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

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++

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// 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;
}

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Java














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// 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 



















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Python3














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# 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) 



















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C#














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// 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*/



















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Output:


1
1
0





Time complexity of this solution is

Best case : O(1) when root has two children.

Worst case : O(h) when tree is skewed tree.



          
          
          

          

    

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