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Print updated levels of each node of a Complete Binary Tree based on difference in weights of subtrees
  • Last Updated : 25 Feb, 2021

Given a complete binary tree with N levels numbered [0, (N – 1 )] from root to the lowest level in decreasing order and having weights numbered between [1, 2N – 1] from the root to the last leaf node in the increasing order, the task for every node is to adjust the values of the levels of all nodes present in its left and right subtree based on the following condition: 

  • Increase the level of all the nodes of lighter subtree by the difference of their weights.
  • Decrease the level of all the nodes of heavier subtree by the difference of their weights.

Examples: 

Input: 

          1
        /   \
       2     3

Output: 0 0 -2 
Explanation: 
The initial levels of the nodes {1,2,3} are {0,-1,-1} respectively. 
The root node remains unchanged. 
The weight of left subtree is 2 and the weight of the right subtree is 3. 
So, the left subtree goes up by (3 – 2) = 1 level to 0. 
The right subtree goes down by 1 level to -2.
Input: 
 

             1
           /   \
          2     3
         / \   / \
        4   5 6   7

Output: 0 4 -6 4 2 -6 -8 
Explanation: 
The initial levels of the nodes {1,2,3,4,5,6,7} are {0,-1,-1,-2,-2,-2,-2} respectively. 
The root node remains unchanged. 
The weight of the left subtree {2,4,5} is 11. 
The weight of the right subtree {3,6,7} is 16. 
Hence, all the nodes in left subtree move up by 5 while those in the right subtree moves down by 5. 
Thus, the new levels of every node are: 
Node 2: -1 + 5 = 4 
Node 3: -1 – 5 = -6 
Node 4,5: -2 + 5 = 3 
Node 6,7: -2 – 5 = -7 
Now, nodes 4,5 further based on the difference of their weights (5 -4 ) = 1. 
Node 4: 3 + 1 = 4 
Node 5: 3 – 1 = 2 
Similarly, nodes 6,7 also get adjusted. 
Node 6: -7 + 1 = -6 
Node 7: -7 – 1 = -8 
Hence, the final adjusted levels of all the nodes are 0 4 -6 4 2 -6 -8. 



Approach: In order to solve this problem, we calculate the weights of the left (w_left) and right (w_right) subtrees for every node and store their difference K. Once calculated, we recursively increase the value of the level of all the nodes of its lighter subtree by K and decrease that of its heavier subtree by K from their respective current values. Once computed for all nodes, we display the final values of the level of every node.
Below code is the implementation of the above approach:

C++




// C++ Program to print updated levels
// of each node of a Complete Binary Tree
// based on difference in weights of subtrees
 
#include <bits/stdc++.h>
using namespace std;
 
// Node for the given binary tree
struct node {
 
    int weight;
 
    // stores the weight of node
    int level;
 
    // stores the level of node
    struct node* left;
    struct node* right;
 
    node(int w, int l)
    {
        this->weight = w;
        this->level = l;
        left = right = NULL;
    }
};
 
// Utility function to insert a node
// in a tree rooted at root
struct node* insert(struct node* root,
 int n_weight,
int n_level, queue<node*>& q)
{
 
    struct node* n
= new node(n_weight, n_level);
 
    // if the tree is empty till now
    // make node n the root
    if (root == NULL)
        root = n;
 
    // If the frontmost node of
    // queue has no left child
    // make node n its left child
    // the frontmost node still
    // remains in the queue because
    // its right child is null yet
    else if (q.front()->left == NULL) {
        q.front()->left = n;
    }
 
    // Make node n the right child of
    // the frontmost node and remove
    // the front node from queue
    else {
        q.front()->right = n;
        q.pop();
    }
    // push the node n into queue
    q.push(n);
 
    return root;
}
 
// Function to create a complete binary tree
struct node* createTree(vector<int> weights,
vector<int> levels)
{
 
    // initialise the root node of tree
    struct node* root = NULL;
 
    // initialise a queue of nodes
    queue<node*> q;
 
    int n = weights.size();
    for (int i = 0; i < n; i++) {
 
        /*
        keep inserting nodes with weight values
        from the weights vector and level values
        from the levels vector
        */
        root = insert(root, weights[i],
        levels[i], q);
    }
    return root;
}
 
// Function to print final levels of nodes
void printNodeLevels(struct node* root)
{
 
    if (root == NULL)
        return;
 
    queue<node*> q;
    q.push(root);
 
    while (!q.empty()) {
 
        cout << q.front()->level << " ";
 
        if (q.front()->left != NULL)
            q.push(q.front()->left);
        if (q.front()->right != NULL)
            q.push(q.front()->right);
        q.pop();
    }
    cout << endl;
}
 
// Function to find the weight of subtree
int findWeight(struct node* root)
{
    // If the root node is null
    // then weight of subtree will be 0
    if (root == NULL)
        return 0;
     
    return root->weight +
        findWeight(root->left)
        + findWeight(root->right);
}
 
// Function to compute new level
// of the nodes based on the
// difference of weight K
void changeLevels(struct node* root, int k)
{
 
    if (root == NULL)
        return;
     
    // Change the level of root node
    root->level = root->level + k;
 
    // Recursively change the level of
    // left and right subtree
    changeLevels(root->left, k);
    changeLevels(root->right, k);
}
 
// Function to calculate weight of
// the left and the right subtrees and
// adjust levels based on their difference
void adjustLevels(struct node* root)
{
 
    // No adjustment required
    // when root is null
    if (root == NULL)
        return;
 
    // Find weights of left
    // and right subtrees
    int w_left = findWeight(root->left);
    int w_right = findWeight(root->right);
 
    // find the difference between the
    // weights of left and right subtree
    int w_diff = w_left - w_right;
 
    // Change the levels of nodes
    // according to weight difference at root
    changeLevels(root->left, -w_diff);
    changeLevels(root->right, w_diff);
 
    // Recursively adjust the levels
    // for left and right subtrees
    adjustLevels(root->left);
    adjustLevels(root->right);
}
 
// Driver code
int main()
{
    // Number of levels
    int N = 3;
 
    // Number of nodes
    int nodes = pow(2, N) - 1;
 
    vector<int> weights;
    // Vector to store weights of tree nodes
    for (int i = 1; i <= nodes; i++) {
        weights.push_back(i);
    }
     
    vector<int> levels;
    // Vector to store levels of every nodes
    for (int i = 0; i < N; i++) {
 
        // 2^i nodes are present at ith level
        for (int j = 0; j < pow(2, i); j++) {
 
            // value of level becomes negative
            // while going down the root
            levels.push_back(-1 * i);
        }
    }
     
    // Create tree with the
// given weights and levels
    struct node* root
= createTree(weights, levels);
     
    // Adjust the levels
    adjustLevels(root);
     
    // Display the final levels
    printNodeLevels(root);
     
    return 0;
}


Java




// Java Program to print updated levels
// of each node of a Complete Binary Tree
// based on difference in weights of subtrees
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Queue;
 
class GFG {
 
    // Node for the given binary tree
    static class node {
 
        int weight;
 
        // stores the weight of node
        int level;
 
        // stores the level of node
        node left;
        node right;
        public node(int w, int l)
        {
            this.weight = w;
            this.level = l;
            left = right = null;
        }
    }
 
    // Utility function to insert a node
    // in a tree rooted at root
    static node insert(node root, int n_weight, int n_level, Queue<node> q)
    {
        node n = new node(n_weight, n_level);
 
        // if the tree is empty till now
        // make node n the root
        if (root == null)
            root = n;
 
        // If the frontmost node of
        // queue has no left child
        // make node n its left child
        // the frontmost node still
        // remains in the queue because
        // its right child isnull yet
        else if (q.peek().left == null)
        {
            q.peek().left = n;
        }
 
        // Make node n the right child of
        // the frontmost node and remove
        // the front node from queue
        else
        {
            q.peek().right = n;
            q.poll();
        }
       
        // push the node n into queue
        q.add(n);
 
        return root;
    }
 
    // Function to create a complete binary tree
    static node createTree(ArrayList<Integer> weights,
                           ArrayList<Integer> levels)
    {
 
        // initialise the root node of tree
        node root = null;
 
        // initialise a queue of nodes
        Queue<node> q = new LinkedList<>();
        int n = weights.size();
        for (int i = 0; i < n; i++)
        {
 
            /*
             * keep inserting nodes with weight values
             * from the weights vector and level
             * values from the levels vector
             */
            root = insert(root, weights.get(i), levels.get(i), q);
        }
        return root;
    }
 
    // Function to print final levels of nodes
    static void printNodeLevels(node root)
    {
 
        if (root == null)
            return;
 
        Queue<node> q = new LinkedList<>();
        q.add(root);
 
        while (!q.isEmpty()) {
            System.out.print(q.peek().level + " ");
 
            if (q.peek().left != null)
                q.add(q.peek().left);
            if (q.peek().right != null)
                q.add(q.peek().right);
            q.poll();
        }
        System.out.println();
    }
 
    // Function to find the weight of subtree
    static int findWeight(node root)
    {
 
        // If the root node isnull
        // then weight of subtree will be 0
        if (root == null)
            return 0;
 
        return root.weight + findWeight(root.left) + findWeight(root.right);
    }
 
    // Function to compute new level
    // of the nodes based on the
    // difference of weight K
    static void changeLevels(node root, int k)
    {
        if (root == null)
            return;
 
        // Change the level of root node
        root.level = root.level + k;
 
        // Recursively change the level of
        // left and right subtree
        changeLevels(root.left, k);
        changeLevels(root.right, k);
    }
 
    // Function to calculate weight of
    // the left and the right subtrees and
    // adjust levels based on their difference
    static void adjustLevels(node root)
    {
 
        // No adjustment required
        // when root isnull
        if (root == null)
            return;
 
        // Find weights of left
        // and right subtrees
        int w_left = findWeight(root.left);
        int w_right = findWeight(root.right);
 
        // find the difference between the
        // weights of left and right subtree
        int w_diff = w_left - w_right;
 
        // Change the levels of nodes
        // according to weight difference at root
        changeLevels(root.left, -w_diff);
        changeLevels(root.right, w_diff);
 
        // Recursively adjust the levels
        // for left and right subtrees
        adjustLevels(root.left);
        adjustLevels(root.right);
    }
 
    // Driver code
    public static void main(String[] args)
    {
 
        // Number of levels
        int N = 3;
 
        // Number of nodes
        int nodes = (int) Math.pow(2, N) - 1;
 
        // Vector to store weights of tree nodes
        ArrayList<Integer> weights = new ArrayList<>();
        for (int i = 1; i <= nodes; i++) {
            weights.add(i);
        }
 
        // Vector to store levels of every nodes
        ArrayList<Integer> levels = new ArrayList<>();
        for (int i = 0; i < N; i++) {
 
            // 2^i nodes are present at ith level
            for (int j = 0; j < (int) Math.pow(2, i); j++) {
 
                // value of level becomes negative
                // while going down the root
                levels.add(-1 * i);
            }
        }
 
        // Create tree with the
        // given weights and levels
        node root = createTree(weights, levels);
 
        // Adjust the levels
        adjustLevels(root);
 
        // Display the final levels
        printNodeLevels(root);
 
    }
}
 
// This code is contributed by sanjeev2552


Python3




# Python3 Program to print
# updated levels of each
# node of a Complete Binary
# Tree based on difference
# in weights of subtrees
import math
 
# Node for the given binary
# tree
class node:
     
    def __init__(self, w, l):
         
        self.weight = w
        self.level = l
        self.left = None
        self.right = None
  
# Utility function to insert
# a node in a tree rooted at
# root
def insert(root, n_weight,
           n_level, q):
  
    n = node(n_weight,
             n_level);
  
    # if the tree is empty
    # till now make node n
    # the root
    if (root == None):
        root = n;
  
    # If the frontmost node of
    # queue has no left child
    # make node n its left child
    # the frontmost node still
    # remains in the queue because
    # its right child is null yet
    elif (q[0].left == None):
        q[0].left = n;
     
  
    # Make node n the right
    # child of the frontmost
    # node and remove the
    # front node from queue
    else:
        q[0].right = n;
        q.pop(0);
     
    # push the node n
    # into queue
    q.append(n);
  
    return root;
 
# Function to create a
# complete binary tree
def createTree(weights,
               levels):
  
    # initialise the root
    # node of tree
    root = None;
  
    # initialise a queue
    # of nodes
    q = []
  
    n = len(weights)
     
    for i in range(n):
        '''
        keep inserting nodes with
        weight values from the weights
        vector and level values from
        the levels vector
        '''       
        root = insert(root, weights[i],
                      levels[i], q);
         
    return root;
 
# Function to print final
# levels of nodes
def printNodeLevels(root):
  
    if (root == None):
        return;
  
    q = []
    q.append(root);
  
    while (len(q) != 0):       
        print(q[0].level,
              end = ' ')
        if (q[0].left != None):
            q.append(q[0].left);
        if (q[0].right != None):
            q.append(q[0].right);
        q.pop(0);
    print()
     
# Function to find the weight
# of subtree
def findWeight(root):
 
    # If the root node is
    # null then weight of
    # subtree will be 0
    if (root == None):
        return 0;
      
    return (root.weight +
            findWeight(root.left) +
            findWeight(root.right));
  
# Function to compute new level
# of the nodes based on the
# difference of weight K
def changeLevels(root, k):
  
    if (root == None):
        return;
      
    # Change the level of
    # root node
    root.level = root.level + k;
  
    # Recursively change the
    # level of left and right
    # subtree
    changeLevels(root.left, k);
    changeLevels(root.right, k);
 
# Function to calculate weight
# of the left and the right
# subtrees and adjust levels
# based on their difference
def adjustLevels(root):
  
    # No adjustment required
    # when root is null
    if (root == None):
        return;
  
    # Find weights of left
    # and right subtrees
    w_left = findWeight(root.left);
    w_right = findWeight(root.right);
  
    # find the difference between
    # the weights of left and
    # right subtree
    w_diff = w_left - w_right;
  
    # Change the levels of nodes
    # according to weight difference
    # at root
    changeLevels(root.left,
                 -w_diff);
    changeLevels(root.right,
                 w_diff);
  
    # Recursively adjust the levels
    # for left and right subtrees
    adjustLevels(root.left);
    adjustLevels(root.right);
 
# Driver code
if __name__=="__main__":
     
    # Number of levels
    N = 3;
  
    # Number of nodes
    nodes = int(math.pow(2, N)) - 1;
  
    weights = []
     
    # Vector to store weights
    # of tree nodes
    for i in range(1, nodes + 1):   
        weights.append(i);   
      
    levels = []
     
    # Vector to store levels
    # of every nodes
    for i in range(N):
         
        # 2^i nodes are present
        # at ith level
        for j in range(pow(2, i)):
             
            # value of level becomes
            # negative while going
            # down the root
            levels.append(-1 * i);               
      
    # Create tree with the
    # given weights and levels
    root = createTree(weights,
                      levels);
      
    # Adjust the levels
    adjustLevels(root);
      
    # Display the final levels
    printNodeLevels(root);
  
# This code is contributed by Rutvik_56


Output: 

0 4 -6 4 2 -6 -8

 

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