Check if all leaves are at same level

2.3

Given a Binary Tree, check if all leaves are at same level or not.

          12
        /    \
      5       7       
    /          \ 
   3            1
  Leaves are at same level

          12
        /    \
      5       7       
    /          
   3          
   Leaves are Not at same level


          12
        /    
      5             
    /   \        
   3     9
  /      /
 1      2
 Leaves are at same level

Method 1 (Recursive)

The idea is to first find level of the leftmost leaf and store it in a variable leafLevel. Then compare level of all other leaves with leafLevel, if same, return true, else return false. We traverse the given Binary Tree in Preorder fashion. An argument leaflevel is passed to all calls. The value of leafLevel is initialized as 0 to indicate that the first leaf is not yet seen yet. The value is updated when we find first leaf. Level of subsequent leaves (in preorder) is compared with leafLevel.

C

// C program to check if all leaves are at same level
#include <stdio.h>
#include <stdlib.h>

// A binary tree node
struct Node
{
    int data;
    struct Node *left, *right;
};

// A utility function to allocate a new tree node
struct Node* newNode(int data)
{
    struct Node* node = (struct Node*) malloc(sizeof(struct Node));
    node->data = data;
    node->left = node->right = NULL;
    return node;
}

/* Recursive function which checks whether all leaves are at same level */
bool checkUtil(struct Node *root, int level, int *leafLevel)
{
    // Base case
    if (root == NULL)  return true;

    // If a leaf node is encountered
    if (root->left == NULL && root->right == NULL)
    {
        // When a leaf node is found first time
        if (*leafLevel == 0)
        {
            *leafLevel = level; // Set first found leaf's level
            return true;
        }

        // If this is not first leaf node, compare its level with
        // first leaf's level
        return (level == *leafLevel);
    }

    // If this node is not leaf, recursively check left and right subtrees
    return checkUtil(root->left, level+1, leafLevel) &&
           checkUtil(root->right, level+1, leafLevel);
}

/* The main function to check if all leafs are at same level.
   It mainly uses checkUtil() */
bool check(struct Node *root)
{
   int level = 0, leafLevel = 0;
   return checkUtil(root, level, &leafLevel);
}

// Driver program to test above function
int main()
{
    // Let us create tree shown in thirdt example
    struct Node *root = newNode(12);
    root->left = newNode(5);
    root->left->left = newNode(3);
    root->left->right = newNode(9);
    root->left->left->left = newNode(1);
    root->left->right->left = newNode(1);
    if (check(root))
        printf("Leaves are at same level\n");
    else
        printf("Leaves are not at same level\n");
    getchar();
    return 0;
}

Java

// Java program to check if all leaves are at same level
 
// A binary tree node
class Node 
{
    int data;
    Node left, right;
 
    Node(int item) 
    {
        data = item;
        left = right = null;
    }
}
 
class Leaf 
{
    int leaflevel=0;
}
 
class BinaryTree 
{
    Node root;
    Leaf mylevel = new Leaf();
    
    /* Recursive function which checks whether all leaves are at same 
       level */
    boolean checkUtil(Node node, int level, Leaf leafLevel) 
    {
        // Base case
        if (node == null)
            return true;
            
        // If a leaf node is encountered
        if (node.left == null && node.right == null) 
        {
            // When a leaf node is found first time
            if (leafLevel.leaflevel == 0) 
            {
                // Set first found leaf's level
                leafLevel.leaflevel = level; 
                return true;
            }
 
            // If this is not first leaf node, compare its level with
            // first leaf's level
            return (level == leafLevel.leaflevel);
        }
 
        // If this node is not leaf, recursively check left and right 
        // subtrees
        return checkUtil(node.left, level + 1, leafLevel)
                && checkUtil(node.right, level + 1, leafLevel);
    }
 
    /* The main function to check if all leafs are at same level.
       It mainly uses checkUtil() */
    boolean check(Node node) 
    {
        int level = 0;
        return checkUtil(node, level, mylevel);
    }
 
    public static void main(String args[]) 
    {
        // Let us create the tree as shown in the example
        BinaryTree tree = new BinaryTree();
        tree.root = new Node(12);
        tree.root.left = new Node(5);
        tree.root.left.left = new Node(3);
        tree.root.left.right = new Node(9);
        tree.root.left.left.left = new Node(1);
        tree.root.left.right.left = new Node(1);
        if (tree.check(tree.root))
            System.out.println("Leaves are at same level");
        else
            System.out.println("Leaves are not at same level");
    }
}
 
// This code has been contributed by Mayank Jaiswal

Python


# Python program to check if all leaves are at same level

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

# Recursive function which check whether all leaves are at
# same level
def checkUtil(root, level):
    
    # Base Case 
    if root is None:
        return True
    
    # If a tree node is encountered
    if root.left is None and root.right is None:
        
        # When a leaf node is found first time
        if check.leafLevel == 0 :
            check.leafLevel = level # Set first leaf found
            return True

        # If this is not first leaf node, compare its level
        # with first leaf's level
        return level == check.leafLevel 

    # If this is not first leaf node, compare its level
    # with first leaf's level
    return (checkUtil(root.left, level+1)and
            checkUtil(root.right, level+1))

def check(root):
    level = 0
    check.leafLevel = 0 
    return (checkUtil(root, level))

# Driver program to test above function
root = Node(12)
root.left = Node(5)
root.left.left = Node(3)
root.left.right = Node(9)
root.left.left.left = Node(1)
root.left.right.left = Node(2)

if(check(root)):
    print "Leaves are at same level"
else:
    print "Leaves are not at same level"

# This code is contributed by Nikhil Kumar Singh(nickzuck_007)


Output:
Leaves are at same level

Time Complexity: The function does a simple traversal of the tree, so the complexity is O(n).

 

Method 1 (Iterative)

It can also be solved by iterative approach.

The idea is to iteratively traverse the tree, and when you encounter the first leaf node, store it’s level in result variable, now whenever you encounter any leaf node, compare it’s level with previously stored result, it they are same then proceed for rest of the tree, else return false.

// CPP program to check if all leaf nodes are at 
// same level of binary tree
#include <bits/stdc++.h>
using namespace std;
 
// tree node
struct Node {
    int data;
    Node *left, *right;
};
 
// returns a new tree Node
Node* newNode(int data)
{
    Node* temp = new Node();
    temp->data = data;
    temp->left = temp->right = NULL;
    return temp;
}
 
// return true if all leaf nodes are
// at same level, else false
int checkLevelLeafNode(Node* root)
{
    if (!root)
        return 1;
 
    // create a queue for level order traversal
    queue<Node*> q;
    q.push(root);
 
    int result = INT_MAX;
     int level = 0;

    // traverse until the queue is empty
    while (!q.empty()) {
        int size = q.size();
        level += 1;

        // traverse for complete level
        while(size > 0){
            Node* temp = q.front();
            q.pop();
        
            // check for left child
            if (temp->left) {
                q.push(temp->left);

                // if its leaf node
                if(!temp->left->right && !temp->left->left){

                    // if it's first leaf node, then update result
                    if (result == INT_MAX)
                        result = level;
                    
                    // if it's not first leaf node, then compare 
                    // the level with level of previous leaf node
                    else if (result != level)
                        return 0;                    
                }
            }
             
             // check for right child
            if (temp->right){
                q.push(temp->right);

                // if it's leaf node
                if (!temp->right->left && !temp->right->right)

                    // if it's first leaf node till now, 
                    // then update the result
                    if (result == INT_MAX)
                        result = level;
                    
                    // if it is not the first leaf node, 
                    // then compare the level with level 
                    // of previous leaf node
                    else if(result != level)
                        return 0;
                    
               }
               size -= 1;
        }    
    }
    
    return 1;
}
 
// driver program
int main()
{
    // construct a tree
    Node* root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->right = newNode(4);
    root->right->left = newNode(5);
    root->right->right = newNode(6);
 
    int result = checkLevelLeafNode(root);
    if (result)
        cout << "All leaf nodes are at same level\n";
    else
        cout << "Leaf nodes not at same level\n";
    return 0;
}

Output:

All leaf nodes are at same level

Time Complexity : O(n)

This code is contributed by Mandeep Singh

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

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