Sink Odd nodes in Binary Tree - GeeksforGeeks

02 Mar, 2022
Given a Binary Tree having odd and even elements, sink all its odd valued nodes such that no node with odd value could be parent of node with even value. There can be multiple outputs for a given tree, we need to print one of them. It is always possible to convert a tree (Note that a node with even nodes and all odd nodes follows the rule) 
Input : 
       1
    /    \
   2      3
Output
       2            2
    /    \   OR   /   \
   1      3      3     1 
  

Input : 
       1
     /    \
    5       8
  /  \     /  \
 2    4   9    10
Output :
    2                 4
  /    \            /    \     
 4       8    OR   2      8    OR .. (any tree with 
/  \    /  \      /  \   / \          same keys and 
5   1  9   10    5    1 9   10        no odd is parent
                                      of even)
We strongly recommend you to minimize your browser and try this yourself first.Basically, we need to swap odd value of a node with even value of one of its descendants. The idea is to traverse the tree in postorder fashion. Since we process in postorder, for each odd node encountered, its left and right subtrees are already balanced (sinked), we check if it’s an odd node and its left or right child has an even value. If even value is found, we swap the node’s data with that of even child node and call the procedure on the even child to balance the subtree. If both children have odd values, that means that all its descendants are odd.Below is the implementation of the idea.  
C++
Python3
// Program to sink odd nodes to the bottom of// binary tree#include<bits/stdc++.h>using namespace std; // A binary tree nodestruct Node{    int data;    Node* left, *right;}; // Helper function to allocates a new nodeNode* newnode(int data){    Node* node = new Node;    node->data = data;    node->left = node->right = NULL;    return node;} // Helper function to check if node is leaf nodebool isLeaf(Node *root){    return (root->left == NULL && root->right == NULL);} // A recursive method to sink a tree with odd root// This method assumes that the subtrees are already// sinked. This method is similar to Heapify of// Heap-Sortvoid sink(Node *&root){    // If NULL or is a leaf, do nothing    if (root == NULL || isLeaf(root))        return;     // if left subtree exists and left child is even    if (root->left && !(root->left->data & 1))    {        // swap root's data with left child and        // fix left subtree        swap(root->data, root->left->data);        sink(root->left);    }     // if right subtree exists and right child is even    else if(root->right && !(root->right->data & 1))    {        // swap root's data with right child and        // fix right subtree        swap(root->data, root->right->data);        sink(root->right);    }} // Function to sink all odd nodes to the bottom of binary// tree. It does a postorder traversal and calls sink()// if any odd node is foundvoid sinkOddNodes(Node* &root){    // If NULL or is a leaf, do nothing    if (root == NULL || isLeaf(root))        return;     // Process left and right subtrees before this node    sinkOddNodes(root->left);    sinkOddNodes(root->right);     // If root is odd, sink it    if (root->data & 1)        sink(root);} // Helper function to do Level Order Traversal of// Binary Tree level by level. This function is used// here only for showing modified tree.void printLevelOrder(Node* root){    queue<Node*> q;    q.push(root);     // Do Level order traversal    while (!q.empty())    {        int nodeCount = q.size();         // Print one level at a time        while (nodeCount)        {            Node *node = q.front();            printf("%d ", node->data);            q.pop();            if (node->left != NULL)                q.push(node->left);            if (node->right != NULL)                q.push(node->right);            nodeCount--;        }         // Line separator for levels        printf("\n");    }} // Driver program to test above functionsint main(){    /* Constructed binary tree is            1          /   \         5      8        / \   /  \       2   4 9   10     */     Node *root = newnode(1);    root->left = newnode(5);    root->right    = newnode(8);    root->left->left = newnode(2);    root->left->right = newnode(4);    root->right->left = newnode(9);    root->right->right = newnode(10);     sinkOddNodes(root);     printf("Level order traversal of modified tree\n");    printLevelOrder(root);     return 0;}
# Python3 program to sink odd nodes# to the bottom of binary tree # A binary tree node# Helper function to allocates a new nodeclass newnode:     # Constructor to create a new node    def __init__(self, key):        self.data = key        self.left = None        self.right = None # Helper function to check# if node is leaf nodedef isLeaf(root):    return (root.left == None and            root.right == None) # A recursive method to sink a tree with odd root# This method assumes that the subtrees are# already sinked. This method is similar to# Heapify of Heap-Sortdef sink(root):         # If None or is a leaf, do nothing    if (root == None or isLeaf(root)):        return         # if left subtree exists and    # left child is even    if (root.left and not(root.left.data & 1)):                 # swap root's data with left child         # and fix left subtree        root.data, \        root.left.data = root.left.data, \                         root.data        sink(root.left)             # if right subtree exists and    # right child is even    else if(root.right and not(root.right.data & 1)):                 # swap root's data with right child        # and fix right subtree        root.data, \        root.right.data = root.right.data, \                          root.data        sink(root.right) # Function to sink all odd nodes to# the bottom of binary tree. It does# a postorder traversal and calls sink()# if any odd node is founddef sinkOddNodes(root):         # If None or is a leaf, do nothing    if (root == None or isLeaf(root)):        return             # Process left and right subtrees    # before this node    sinkOddNodes(root.left)    sinkOddNodes(root.right)         # If root is odd, sink it    if (root.data & 1):        sink(root) # Helper function to do Level Order Traversal# of Binary Tree level by level. This function# is used here only for showing modified tree.def printLevelOrder(root):    q = []    q.append(root)         # Do Level order traversal    while (len(q)):                 nodeCount = len(q)                 # Print one level at a time        while (nodeCount):            node = q[0]            print(node.data, end = " ")            q.pop(0)            if (node.left != None):                q.append(node.left)            if (node.right != None):                q.append(node.right)            nodeCount -= 1                 # Line separator for levels        print() # Driver Code""" Constructed binary tree is            1        / \        5 8        / \ / \    2 4 9 10     """root = newnode(1)root.left = newnode(5)root.right = newnode(8)root.left.left = newnode(2)root.left.right = newnode(4)root.right.left = newnode(9)root.right.right = newnode(10) sinkOddNodes(root) print("Level order traversal of modified tree")printLevelOrder(root) # This code is contributed by SHUBHAMSINGH10
Output : 
Level order traversal of modified tree
2 
4 8 
5 1 9 10 
 
YouTubeGeeksforGeeks507K subscribersSink Odd nodes in Binary Tree | GeeksforGeeksWatch laterShareCopy linkInfoShoppingTap to unmuteIf playback doesn't begin shortly, try restarting your device.You're signed outVideos you watch may be added to the TV's watch history and influence TV recommendations. To avoid this, cancel and sign in to YouTube on your computer.CancelConfirmMore videosMore videosSwitch cameraShareInclude playlistAn error occurred while retrieving sharing information. Please try again later.Watch on0:000:000:00 / 2:32•Live•<div class="player-unavailable"><h1 class="message">An error occurred.</h1><div class="submessage"><a href="https://www.youtube.com/watch?v=w87SVBrXA9U" target="_blank">Try watching this video on www.youtube.com</a>, or enable JavaScript if it is disabled in your browser.</div></div>
This article is contributed by Aditya Goel. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above 
SHUBHAMSINGH10
surinderdawra388
Tree
Tree
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Binary Tree | Set 3 (Types of Binary Tree)
Inorder Tree Traversal without Recursion
Binary Tree | Set 2 (Properties)
Decision Tree
A program to check if a binary tree is BST or not
Construct Tree from given Inorder and Preorder traversals
Introduction to Tree Data Structure
Lowest Common Ancestor in a Binary Tree | Set 1
Complexity of different operations in Binary tree, Binary Search Tree and AVL tree