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 coefficient of range is ((9 – 1)/ ( 9 + 1)) = 0.8. 

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: 

C++

// CPP program to find Coefficient of
// Range in a Binary Tree

#include <bits/stdc++.h>
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* newnode = new Node();
    newnode->data = data;
    newnode->left = newnode->right = NULL;
    return (newnode);
}

// 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)
{
    // Construct 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;
}

Java

// JAVA program to find Coefficient of
// Range in a Binary Tree

class GFG
{

// A tree node
static class Node
{
    float data;
    Node left, right;
};

// A utility function to create a new node
static Node newNode(float data)
{
    Node node = new Node();
    node.data = data;
    node.left = node.right = null;
    return (node);
}

// Returns maximum value in a given Binary Tree
static float findMax(Node root)
{
    // Base case
    if (root == null)
        return Integer.MIN_VALUE;

    // 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
static float findMin(Node root)
{
    // Base case
    if (root == null)
        return Integer.MAX_VALUE;

    // 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
static float coefRange(Node root)
{
    float max = findMax(root);
    float min = findMin(root);

    return (max - min) / (max + min);
}

// Driver Code
public static void main(String[] args)
{
    // Construct the Binary Tree
    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);

    System.out.print("Coefficient of Range is " + coefRange(root));
}
}

// This code is contributed by PrinciRaj1992

Python3

# Python3 program to find Coefficient of
# Range in a Binary Tree
from sys import maxsize
INT_MIN = -maxsize
INT_MAX = maxsize

# A tree node
class Node:
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

# Returns maximum value in a given Binary Tree
def findMax(root: Node) -> float:

    # Base case
    if root is None:
        return INT_MIN

    # Return maximum of 3 values:
    # 1) Root's data 2) Max in Left Subtree
    # 3) Max in right subtree
    res = root.data
    lres = findMax(root.left)
    rres = findMax(root.right)
    if lres > res:
        res = lres
    if rres > res:
        res = rres

    return res

# Returns minimum value in a given Binary Tree
def findMin(root: Node) -> float:

    # Base case
    if root is None:
        return INT_MAX

    # Return minimum of 3 values:
    # 1) Root's data 2) Min in Left Subtree
    # 3) Min in right subtree
    res = root.data
    lres = findMin(root.left)
    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
def coefRange(root: Node) -> float:
    maxx = findMax(root)
    minn = findMin(root)

    return (maxx - minn) / (maxx + minn)

# Driver Code
if __name__ == "__main__":

    # Construct the Binary Tree
    root = Node(2)
    root.left = Node(7)
    root.right = Node(5)
    root.left.right = Node(6)
    root.left.right.left = Node(1)
    root.left.right.right = Node(11)
    root.right.right = Node(9)
    root.right.right.left = Node(4)

    print("Coefficient of Range is", coefRange(root))

# This code is contributed by
# sanjeev2552

C#

// C# program to find Coefficient of
// Range in a Binary Tree
using System;

class GFG
{

// A tree node
class Node
{
    public float data;
    public Node left, right;
};

// A utility function to create a new node
static Node newNode(float data)
{
    Node node = new Node();
    node.data = data;
    node.left = node.right = null;
    return (node);
}

// Returns maximum value in a given Binary Tree
static float findMax(Node root)
{
    // Base case
    if (root == null)
        return int.MinValue;

    // 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
static float findMin(Node root)
{
    // Base case
    if (root == null)
        return int.MaxValue;

    // 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
static float coefRange(Node root)
{
    float max = findMax(root);
    float min = findMin(root);

    return (max - min) / (max + min);
}

// Driver Code
public static void Main(String[] args)
{
    // Construct the Binary Tree
    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);

    Console.Write("Coefficient of Range is " +
                             coefRange(root));
}
}

// This code is contributed by Rajput-Ji

Javascript

<script>
// javascript program to find Coefficient of
// Range in a Binary Tree
    // A tree node
class Node {
    constructor(val) {
        this.data = val;
        this.left = null;
        this.right = null;
    }
}

    // A utility function to create a new node
    function newNode(data) {
var node = new Node();
        node.data = data;
        node.left = node.right = null;
        return (node);
    }

    // Returns maximum value in a given Binary Tree
    function findMax(root) {
        // Base case
        if (root == null)
            return Number.MIN_VALUE;

        // Return maximum of 3 values:
        // 1) Root's data 2) Max in Left Subtree
        // 3) Max in right subtree
        var res = root.data;
        var lres = findMax(root.left);
        var rres = findMax(root.right);
        if (lres > res)
            res = lres;
        if (rres > res)
            res = rres;

        return res;
    }

    // Returns minimum value in a given Binary Tree
    function findMin(root) {
        // Base case
        if (root == null)
            return Number.MAX_VALUE;

        // Return minimum of 3 values:
        // 1) Root's data 2) Min in Left Subtree
        // 3) Min in right subtree
        var res = root.data;
        var lres = findMin(root.left);
        var 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
    function coefRange(root) {
        var max = findMax(root);
        var min = findMin(root);

        return (max - min) / (max + min);
    }

    // Driver Code

        // Construct the Binary Tree
var 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);

        document.write("Coefficient of Range is " + coefRange(root).toFixed(6));

// This code contributed by umadevi9616
</script>

Output:

Coefficient of Range is 0.833333

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