Replace each node in binary tree with the sum of its inorder predecessor and successor

Software Development
#1

Hello Everyone,

Given a binary tree containing n nodes. The problem is to replace each node in the binary tree with the sum of its inorder predecessor and inorder successor.

Approach:
Create an array arr . Store 0 at index 0. Now, store the inorder traversal of tree in the array arr . Then, store 0 at last index. 0’s are stored as inorder predecessor of leftmost leaf and inorder successor of rightmost leaf is not present. Now, perform inorder traversal and while traversing node replace node’s value with arr[i-1] + arr[i+1] and then increment i . In the beginning initialize i = 1. For an element arr[i] , the values arr[i-1] and arr[i+1] are its inorder predecessor and inorder successor respectively.

// C++ implementation to replace each node

// in binary tree with the sum of its inorder

// predecessor and successor

#include <bits/stdc++.h>

using namespace std;

// node of a binary tree

struct Node {

int data;

struct Node* left, *right;

};

// function to get a new node of a binary tree

struct Node* getNode( int data)

{

// allocate node

struct Node* new_node =

( struct Node*) malloc ( sizeof ( struct Node));

// put in the data;

new_node->data = data;

new_node->left = new_node->right = NULL;

return new_node;

}

// function to store the inorder traversal

// of the binary tree in 'arr'

void storeInorderTraversal( struct Node* root,

vector< int >& arr)

{

// if root is NULL

if (!root)

return ;

// first recur on left child

storeInorderTraversal(root->left, arr);

// then store the root's data in 'arr'

arr.push_back(root->data);

// now recur on right child

storeInorderTraversal(root->right, arr);

}

// function to replace each node with the sum of its

// inorder predecessor and successor

void replaceNodeWithSum( struct Node* root,

vector< int > arr, int * i)

{

// if root is NULL

if (!root)

return ;

// first recur on left child

replaceNodeWithSum(root->left, arr, i);

// replace node's data with the sum of its

// inorder predecessor and successor

root->data = arr[*i - 1] + arr[*i + 1];

// move 'i' to point to the next 'arr' element

++*i;

// now recur on right child

replaceNodeWithSum(root->right, arr, i);

}

// Utility function to replace each node in binary

// tree with the sum of its inorder predecessor

// and successor

void replaceNodeWithSumUtil( struct Node* root)

{

// if tree is empty

if (!root)

return ;

vector< int > arr;

// store the value of inorder predecessor

// for the leftmost leaf

arr.push_back(0);

// store the inoder traversal of the tree in 'arr'

storeInorderTraversal(root, arr);

// store the value of inorder successor

// for the rightmost leaf

arr.push_back(0);

// replace each node with the required sum

int i = 1;

replaceNodeWithSum(root, arr, &i);

}

// function to print the preorder traversal

// of a binary tree

void preorderTraversal( struct Node* root)

{

// if root is NULL

if (!root)

return ;

// first print the data of node

cout << root->data << " " ;

// then recur on left subtree

preorderTraversal(root->left);

// now recur on right subtree

preorderTraversal(root->right);

}

// Driver program to test above

int main()

{

// binary tree formation

struct Node* root = getNode(1); /* 1 */

root->left = getNode(2); /* / \ */

root->right = getNode(3); /* 2 3 */

root->left->left = getNode(4); /* / \ / \ */

root->left->right = getNode(5); /* 4 5 6 7 */

root->right->left = getNode(6);

root->right->right = getNode(7);

cout << "Preorder Traversal before tree modification:n" ;

preorderTraversal(root);

replaceNodeWithSumUtil(root);

cout << "\nPreorder Traversal after tree modification:n" ;

preorderTraversal(root);

return 0;

}

Output:

Preorder Traversal before tree modification: 1 2 4 5 3 6 7 Preorder Traversal after tree modification: 11 9 2 3 13 4 3

Time Complexity: O(n)
Auxiliary Space: O(n)