Sink even nodes in Binary Tree

Given a Binary Tree having odd and even elements, sink all its even valued nodes such that no node with an even value could be a parent of a node with an odd 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 odd nodes and all even nodes follow the rule)

Examples: 

Input: 
       1
     /    \
    5       8
  /  \     /  \
 2    4   9    10
Output: 
1 
5 9 
2 4 8 10

Level order traversal after
sinking all the nodes

Input: 
  4
 /  \
2    1
Output: 
4
2 1

Explanation: 
In the first case
Given tree
       4
    /    \
   2      1

There are two trees possible
       1            1
    /    \   OR   /   \
   2      4      4     2 
  

In the second example also,
Given tree
       1
     /    \
    5       8
  /  \     /  \
 2    4   9    10

There are more than one tree
that can satisfy the condition
      1                 1
   /    \            /    \     
  5       9    OR   5      9   
 /  \    /  \      /  \   / \   
2   4  8   10    4    2  8  10

Approach:

• Basically, it is required to swap the even value of a node with the odd value of one of its descendants.
• The idea is to traverse the tree in a postorder fashion.
• Since we process in postorder, for each even node encountered, its left and right subtrees are already balanced (sinked).
• Check if it’s an even node and its left or right child has an odd value. If the odd value is found, swap the node’s data with that of the odd child node and call the procedure on the odd child to balance the subtree.
• If both children have even values, that means that all their descendants are even.

Below is the implementation of the idea: 

C++

//C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

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

// Helper function to create a new node
Node* newNode(int key)
{
    Node* node = new Node;
    node->data = key;
    node->left = node->right = NULL;
    return node;
}

// Helper function to check
// if node is leaf node
bool isLeaf(Node* root)
{
    return (root->left == NULL && root->right == NULL);
}

// A recursive method to sink a tree with even root
// This method assumes that the subtrees are
// already sinked. This method is similar to
// Heapify of Heap-Sort
void 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 even nodes to
// the bottom of binary tree. It does
// a postorder traversal and calls sink()
// if any even node is found
void sinkEvenNodes(Node* root)
{
    // If NULL or is a leaf, do nothing
    if (root == NULL || isLeaf(root))
        return;

    // Process left and right subtrees
    // before this node
    sinkEvenNodes(root->left);
    sinkEvenNodes(root->right);

    // If root is even, 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();
            cout << 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
        cout << endl;
    }
}

int 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);
    sinkEvenNodes(root);

    printLevelOrder(root);

    return 0;
}
//This code is contributed by Potta Lokesh

Java

import java.util.Queue;
import java.util.LinkedList;

// A binary tree node
class Node {
  int data;
  Node left, right;

  public Node(int data)
  {
    this.data = data;
    left = right = null;
  }
}
class Main
{

  // Helper function to check
  // if node is leaf node
  static boolean isLeaf(Node root)
  {
    return (root.left == null && root.right == null);
  }

  // A recursive method to sink a tree with even root
  // This method assumes that the subtrees are
  // already sinked. This method is similar to
  // Heapify of Heap-Sort
  static void 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 != null && (root.left.data & 1) != 0)
    {

      // swap root's data with left child
      // and fix left subtree
      //swap(root.data, root.left.data);
      int temp = root.data;
      root.data = root.left.data;
      root.left.data = temp;
      sink(root.left);
    }

    // if right subtree exists and
    // right child is even
    else if (root.right != null && (root.right.data & 1) != 0)
    {

      // swap root's data with right child
      // and fix right subtree
      //swap(root.data, root.right.data);
      int temp = root.data;
      root.data = root.right.data;
      root.right.data = temp;
      sink(root.right);
    }
  }

  // Function to sink all even nodes to
  // the bottom of binary tree. It does
  // a postorder traversal and calls sink()
  // if any even node is found
  static void sinkEvenNodes(Node root)
  {

    // If null or is a leaf, do nothing
    if (root == null || isLeaf(root))
      return;

    // Process left and right subtrees
    // before this node
    sinkEvenNodes(root.left);
    sinkEvenNodes(root.right);

    if ((root.data & 1) == 0)
      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.
  static void printLevelOrder(Node root)
  {

    // Do Level order traversal
    Queue<Node> q = new LinkedList<Node>();
    q.add(root);

    while (q.size() > 0) {
      int nodeCount = q.size();

      while (nodeCount > 0) {
        Node node = q.peek();
        System.out.print(node.data + " ");
        q.remove();
        if (node.left != null)
          q.add(node.left);
        if (node.right != null)
          q.add(node.right);
        nodeCount--;
      }
      System.out.println();
    }
  }

  // Driver code
  public static void main(String[] args)
  {
    Node root = new Node(1);
    root.left = new Node(5);
    root.right = new Node(8);
    root.left.left = new Node(2);
    root.left.right = new Node(4);
    root.right.left = new Node(9);
    root.right.right = new Node(10);
    sinkEvenNodes(root);

    printLevelOrder(root);
  }
}

// This code is contributed by unstoppablepandu.

Python

# Python3 program to sink even nodes
# to the bottom of binary tree

# A binary tree node
# Helper function to allocates a new node
class 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 node
def isLeaf(root):
    return (root.left == None and
            root.right == None)

# A recursive method to sink a tree with even root
# This method assumes that the subtrees are
# already sinked. This method is similar to
# Heapify of Heap-Sort
def 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 (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
    elif(root.right and (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 even nodes to
# the bottom of binary tree. It does
# a postorder traversal and calls sink()
# if any even node is found
def sinkevenNodes(root):

    # If None or is a leaf, do nothing
    if (root == None or isLeaf(root)):
        return

    # Process left and right subtrees
    # before this node
    sinkevenNodes(root.left)
    sinkevenNodes(root.right)

    # If root is even, sink it
    if not (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)

sinkevenNodes(root)

printLevelOrder(root)

# This code is contributed by SHUBHAMSINGH10

C#

// C# program for the above approach
using System;
using System.Collections.Generic;

class GFG
{
    // A binary tree node
    class Node {
        public int data;
        public Node left, right;
    }

    // Helper function to create a new node
    static Node newNode(int key)
    {
        Node node = new Node();
        node.data = key;
        node.left = node.right = null;
        return node;
    }

    // Helper function to check
    // if node is leaf node
    static bool isLeaf(Node root)
    {
        return (root.left == null && root.right == null);
    }

    // A recursive method to sink a tree with even root
    // This method assumes that the subtrees are
    // already sinked. This method is similar to
    // Heapify of Heap-Sort
    static void 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 != null && (root.left.data & 1) != 0)
        {

            // swap root's data with left child
            // and fix left subtree
            //swap(root.data, root.left.data);
            int temp=root.data;
            root.data=root.left.data;
            root.left.data=temp;
            sink(root.left);
        }
        // if right subtree exists and
        // right child is even
        else if (root.right != null && (root.right.data & 1) != 0)
        {

            // swap root's data with right child
            // and fix right subtree
            //swap(root.data, root.right.data);
            int temp=root.data;
            root.data=root.right.data;
            root.right.data=temp;
            sink(root.right);
        }
    }

    // Function to sink all even nodes to
    // the bottom of binary tree. It does
    // a postorder traversal and calls sink()
    // if any even node is found
    static void sinkEvenNodes(Node root)
    {
        // If null or is a leaf, do nothing
        if (root == null || isLeaf(root))
            return;

        // Process left and right subtrees
        // before this node
        sinkEvenNodes(root.left);
        sinkEvenNodes(root.right);

        // If root is even, sink it
        if ((root.data & 1)==0)
            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.
    static void printLevelOrder(Node root)
    {
        Queue<Node> q = new Queue<Node>();
        q.Enqueue(root);

        // Do Level order traversal
        while (q.Count>0) {
            int nodeCount = q.Count;

            // Print one level at a time
            while (nodeCount>0) {
                Node node = q.Peek();
                Console.Write(node.data+" ");
                q.Dequeue();
                if (node.left != null)
                    q.Enqueue(node.left);
                if (node.right != null)
                    q.Enqueue(node.right);
                nodeCount--;
            }
            // Line separator for levels
            Console.Write("\n");
        }
    }

    static void Main(string[] args)
    {
        /* 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);
        sinkEvenNodes(root);

        printLevelOrder(root);
    }
}

// This code is contributed by poojaagarwal2.

Javascript

<script>


// Program to sink even nodes
// to the bottom of binary tree

// A binary tree node
class Node {

    constructor()
    {
        this.data = 0;
        this.left = null;
        this.right = null;
    }
};

// Helper function to allocates
// a new node
function newnode(data)
{
    var node = new Node;
    node.data = data;
    return node;
}

// Helper function to check
// if node is leaf node
function isLeaf(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-Sort
function sink(root)
{
    // If null or is a leaf, do nothing
    if (root == null || isLeaf(root))
        return;

    // If left subtree exists
    // and left child is odd
    if (root.left
        && (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 odd
    else if (root.right
             && (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 even
// nodes to the bottom of
// binary tree. It does a
// postorder traversal and
// calls sink()
// if any even node is found
function sinkevenNodes( root)
{
    // If null or is a
    // leaf, do nothing
    if (root == null || isLeaf(root))
        return;

    // Process left and right
    // subtrees before this node
    sinkevenNodes(root.left);
    sinkevenNodes(root.right);

    // If root is even, 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.
function printLevelOrder(root)
{
    var q = [];
    q.push(root);

    // Do Level order traversal
    while (q.length!=0) {
        var nodeCount = q.length;

        // Print one level at a time
        while (nodeCount) {

            var node = q[0];

            document.write(node.data + " ");

            q.shift();

            // If the node has a left
            // child then push into queue
            if (node.left != null)
                q.push(node.left);

            // If the node has a right
            // child then push into queue
            if (node.right != null)
                q.push(node.right);

            nodeCount--;
        }

        // Line separator for levels
        document.write("<br>");
    }
}

// Driver code

    /* Constructed binary tree is
        1
      /  \
     5    8
    / \  / \
   2  4 9  10     */

    var 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);

    // Calling function to perform
    // sink operation
    sinkevenNodes(root);

    // Printing the updated tree
    // using level order traversal
    printLevelOrder(root);



</script>

Output:

1 
5 9 
2 4 8 10