Level order traversal of a tree is or the tree.
Example Tree
Level order traversal of the above tree is 1 2 3 4 5
METHOD 1 (Use function to print a given level)
Algorithm:
There are basically two functions in this method. One is to print all nodes at a given level (printGivenLevel), and other is to print level order traversal of the tree (printLevelorder). printLevelorder makes use of printGivenLevel to print nodes at all levels one by one starting from root./*Function to print level order traversal of tree*/printLevelorder(tree)for d = 1 to height(tree) printGivenLevel(tree, d);/*Function to print all nodes at a given level*/printGivenLevel(tree, level)if tree is NULL then return;if level is 1, then print(tree->data);else if level greater than 1, then printGivenLevel(tree->left, level-1); printGivenLevel(tree->right, level-1);
Implementation:
- c
- Java
- Python
# Recursive Python program for level order traversal of Binary Tree# A node structureclass Node: # A utility function to create a new node def __init__(self, key): self.data = key self.left = None self.right = None# Function to print level order traversal of treedef printLevelOrder(root): h = height(root) for i in range(1, h+1): printGivenLevel(root, i)# Print nodes at a given leveldef printGivenLevel(root , level): if root is None: return if level == 1: print "%d" %(root.data), elif level > 1 : printGivenLevel(root.left , level-1) printGivenLevel(root.right , level-1)""" Compute the height of a tree--the number of nodes along the longest path from the root node down to the farthest leaf node"""def height(node): if node is None: return 0 else : # Compute the height of each subtree lheight = height(node.left) rheight = height(node.right) #Use the larger one if lheight > rheight : return lheight+1 else: return rheight+1# Driver program to test above functionroot = Node(1)root.left = Node(2)root.right = Node(3)root.left.left = Node(4)root.left.right = Node(5)print "Level order traversal of binary tree is -"printLevelOrder(root)#This code is contributed by Nikhil Kumar Singh(nickzuck_007)
Level order traversal of binary tree is - 1 2 3 4 5
Time Complexity: O(n^2) in worst case. For a skewed tree, printGivenLevel() takes O(n) time where n is the number of nodes in the skewed tree. So time complexity of printLevelOrder() is O(n) + O(n-1) + O(n-2) + .. + O(1) which is O(n^2).
METHOD 2 (Use Queue)Algorithm:
For each node, first the node is visited and then it’s child nodes are put in a FIFO queue.printLevelorder(tree)1) Create an empty queue q2) temp_node = root /*start from root*/3) Loop while temp_node is not NULL a) print temp_node->data. b) Enqueue temp_node’s children (first left then right children) to q c) Dequeue a node from q and assign it’s value to temp_node
Implementation:
Here is a simple implementation of the above algorithm. Queue is implemented using an array with maximum size of 500. We can implement queue as linked list also.- C
- C++
- Java
- Python
# Python program to print level order traversal using Queue# A node structureclass Node: # A utility function to create a new node def __init__(self ,key): self.data = key self.left = None self.right = None# Iterative Method to print the height of binary treedef printLevelOrder(root): # Base Case if root is None: return # Create an empty queue for level order traversal queue = [] # Enqueue Root and initialize height queue.append(root) while(len(queue) > 0): # Print front of queue and remove it from queue print queue[0].data, node = queue.pop(0) #Enqueue left child if node.left is not None: queue.append(node.left) # Enqueue right child if node.right is not None: queue.append(node.right)#Driver Program to test above functionroot = Node(1)root.left = Node(2)root.right = Node(3)root.left.left = Node(4)root.left.right = Node(5)print "Level Order Traversal of binary tree is -"printLevelOrder(root)#This code is contributed by Nikhil Kumar Singh(nickzuck_007)
Level order traversal of binary tree is - 1 2 3 4 5
Time Complexity: O(n) where n is number of nodes in the binary tree