# Program to print the longest leaf to leaf path in a Binary tree using C++

In this tutorial, we will be discussing a program to print the longest path that exists from a leaf node to another leaf node in a given binary tree.

In other words, we have to print all the nodes that appear in the diameter of the Binary tree. Here, diameter (or width) for a particular binary tree is defined as the number of nodes in the longest path from one end node to another.

To solve this, we calculate the diameter of the binary tree using the height function. Then we find the longest path in the left portion of the binary tree and the right portion. Then finally to print the nodes in the diameter we print the left portion nodes, the root node and then the right portion nodes.

## Example

#include <bits/stdc++.h>
using namespace std;
struct Node {
int data;
Node *left, *right;
};
struct Node* create_node(int data){
struct Node* node = new Node;
node->data = data;
node->left = node->right = NULL;
return (node);
}
int tree_height(Node* root, int& ans, Node*(&k), int& lh, int& rh, int& f){
if (root == NULL)
return 0;
int left_tree_height = tree_height(root->left, ans, k, lh, rh, f);
int right_tree_height = tree_height(root->right, ans, k, lh, rh, f);
if (ans < 1 + left_tree_height + right_tree_height){
ans = 1 + left_tree_height + right_tree_height;
k = root;
lh = left_tree_height;
rh = right_tree_height;
}
return 1 + max(left_tree_height, right_tree_height);
}
void print_roottonode(int ints[], int len, int f){
int i;
if (f == 0){
for (i = len - 1; i >= 0; i--) {
printf("%d ", ints[i]);
}
}
else if (f == 1) {
for (i = 0; i < len; i++) {
printf("%d ", ints[i]);
}
}
}
void print_pathr(Node* node, int path[], int pathLen, int max, int& f){
if (node == NULL)
return;
path[pathLen] = node->data;
pathLen++;
if (node->left == NULL && node->right == NULL) {
if (pathLen == max && (f == 0 || f == 1)) {
print_roottonode(path, pathLen, f);
f = 2;
}
}
else {
print_pathr(node->left, path, pathLen, max, f);
print_pathr(node->right, path, pathLen, max, f);
}
}
void calc_diameter(Node* root){
if (root == NULL)
return;
int ans = INT_MIN, lh = 0, rh = 0;
int f = 0;
Node* k;
int tree_height_of_tree = tree_height(root, ans, k, lh, rh, f);
int lPath, pathlen = 0;
print_pathr(k->left, lPath, pathlen, lh, f);
printf("%d ", k->data);
int rPath;
f = 1;
print_pathr(k->right, rPath, pathlen, rh, f);
}
int main(){
struct Node* root = create_node(12);
root->left = create_node(22);
root->right = create_node(33);
root->left->left = create_node(45);
root->left->right = create_node(57);
root->left->right->left = create_node(26);
root->left->right->right = create_node(76);
root->left->left->right = create_node(84);
root->left->left->right->left = create_node(97);
calc_diameter(root);
return 0;
}

## Output

97 84 45 22 57 26