Replace each node of a Binary Tree with the sum of all the nodes present in its diagonal
Given a Binary Tree, the task is to print the level order traversal of the tree after replacing the value of each node of the tree with the sum of all the nodes on the same diagonal.
Examples:
Input:
9 / \ 6 10 / \ \ 4 7 11 / \ \ 3 5 8Output: 30 21 30 9 21 30 3 9 21
Explanation:
30 / \ 21 30 / \ \ 9 21 30 / \ \ 3 9 21Diagonal traversal of the binary tree
9 10 11
6 7 8
4 5
3
Input:
5 / \ 6 3 / \ \ 4 9 2Output: 10 15 10 4 15 10
Explanation:
10 / \ 15 10 / \ \ 4 15 10
Approach: The idea is to perform the diagonal traversal of the binary tree and store the sum of each node on the same diagonal. Finally, traverse the tree and replace each node with the sum of nodes at that diagonal. Follow the steps below to solve the problem:
- Use diagonal traversal of the tree and store the sum of all the nodes at each diagonal of the tree and store the sum of each diagonal into a map.
- Traverse the tree using level order traversal and replace each node of the tree with the sum of all the nodes at that diagonal.
- Finally, print the tree using level order traversal.
Below is the implementation of the above approach:
C++
// CPP program to implement// the above approach#include <bits/stdc++.h>using namespace std;// Structure of a tree nodestruct TreeNode{ int val; struct TreeNode *left,*right; TreeNode(int x) { val = x; left = NULL; right = NULL; }};// Function to replace each node with// the sum of nodes at the same diagonalvoid replaceDiag(TreeNode *root, int d, unordered_map<int,int> &diagMap){ // IF root is NULL if (!root) return; // Replace nodes root->val = diagMap[d]; // Traverse the left subtree replaceDiag(root->left, d + 1, diagMap); // Traverse the right subtree replaceDiag(root->right, d, diagMap);}// Function to find the sum of all the nodes// at each diagonal of the treevoid getDiagSum(TreeNode *root, int d, unordered_map<int,int> &diagMap){ // If root is not NULL if (!root) return; // If update sum of nodes // at current diagonal if (diagMap[d] > 0) diagMap[d] += root->val; else diagMap[d] = root->val; // Traverse the left subtree getDiagSum(root->left, d + 1, diagMap); // Traverse the right subtree getDiagSum(root->right, d, diagMap);}// Function to print the nodes of the tree// using level order traversalvoid levelOrder(TreeNode *root){ // Stores node at each level of the tree queue<TreeNode*> q; q.push(root); while (true) { // Stores count of nodes // at current level int length = q.size(); if (!length) break; while (length) { // Stores front element // of the queue auto temp = q.front(); q.pop(); cout << temp->val << " "; // Insert left subtree if (temp->left) q.push(temp->left); // Insert right subtree if (temp->right) q.push(temp->right); // Update length length -= 1; } }}// Driver Codeint main(){ // Build tree TreeNode *root = new TreeNode(5); root->left = new TreeNode(6); root->right = new TreeNode(3); root->left->left =new TreeNode(4); root->left->right = new TreeNode(9); root->right->right = new TreeNode(2); // Store sum of nodes at each // diagonal of the tree unordered_map<int,int> diagMap; // Find sum of nodes at each // diagonal of the tree getDiagSum(root, 0, diagMap); // Replace nodes with the sum // of nodes at the same diagonal replaceDiag(root, 0, diagMap); // Print tree levelOrder(root); return 0;}// This code is contributed by mohit kumar 29 |
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Python3
# Python program to implement# the above approach# Structure of a tree nodeclass TreeNode: def __init__(self, val = 0, left = None, right = None): self.val = val self.left = left self.right = right# Function to replace each node with # the sum of nodes at the same diagonaldef replaceDiag(root, d, diagMap): # IF root is NULL if not root: return # Replace nodes root.val = diagMap[d] # Traverse the left subtree replaceDiag(root.left, d + 1, diagMap) # Traverse the right subtree replaceDiag(root.right, d, diagMap)# Function to find the sum of all the nodes# at each diagonal of the treedef getDiagSum(root, d, diagMap): # If root is not NULL if not root: return # If update sum of nodes # at current diagonal if d in diagMap: diagMap[d] += root.val else: diagMap[d] = root.val # Traverse the left subtree getDiagSum(root.left, d + 1, diagMap) # Traverse the right subtree getDiagSum(root.right, d, diagMap)# Function to print the nodes of the tree# using level order traversaldef levelOrder(root): # Stores node at each level of the tree que = [root] while True: # Stores count of nodes # at current level length = len(que) if not length: break while length: # Stores front element # of the queue temp = que.pop(0) print(temp.val, end =' ') # Insert left subtree if temp.left: que.append(temp.left) # Insert right subtree if temp.right: que.append(temp.right) # Update length length -= 1# Driver codeif __name__ == '__main__': # Build tree root = TreeNode(5) root.left = TreeNode(6) root.right = TreeNode(3) root.left.left = TreeNode(4) root.left.right = TreeNode(9) root.right.right = TreeNode(2) # Store sum of nodes at each # diagonal of the tree diagMap = {} # Find sum of nodes at each # diagonal of the tree getDiagSum(root, 0, diagMap) # Replace nodes with the sum # of nodes at the same diagonal replaceDiag(root, 0, diagMap) # Print tree levelOrder(root) |
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Output:
10 15 10 4 15 10
Time Complexity: O(N)
Auxiliary Space: O(N)
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