Convert a BST to a Binary Tree such that sum of all greater keys is added to every key

Convert a BST to a Binary Tree such that sum of all greater keys is added to every key
Convert a BST to a Binary Tree such that sum of all greater keys is added to every key

Given a Binary Search Tree (BST), convert it to a Binary Tree such that every key of the original BST is changed to key plus sum of all greater keys in BST.

Input: Root of following BST
              5
            /   \
           2     13

Output: The given BST is converted to following Binary Tree
              18
            /   \
          20     13

Solution: Do reverse Inoorder traversal. Keep track of the sum of nodes visited so far. Let this sum besum. For every node currently being visited, first add the key of this node to sum, i.e. sum = sum +node->key. Then change the key of current node to sum, i.e., node->key = sum.
When a BST is being traversed in reverse Inorder, for every key currently being visited, all keys that are already visited are all greater keys.

// A recursive function that traverses the given BST in reverse inorder and

// for every key, adds all greater keys to it

void addGreaterUtil(struct node *root, int *sum_ptr)

{

    // Base Case

    if (root == NULL)

        return;

    // Recur for right subtree first so that sum of all greater

    // nodes is stored at sum_ptr

    addGreaterUtil(root->right, sum_ptr);

    // Update the value at sum_ptr

    *sum_ptr = *sum_ptr + root->key;

    // Update key of this node

    root->key = *sum_ptr;

    // Recur for left subtree so that the updated sum is added

    // to smaller nodes

    addGreaterUtil(root->left, sum_ptr);

}

// A wrapper over addGreaterUtil().  It initializes sum and calls

// addGreaterUtil() to recursivel upodate and use value of sum

void addGreater(struct node *root)

{

    int sum = 0;

    addGreaterUtil(root, &sum);

}

int sum_so_far = 0;

 

void convert_bst_to_bt_helper(Node* root)

{

    if(root->right != NULL)

        convert_bst_to_bt_helper(root->right);

    root->data += sum_so_far;    

    sum_so_far = root->data;

    if(root->left != NULL)

        convert_bst_to_bt_helper(root->left);

}

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