Given a binary tree, the task is to flatten it in order of its post-order traversal. In the flattened binary tree, the left node of all the nodes must be NULL.
Examples:
Input: 5 / \ 3 7 / \ / \ 2 4 6 8 Output: 2 4 3 6 8 7 5 Input: 1 \ 2 \ 3 \ 4 \ 5 Output: 5 4 3 2 1
A simple approach will be to recreate the Binary Tree from its post-order traversal. This will take O(N) extra space were N is the number of nodes in BST.
A better solution is to simulate post-order traversal of the given binary tree.
- Create a dummy node.
- Create variable called ‘prev’ and make it point to the dummy node.
- Perform post-order traversal and at each step.
- Set prev -> right = curr
- Set prev -> left = NULL
- Set prev = curr
This will improve the space complexity to O(H) in the worst case as post-order traversal takes O(H) extra space.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Node of the binary tree struct node { int data; node* left; node* right; node( int data) { this ->data = data; left = NULL; right = NULL; } }; // Function to print the flattened // binary Tree void print(node* parent) { node* curr = parent; while (curr != NULL) cout << curr->data << " " , curr = curr->right; } // Function to perform post-order traversal // recursively void postorder(node* curr, node*& prev) { // Base case if (curr == NULL) return ; postorder(curr->left, prev); postorder(curr->right, prev); prev->left = NULL; prev->right = curr; prev = curr; } // Function to flatten the given binary tree // using post order traversal node* flatten(node* parent) { // Dummy node node* dummy = new node(-1); // Pointer to previous element node* prev = dummy; // Calling post-order traversal postorder(parent, prev); prev->left = NULL; prev->right = NULL; node* ret = dummy->right; // Delete dummy node delete dummy; return ret; } // Driver code int main() { node* root = new node(5); root->left = new node(3); root->right = new node(7); root->left->left = new node(2); root->left->right = new node(4); root->right->left = new node(6); root->right->right = new node(8); print(flatten(root)); return 0; } |
Java
// Java implementation of the approach class GFG { // Node of the binary tree static class node { int data; node left; node right; node( int data) { this .data = data; left = null ; right = null ; } }; static node prev; // Function to print the flattened // binary Tree static void print(node parent) { node curr = parent; while (curr != null ) { System.out.print(curr.data + " " ); curr = curr.right; } } // Function to perform post-order traversal // recursively static void postorder(node curr) { // Base case if (curr == null ) return ; postorder(curr.left); postorder(curr.right); prev.left = null ; prev.right = curr; prev = curr; } // Function to flatten the given binary tree // using post order traversal static node flatten(node parent) { // Dummy node node dummy = new node(- 1 ); // Pointer to previous element prev = dummy; // Calling post-order traversal postorder(parent); prev.left = null ; prev.right = null ; node ret = dummy.right; // Delete dummy node dummy = null ; return ret; } // Driver code public static void main(String[] args) { node root = new node( 5 ); root.left = new node( 3 ); root.right = new node( 7 ); root.left.left = new node( 2 ); root.left.right = new node( 4 ); root.right.left = new node( 6 ); root.right.right = new node( 8 ); print(flatten(root)); } } // This code is contributed by PrinciRaj1992 |
Python3
# Python implementation of above algorithm # Utility class to create a node class node: def __init__( self , key): self .data = key self .left = self .right = None # Function to print the flattened # binary Tree def print_(parent): curr = parent while (curr ! = None ): print ( curr.data ,end = " " ) curr = curr.right prev = None # Function to perform post-order traversal # recursively def postorder( curr ): global prev # Base case if (curr = = None ): return postorder(curr.left) postorder(curr.right) prev.left = None prev.right = curr prev = curr # Function to flatten the given binary tree # using post order traversal def flatten(parent): global prev # Dummy node dummy = node( - 1 ) # Pointer to previous element prev = dummy # Calling post-order traversal postorder(parent) prev.left = None prev.right = None ret = dummy.right return ret # Driver code root = node( 5 ) root.left = node( 3 ) root.right = node( 7 ) root.left.left = node( 2 ) root.left.right = node( 4 ) root.right.left = node( 6 ) root.right.right = node( 8 ) print_(flatten(root)) # This code is contributed by Arnab Kundu |
C#
// C# implementation of the approach using System; class GFG { // Node of the binary tree public class node { public int data; public node left; public node right; public node( int data) { this .data = data; left = null ; right = null ; } }; static node prev; // Function to print the flattened // binary Tree static void print(node parent) { node curr = parent; while (curr != null ) { Console.Write(curr.data + " " ); curr = curr.right; } } // Function to perform post-order traversal // recursively static void postorder(node curr) { // Base case if (curr == null ) return ; postorder(curr.left); postorder(curr.right); prev.left = null ; prev.right = curr; prev = curr; } // Function to flatten the given binary tree // using post order traversal static node flatten(node parent) { // Dummy node node dummy = new node(-1); // Pointer to previous element prev = dummy; // Calling post-order traversal postorder(parent); prev.left = null ; prev.right = null ; node ret = dummy.right; // Delete dummy node dummy = null ; return ret; } // Driver code public static void Main(String[] args) { node root = new node(5); root.left = new node(3); root.right = new node(7); root.left.left = new node(2); root.left.right = new node(4); root.right.left = new node(6); root.right.right = new node(8); print(flatten(root)); } } // This code is contributed by Princi Singh |
Javascript
<script> // Javascript implementation of the approach // Node of the binary tree class node { constructor(data) { this .data = data; this .left = null ; this .right = null ; } }; var prev = null ; // Function to print the flattened // binary Tree function print(parent) { var curr = parent; while (curr != null ) { document.write(curr.data + " " ); curr = curr.right; } } // Function to perform post-order traversal // recursively function postorder(curr) { // Base case if (curr == null ) return ; postorder(curr.left); postorder(curr.right); prev.left = null ; prev.right = curr; prev = curr; } // Function to flatten the given binary tree // using post order traversal function flatten(parent) { // Dummy node var dummy = new node(-1); // Pointer to previous element prev = dummy; // Calling post-order traversal postorder(parent); prev.left = null ; prev.right = null ; var ret = dummy.right; // Delete dummy node dummy = null ; return ret; } // Driver code var root = new node(5); root.left = new node(3); root.right = new node(7); root.left.left = new node(2); root.left.right = new node(4); root.right.left = new node(6); root.right.right = new node(8); print(flatten(root)); // This code is contributed by noob2000 </script> |
2 4 3 6 8 7 5
Time complexity: O(N)
Auxiliary Space: O(N). since N extra space has been taken.
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