Sum and Product of maximum and minimum element in Binary Tree
Given a Binary Tree. The task is to find the sum and product of maximum and minimum element in it.
For example, sum of the maximum and minimum element in the following Binary Tree is 10 and the product is 9.
The idea is to traverse the tree and find the maximum and minimum elements in the tree and print their product and sum.
To find the maximum element in the Binary Tree, recursively traverse the tree and return the maximum of below three:
- Current Node’s data.
- Maximum in node’s left subtree.
- Maximum in node’s right subtree.
Similarly, we can find the minimum element in the Binary tree by comparing three values.
Below program illiustrate the above approach:
C++
// CPP program to find sum and product of // maximum and minimum in a Binary Tree #include<bits/stdc++.h> #include<iostream> using namespace std; // A tree node class Node { public: int data; Node *left, *right; /* Constructor that allocates a new node with the given data and NULL left and right pointers. */ Node(int data) { this->data = data; this->left = NULL; this->right = NULL; } }; // Function to return minimum value // in a given Binary Tree int findMin(Node* root) { // Base case if (root == NULL) return INT_MAX; // Return minimum of 3 values: // 1) Root's data 2) Max in Left Subtree // 3) Max in right subtree int res = root->data; int lres = findMin(root->left); int rres = findMin(root->right); if (lres < res) res = lres; if (rres < res) res = rres; return res; } // Function to returns maximum value // in a given Binary Tree int findMax(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 int res = root->data; int lres = findMax(root->left); int rres = findMax(root->right); if (lres > res) res = lres; if (rres > res) res = rres; return res; } // Function to find sum of max and min // elements in the Binary Tree int findSum(int max , int min) { return max + min; } // Function to find product of max and min // elements in the Binary Tree int findProduct(int max, int min) { return max*min; } // Driver Code int main() { // Create Binary Tree Node* NewRoot = NULL; Node* root = new Node(2); root->left = new Node(7); root->right = new Node(5); root->left->right = new Node(6); root->left->right->left = new Node(1); root->left->right->right = new Node(11); root->right->right = new Node(9); root->right->right->left = new Node(4); int max = findMax(root); int min = findMin(root); cout << "Sum of Maximum and Minimum element is " << findSum(max,min); cout << "\nProduct of Maximum and Minimum element is " << findProduct(max,min); return 0; } // This code is contributed by rathbhupendra |
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C
// C program to find sum and product of // maximum and minimum in a Binary Tree #include <limits.h> #include <stdio.h> #include <stdlib.h> // A tree node struct Node { int data; struct Node *left, *right; }; // A utility function to create a new node struct Node* newNode(int data) { struct Node* node = (struct Node*) malloc(sizeof(struct Node)); node->data = data; node->left = node->right = NULL; return (node); } // Function to return minimum value // in a given Binary Tree int findMin(struct Node* root) { // Base case if (root == NULL) return INT_MAX; // Return minimum of 3 values: // 1) Root's data 2) Max in Left Subtree // 3) Max in right subtree int res = root->data; int lres = findMin(root->left); int rres = findMin(root->right); if (lres < res) res = lres; if (rres < res) res = rres; return res; } // Function to returns maximum value // in a given Binary Tree int 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 int res = root->data; int lres = findMax(root->left); int rres = findMax(root->right); if (lres > res) res = lres; if (rres > res) res = rres; return res; } // Function to find sum of max and min // elements in the Binary Tree int findSum(int max , int min) { return max + min; } // Function to find product of max and min // elements in the Binary Tree int findProduct(int max, int min) { return max*min; } // Driver Code int main(void) { // Create Binary Tree struct Node* NewRoot = NULL; 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); int max = findMax(root); int min = findMin(root); printf("Sum of Maximum and Minimum element is %d", findSum(max,min)); printf("\nProduct of Maximum and Minimum element is %d", findProduct(max,min)); return 0; } |
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Java
// JAVA program to find sum and product of // maximum and minimum in a Binary Tree import java.util.*; class GFG { // A tree node static class Node { public int data; Node left, right; /* Constructor that allocates a new node with the given data and null left and right pointers. */ Node(int data) { this.data = data; this.left = null; this.right = null; } }; // Function to return minimum value // in a given Binary Tree static int findMin(Node root) { // Base case if (root == null) return Integer.MAX_VALUE; // Return minimum of 3 values: // 1) Root's data 2) Max in Left Subtree // 3) Max in right subtree int res = root.data; int lres = findMin(root.left); int rres = findMin(root.right); if (lres < res) res = lres; if (rres < res) res = rres; return res; } // Function to returns maximum value // in a given Binary Tree static int 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 int res = root.data; int lres = findMax(root.left); int rres = findMax(root.right); if (lres > res) res = lres; if (rres > res) res = rres; return res; } // Function to find sum of max and min // elements in the Binary Tree static int findSum(int max , int min) { return max + min; } // Function to find product of max and min // elements in the Binary Tree static int findProduct(int max, int min) { return max * min; } // Driver Code public static void main(String[] args) { // Create Binary Tree Node root = new Node(2); root.left = new Node(7); root.right = new Node(5); root.left.right = new Node(6); root.left.right.left = new Node(1); root.left.right.right = new Node(11); root.right.right = new Node(9); root.right.right.left = new Node(4); int max = findMax(root); int min = findMin(root); System.out.print("Sum of Maximum and Minimum element is " + findSum(max, min)); System.out.print("\nProduct of Maximum and Minimum element is " + findProduct(max, min)); } } // This code is contributed by 29AjayKumar |
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Python3
# Python program to find sum and product of # maximum and minimum in a Binary Tree _MIN=-2147483648_MAX=2147483648 # Helper function that allocates a new # node with the given data and None left # and right poers. class newNode: # Constructor to create a new node def __init__(self, data): self.data = data self.left = None self.right = None # Function to return minimum value # in a given Binary Tree def findMin(root): # Base case if (root == None): return _MAX # Return minimum of 3 values: # 1) Root's data 2) Max in Left Subtree # 3) Max 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 returns maximum value # in a given Binary Tree def findMax( root): # Base case if (root == None): return _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 # Function to find sum of max and min # elements in the Binary Tree def findSum( max , min): return max + min # Function to find product of max and min # elements in the Binary Tree def findProduct( max, min): return max*min # Driver Code if __name__ == '__main__': """ Create binary Tree """ 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) max = findMax(root); min = findMin(root); print("Sum of Maximum and " + "Minimum element is ", findSum(max,min)) print("Product of Maximum and" + "Minimum element is", findProduct(max,min)) # This code is contributed # Shubham Singh(SHUBHAMSINGH10) |
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C#
// C# program to find sum and product of // maximum and minimum in a Binary Tree using System; class GFG { // A tree node class Node { public int data; public Node left, right; /* Constructor that allocates a new node with the given data and null left and right pointers. */ public Node(int data) { this.data = data; this.left = null; this.right = null; } }; // Function to return minimum value // in a given Binary Tree static int findMin(Node root) { // Base case if (root == null) return int.MaxValue; // Return minimum of 3 values: // 1) Root's data 2) Max in Left Subtree // 3) Max in right subtree int res = root.data; int lres = findMin(root.left); int rres = findMin(root.right); if (lres < res) res = lres; if (rres < res) res = rres; return res; } // Function to returns maximum value // in a given Binary Tree static int 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 int res = root.data; int lres = findMax(root.left); int rres = findMax(root.right); if (lres > res) res = lres; if (rres > res) res = rres; return res; } // Function to find sum of max and min // elements in the Binary Tree static int findSum(int max , int min) { return max + min; } // Function to find product of max and min // elements in the Binary Tree static int findProduct(int max, int min) { return max * min; } // Driver Code public static void Main(String[] args) { // Create Binary Tree Node root = new Node(2); root.left = new Node(7); root.right = new Node(5); root.left.right = new Node(6); root.left.right.left = new Node(1); root.left.right.right = new Node(11); root.right.right = new Node(9); root.right.right.left = new Node(4); int max = findMax(root); int min = findMin(root); Console.Write("Sum of Maximum and " + "Minimum element is " + findSum(max, min)); Console.Write("\nProduct of Maximum and " + "Minimum element is " + findProduct(max, min)); } } // This code is contributed by Rajput-Ji |
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Output:
Sum of Maximum and Minimum element is 12 Product of Maximum and Minimum element is 11
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