The best programs are written so that computing machines can perform them quickly and so that human beings can understand them clearly. A programmer is ideally an essayist who works with traditional aesthetic and literary forms as
well as mathematical concepts, to communicate the way that an algorithm works and to convince a reader that the results will be correct. Donald E. Knuth

Tree

Problem :-
Given a Binary Tree, create another tree which is a mirror image of the given tree.
Following diagram shows a Binary Tree and its mirror image.

level of node in a tree

Solution :-
Suppose the root node is ( X ) . We will construct a new root node ( Y ) . Then Y -> left = right subtree of X and Y -> right = left subtree of X . We will follow this procedure for all other nodes of the original tree recursively. See the implementation below.

#include<iostream>
using namespace std;

typedef struct tree_node {
   int value;
   struct tree_node *left, *right;
}node;

// create a new node
node *getNewNode(int value) {
   node *new_node = new node;
   new_node->value = value;
   new_node->left = NULL;
   new_node->right = NULL;
   return new_node;
}

// create the tree
node *createTree() {
   node *root = getNewNode(31);
   root->left = getNewNode(16);
   root->right = getNewNode(45);
   root->left->left = getNewNode(7);
   root->left->right = getNewNode(24);
   root->left->right->left = getNewNode(19);
   root->left->right->right = getNewNode(29);
   return root;
}

// Inorder traversal of a tree
void inorderTraversal(node *ptr) {
   if(ptr == NULL)
      return;
   else {
      inorderTraversal(ptr->left);
      cout<<ptr->value<<"\t";
      inorderTraversal(ptr->right);
   }
}

// create mirror tree 
node* mirror(node* root) {
   node* m_root = NULL;
   if(!root) return NULL;
   m_root = getNewNode(root->value);
   m_root->left = mirror(root->right);
   m_root->right = mirror(root->left);
   return m_root;
}

// main
int main() {
   node *root = createTree();
   cout<<"\n Inorder traversal before conversion ";
   inorderTraversal(root);
   node *m_root = mirror(root);
   cout<<"\n Inorder traversal after conversion ";
   inorderTraversal(m_root);
   cout<<endl;
   return 0;
}

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All problems on Trees
* Implement the inorder , preorder and postorder traversal mechanisms of a tree
* Implement an algorithm to insert a node in a Binary Search Tree ( BST )
* Implement an algorithm to find the height of a Binary Tree
* Implement an algorithm to get the level of a node in a Binary Tree assuming root node to be at level 1
* Get the root to leaf path in a Binary Tree such that the sum of the node values in that path is minimum among all possible root to leaf paths
* Print all the ancestors of a given node in a Binary Tree
* Replace all the node values with the sum of the node values of ancestral nodes in a Binary Tree
* Check if the given tree is a sum tree i.e value at each node is equal to the value of all elements in its left subtree and right subtree
* Given a Binary Tree, create another tree which is a mirror image of the given tree
* Construct a tree, given its inorder and preorder traversals
* Find the Least Common Ancestor ( LCA ) of two nodes in a Binary Search Tree
* Find the Least Common Ancestor ( LCA ) of two nodes in a Binary Tree
* Compute the Diameter of a given Binary Tree
* Check if a given tree is a Binary Search Tree ( BST )