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.
- Node’s data.
- Maximum in node’s left subtree.
- 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)
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