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

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)