# Using BST with 2 extra fields

Hello Everyone,

Another approach to solve the above problem would be to use a simple Binary Search Tree with 2 extra fields:

1. to hold the elements on the left side of a node
2. to store the frequency of element.

In this approach, we traverse the input array from the ending to the begging and add the elements into the BST.
While inserting the elements to the BST, we can compute the number of elements which are lesser elements simply by computing the sum of frequency of the element and the number of elements to the left side of current node, if we are moving to right side of the current node.

Once we place an element in it’s correct position, we can return it’s this sum value

• C++14
• Python

`#include<bits/stdc++.h>`

`using` `namespace` `std;`

`// BST node structure`

`class` `Node{`

` `

`public` `:`

` ` `int` `val;`

` ` `int` `count;`

` ` `Node* left;`

` ` `Node* right;`

` `

` ` `// Constructor`

` ` `Node(` `int` `num1, ` `int` `num2)`

` ` `{`

` ` `this` `->val = num1;`

` ` `this` `->count = num2;`

` ` `this` `->left = ` `this` `->right = NULL;`

` ` `}`

`};`

`// Function to addNode and find the smaller`

`// elements on the right side`

`int` `addNode(Node*& root, ` `int` `value,`

` ` `int` `countSmaller)`

`{`

` `

` ` `// Base case`

` ` `if` `(root == NULL)`

` ` `{`

` ` `root = ` `new` `Node(value, 0);`

` ` `return` `countSmaller;`

` ` `}`

` ` `if` `(root->val < value)`

` ` `{`

` ` `return` `root->count +`

` ` `addNode(root->right,`

` ` `value,`

` ` `countSmaller + 1);`

` ` `}`

` ` `else`

` ` `{`

` ` `root->count++;`

` ` `return` `addNode(root->left, value,`

` ` `countSmaller);`

` ` `}`

`}`

`// Driver code`

`int` `main()`

`{`

` ` `ios_base::sync_with_stdio(` `false` `);`

` ` `cin.tie(0);`

` ` `int` `data[] = { 10, 6, 15, 20, 30, 5, 7 };`

` ` `int` `size = ` `sizeof` `(data) / ` `sizeof` `(data);`

` ` `int` `ans[size] = {0};`

` ` `Node* root = NULL;`

` `

` ` `for` `(` `int` `i = size - 1; i >= 0; i--)`

` ` `{`

` ` `ans[i] = addNode(root, data[i], 0);`

` ` `}`

` ` `for` `(` `int` `i = 0; i < size; i++)`

` ` `cout << ans[i] << ` `" "` `;`

` ` `return` `0;`

`}`

`// This code is contributed by Brahmajit Mohapatra`

Output:

3 1 2 2 2 0 0

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