Merge pull request #824 from swapnilnarad2000/swapnilnarad2000

added diameter of Tree implementation in C++

Program's_Contributed_By_Contributors/C++ Programs/DiameterOfTree.cpp

@@ -0,0 +1,81 @@
+// Diameter of a Binary Tree
+// The diameter of a tree (sometimes called the width) is the number of nodes on the longest path between two end nodes. 
+// Recursive optimized C program to find the diameter of a
+// Binary Tree
+//with helper comments :)
+#include <bits/stdc++.h>
+using namespace std;
+
+struct node {
+	int data;
+	struct node *left, *right;
+};
+
+struct node* newNode(int data);
+
+int max(int a, int b) { return (a > b) ? a : b; }
+
+int height(struct node* node);
+
+int diameter(struct node* tree)
+{
+	// base case where tree is empty
+	if (tree == NULL)
+		return 0;
+
+	// get the height of left and right sub-trees
+	int lheight = height(tree->left);
+	int rheight = height(tree->right);
+
+	// get the diameter of left and right sub-trees
+	int ldiameter = diameter(tree->left);
+	int rdiameter = diameter(tree->right);
+
+	// Return max of following three
+	// 1) Diameter of left subtree
+	// 2) Diameter of right subtree
+	// 3) Height of left subtree + height of right subtree + 1
+	return max(lheight + rheight + 1,
+			max(ldiameter, rdiameter));
+}
+
+// UTILITY FUNCTIONS TO TEST diameter() FUNCTION
+
+// The function Compute the "height" of a tree. Height is
+// the number f nodes along the longest path from the root
+// node down to the farthest leaf node.
+int height(struct node* node)
+{
+	// base case tree is empty
+	if (node == NULL)
+		return 0;
+
+	// If tree is not empty then height = 1 + max of left
+	// height and right heights
+	return 1 + max(height(node->left), height(node->right));
+}
+
+
+struct node* newNode(int data)
+{
+	struct node* node
+		= (struct node*)malloc(sizeof(struct node));
+	node->data = data;
+	node->left = NULL;
+	node->right = NULL;
+
+	return (node);
+}
+
+int main(){
+	struct node* root = newNode(1);
+	root->left = newNode(2);
+	root->right = newNode(3);
+	root->left->left = newNode(4);
+	root->left->right = newNode(5);
+
+	cout << "Diameter of the given binary tree is " <<
+		diameter(root);
+
+	return 0;
+}