 15
            / \ / \
        21 22 23 24
        Let us create Binary Tree shown in above example */
        Node root = newNode(10);
        root.left = newNode(12);
        root.left.right = newNode(15);
        Console.WriteLine(isSkewedBT(root) ? 1 : 0);
 
        root = newNode(5);
        root.right = newNode(4);
        root.right.left = newNode(3);
        root.right.left.right = newNode(2);
        Console.WriteLine(isSkewedBT(root) ? 1 : 0);
 
        root = newNode(5);
        root.left = newNode(4);
        root.left.right = newNode(3);
        root.left.right.left = newNode(2);
        root.left.right.right = newNode(4);
        Console.WriteLine(isSkewedBT(root) ? 1 : 0);
    }
}
 
/* This code is contributed by Abhijeet
 * Kumar(abhijeet19403)*/

Javascript

<script>
    // Javascript program to Check whether a given 
    // binary tree is skewed binary tree or not?
     
    // Binary tree node
    class Node
    {
        constructor(key) {
           this.left = null;
           this.right = null;
           this.data = key;
        }
    }
     
    // Utility function to create a new node 
    function newNode(key) 
    { 
        let temp = new Node(key); 
        return (temp); 
    } 
 
    function isSkewedBT(root) 
    { 
          while (root != null) {
            // check if the node is a leaf node
            if (root.left == null && root.right == null)
                return true;
            // check if node has two children if
            // yes, return false
            if (root.left != null && root.right != null)
                return false;
            // move towards left if it has a left child
            if (root.left != null)
                root = root.left;
            // or move towards right if it has a right child
            else
                root = root.right;
        }
        return true;
    }
     
    /* 10 
    /     \ 
    12     13 
        /     \ 
        14     15     
        / \     / \ 
    21 22 23 24         
    Let us create Binary Tree shown in above example */
    let root = newNode(10); 
    root.left = newNode(12); 
    root.left.right = newNode(15); 
    document.write(isSkewedBT(root)?1 + "</br>":0 + "</br>"); 
   
    root = newNode(5); 
    root.right = newNode(4); 
    root.right.left = newNode(3); 
    root.right.left.right = newNode(2); 
    document.write(isSkewedBT(root)?1 + "</br>":0 + "</br>"); 
   
    root = newNode(5); 
    root.left = newNode(4); 
    root.left.right = newNode(3); 
    root.left.right.left = newNode(2); 
    root.left.right.right = newNode(4); 
    document.write(isSkewedBT(root)?1 + "</br>":0 + "</br>"); 
  
 // This code is contributed by Abhijeet Kumar(abhijeet19403)
</script>

Output

1
1
0

Complexity Analysis:

Time Complexity: O(n)
- As in the worst case we have to visit every node.
Auxiliary Space: O(1)
- As constant extra space is used.

This approach was contributed by Ahijeet Kumar.

gaddevarunteja

Improve

Check whether a binary tree is a full binary tree or not

Check whether a given binary tree is skewed binary tree or not?

C++

Java

Python3

C#

Javascript

C++

Java

Python3

C#

Javascript

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