# Coefficient of Range in a Binary Tree

Given a Binary Tree, the task is to find the Coefficient of Range in it.

Range is defined as the difference between the maximum and minimum value in a set of data and Coefficient of Range is the relative measure of the dispersion of the range. Suppose the maximum value in a data set is maxVal and minimum value is minVal then the coefficient of range can be defined as:

Coefficient of range = (maxVal – minVal)/(maxVal + minVal)

Consider the below Binary Tree: For example, maximum in the above Binary Tree is 9 and minimum is 1 so coeffcient of range is ((9 – 1)/ ( 9 + 1)) = 0.8.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: In Binary Search Tree, we can find maximum by traversing right pointers until we reach rightmost node. But in Binary Tree, we must visit every node to figure out maximum. So the idea is to traverse the given tree and for every node return maximum of 3 values.

1. Node’s data.
2. Maximum in node’s left subtree.
3. Maximum in node’s right subtree.

Similarly, find the minimum value in the Binary Tree and calculate the coefficient of range.

Below is the implementation of the above approach:

 `// CPP program to find Coefficient of ` `// Range in a Binary Tree ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// A tree node ` `struct` `Node { ` `    ``float` `data; ` `    ``struct` `Node *left, *right; ` `}; ` ` `  `// A utility function to create a new node ` `struct` `Node* newNode(``float` `data) ` `{ ` `    ``struct` `Node* node = (``struct` `Node*) ` `        ``malloc``(``sizeof``(``struct` `Node)); ` `    ``node->data = data; ` `    ``node->left = node->right = NULL; ` `    ``return` `(node); ` `} ` ` `  `// Returns maximum value in a given Binary Tree ` `float` `findMax(``struct` `Node* root) ` `{ ` `    ``// Base case ` `    ``if` `(root == NULL) ` `        ``return` `INT_MIN; ` ` `  `    ``// Return maximum of 3 values: ` `    ``// 1) Root's data 2) Max in Left Subtree ` `    ``// 3) Max in right subtree ` `    ``float` `res = root->data; ` `    ``float` `lres = findMax(root->left); ` `    ``float` `rres = findMax(root->right); ` `    ``if` `(lres > res) ` `        ``res = lres; ` `    ``if` `(rres > res) ` `        ``res = rres; ` ` `  `    ``return` `res; ` `} ` ` `  `// Returns minimum value in a given Binary Tree ` `float` `findMin(``struct` `Node* root) ` `{ ` `    ``// Base case ` `    ``if` `(root == NULL) ` `        ``return` `INT_MAX; ` ` `  `    ``// Return minimum of 3 values: ` `    ``// 1) Root's data 2) Min in Left Subtree ` `    ``// 3) Min in right subtree ` `    ``float` `res = root->data; ` `    ``float` `lres = findMin(root->left); ` `    ``float` `rres = findMin(root->right); ` `    ``if` `(lres < res) ` `        ``res = lres; ` `    ``if` `(rres < res) ` `        ``res = rres; ` ` `  `    ``return` `res; ` `} ` ` `  `// Function to find the value of the Coefficient ` `// of range in the Binary Tree ` `float` `coefRange(Node* root) ` `{ ` `    ``float` `max = findMax(root); ` `    ``float` `min = findMin(root); ` ` `  `    ``return` `(max - min) / (max + min); ` `} ` ` `  `// Driver Code ` `int` `main(``void``) ` `{ ` `    ``// Contruct the Binary Tree ` `    ``struct` `Node* root = newNode(2); ` `    ``root->left = newNode(7); ` `    ``root->right = newNode(5); ` `    ``root->left->right = newNode(6); ` `    ``root->left->right->left = newNode(1); ` `    ``root->left->right->right = newNode(11); ` `    ``root->right->right = newNode(9); ` `    ``root->right->right->left = newNode(4); ` ` `  `    ``cout << ``"Coefficient of Range is "` `<< coefRange(root); ` ` `  `    ``return` `0; ` `} `

Output:

```Coefficient of Range is 0.833333
```

Time complexity : O(n) where n is the number of nodes.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : VishalBachchas, nidhi_biet