# Find mirror of a given node in Binary tree

Given a Binary tree, the problem is to find mirror of a given node. The mirror of a node is a node which exist at the mirror position of node in opposite subtree at the root.

Examples:

```In above tree-
Node 2 and 3 are mirror nodes
Node 4 and 6 are mirror nodes.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

We can have a recursive solution for finding mirror nodes. The algorithm is following –

```1) Start from the root of the tree and recur
nodes from both subtree simultaneously
using two pointers for left and right nodes.
2) First recur all the external nodes and
store returned value in mirror variable.
3) If current node value is equal to target node,
return the value of opposite pointer else
repeat step 2.
4) If no external node is left and mirror is
none, recur internal nodes.
```

## C

 `// C program to find the mirror Node in Binary tree ` `#include ` `#include ` ` `  `/* A binary tree Node has data, pointer to left child ` `  ``and a pointer to right child */` `struct` `Node ` `{ ` `    ``int` `key; ` `    ``struct` `Node* left, *right; ` `}; ` ` `  `// create new Node and initialize it ` `struct` `Node* newNode(``int` `key) ` `{ ` `    ``struct` `Node* n = (``struct` `Node*) ` `                     ``malloc``(``sizeof``(``struct` `Node*)); ` `    ``if` `(n != NULL) ` `    ``{ ` `        ``n->key = key; ` `        ``n->left = NULL; ` `        ``n->right = NULL; ` `        ``return` `n; ` `    ``} ` `    ``else` `    ``{ ` `        ``printf``(``"Memory allocation failed!"``); ` `        ``exit``(1); ` `    ``} ` `} ` ` `  `// recursive function to find mirror of Node ` `int` `findMirrorRec(``int` `target, ``struct` `Node* left, ` `                              ``struct` `Node* right) ` `{ ` `    ``/* if any of the Node is none then Node itself ` `       ``and decendent have no mirror, so return ` `       ``none, no need to further explore! */` `    ``if` `(left==NULL || right==NULL) ` `        ``return` `0; ` ` `  `    ``/* if left Node is target Node, then return ` `       ``right's key (that is mirror) and vice ` `       ``versa */` `    ``if` `(left->key == target) ` `        ``return` `right->key; ` ` `  `    ``if` `(right->key == target) ` `        ``return` `left->key; ` ` `  `    ``// first recur external Nodes ` `    ``int` `mirror_val = findMirrorRec(target, ` `                                     ``left->left, ` `                                     ``right->right); ` `    ``if` `(mirror_val) ` `        ``return` `mirror_val; ` ` `  `    ``// if no mirror found, recur internal Nodes ` `    ``findMirrorRec(target, left->right, right->left); ` `} ` ` `  `// interface for mirror search ` `int` `findMirror(``struct` `Node* root, ``int` `target) ` `{ ` `    ``if` `(root == NULL) ` `        ``return` `0; ` `    ``if` `(root->key == target) ` `        ``return` `target; ` `    ``return` `findMirrorRec(target, root->left, root->right); ` `} ` ` `  `// Driver ` `int` `main() ` `{ ` `    ``struct` `Node* root           = newNode(1); ` `    ``root-> left                 = newNode(2); ` `    ``root->left->left            = newNode(4); ` `    ``root->left->left->right     = newNode(7); ` `    ``root->right                 = newNode(3); ` `    ``root->right->left           = newNode(5); ` `    ``root->right->right          = newNode(6); ` `    ``root->right->left->left     = newNode(8); ` `    ``root->right->left->right    = newNode(9); ` ` `  `    ``// target Node whose mirror have to be searched ` `    ``int` `target = root->left->left->key; ` ` `  `    ``int` `mirror = findMirror(root, target); ` ` `  `    ``if` `(mirror) ` `        ``printf``(````"Mirror of Node %d is Node %d "````, ` `                                    ``target, mirror); ` `    ``else` `        ``printf``(````"Mirror of Node %d is NULL! "````, target); ` `} `

## Java

 `// Java program to find the mirror Node in Binary tree  ` `class` `GfG { ` ` `  `/* A binary tree Node has data, pointer to left child  ` `and a pointer to right child */` `static` `class` `Node  ` `{  ` `    ``int` `key;  ` `    ``Node left, right;  ` `} ` ` `  `// create new Node and initialize it  ` `static` `Node newNode(``int` `key)  ` `{  ` `    ``Node n = ``new` `Node();  ` `      `  `        ``n.key = key;  ` `        ``n.left = ``null``;  ` `        ``n.right = ``null``;  ` `        ``return` `n;  ` `}  ` ` `  `// recursive function to find mirror of Node  ` `static` `int` `findMirrorRec(``int` `target, Node left, Node right)  ` `{  ` `    ``/* if any of the Node is none then Node itself  ` `    ``and decendent have no mirror, so return  ` `    ``none, no need to further explore! */` `    ``if` `(left==``null` `|| right==``null``)  ` `        ``return` `0``;  ` ` `  `    ``/* if left Node is target Node, then return  ` `    ``right's key (that is mirror) and vice  ` `    ``versa */` `    ``if` `(left.key == target)  ` `        ``return` `right.key;  ` ` `  `    ``if` `(right.key == target)  ` `        ``return` `left.key;  ` ` `  `    ``// first recur external Nodes  ` `    ``int` `mirror_val = findMirrorRec(target, left.left, right.right);  ` `    ``if` `(mirror_val != ``0``)  ` `        ``return` `mirror_val;  ` ` `  `    ``// if no mirror found, recur internal Nodes  ` `    ``return` `findMirrorRec(target, left.right, right.left);  ` `}  ` ` `  `// interface for mirror search  ` `static` `int` `findMirror(Node root, ``int` `target)  ` `{  ` `    ``if` `(root == ``null``)  ` `        ``return` `0``;  ` `    ``if` `(root.key == target)  ` `        ``return` `target;  ` `    ``return` `findMirrorRec(target, root.left, root.right);  ` `}  ` ` `  `// Driver  ` `public` `static` `void` `main(String[] args)  ` `{  ` `    ``Node root         = newNode(``1``);  ` `    ``root.left                 = newNode(``2``);  ` `    ``root.left.left         = newNode(``4``);  ` `    ``root.left.left.right     = newNode(``7``);  ` `    ``root.right                 = newNode(``3``);  ` `    ``root.right.left         = newNode(``5``);  ` `    ``root.right.right         = newNode(``6``);  ` `    ``root.right.left.left     = newNode(``8``);  ` `    ``root.right.left.right = newNode(``9``);  ` ` `  `    ``// target Node whose mirror have to be searched  ` `    ``int` `target = root.left.left.key;  ` ` `  `    ``int` `mirror = findMirror(root, target);  ` ` `  `    ``if` `(mirror != ``0``)  ` `        ``System.out.println(``"Mirror of Node "` `+ target + ``" is Node "` `+ mirror); ` `    ``else` `        ``System.out.println(``"Mirror of Node "` `+ target + ``" is null "``); ` `}  ` `} `

## Python3

 `# Python3 program to find the mirror node in ` `# Binary tree ` ` `  `class` `Node: ` `    ``'''A binary tree node has data, reference to left child ` `         ``and a reference to right child '''` ` `  `    ``def` `__init__(``self``, key, lchild``=``None``, rchild``=``None``): ` `        ``self``.key ``=` `key ` `        ``self``.lchild ``=` `None` `        ``self``.rchild ``=` `None` ` `  ` `  `# recursive function to find mirror ` `def` `findMirrorRec(target, left, right): ` ` `  `    ``# If any of the node is none then node itself ` `    ``# and decendent have no mirror, so return ` `    ``# none, no need to further explore! ` `    ``if` `left ``=``=` `None` `or` `right ``=``=` `None``: ` `        ``return` `None` ` `  `    ``# if left node is target node, then return ` `    ``# right's key (that is mirror) and vice versa ` `    ``if` `left.key ``=``=` `target: ` `        ``return` `right.key ` `    ``if` `right.key ``=``=` `target: ` `        ``return` `left.key ` ` `  `    ``# first recur external nodes ` `    ``mirror_val ``=` `findMirrorRec(target, left.lchild, right.rchild) ` `    ``if` `mirror_val !``=` `None``: ` `        ``return` `mirror_val ` ` `  `    ``# if no mirror found, recur internal nodes ` `    ``findMirrorRec(target, left.rchild, right.lchild) ` ` `  `# interface for mirror search ` `def` `findMirror(root, target): ` `    ``if` `root ``=``=` `None``: ` `        ``return` `None` ` `  `    ``if` `root.key ``=``=` `target: ` `        ``return` `target ` ` `  `    ``return` `findMirrorRec(target, root.lchild, root.rchild) ` ` `  `# Driver ` `def` `main(): ` `    ``root ``=` `Node(``1``) ` `    ``n1 ``=` `Node(``2``) ` `    ``n2 ``=` `Node(``3``) ` `    ``root.lchild ``=` `n1 ` `    ``root.rchild ``=` `n2 ` `    ``n3 ``=` `Node(``4``) ` `    ``n4 ``=` `Node(``5``) ` `    ``n5 ``=` `Node(``6``) ` `    ``n1.lchild ``=` `n3 ` `    ``n2.lchild ``=` `n4 ` `    ``n2.rchild ``=` `n5 ` `    ``n6 ``=` `Node(``7``) ` `    ``n7 ``=` `Node(``8``) ` `    ``n8 ``=` `Node(``9``) ` `    ``n3.rchild ``=` `n6 ` `    ``n4.lchild ``=` `n7 ` `    ``n4.rchild ``=` `n8 ` ` `  `    ``# target node whose mirror have to be searched ` `    ``target ``=` `n3.key ` ` `  `    ``mirror ``=` `findMirror(root, target) ` `    ``print``(``"Mirror of node {} is node {}"``.``format``(target, mirror)) ` ` `  `if` `__name__ ``=``=` `'__main__'``: ` `    ``main() `

## C#

 `// C# program to find the  ` `// mirror Node in Binary tree ` `using` `System; ` ` `  `class` `GfG  ` `{ ` ` `  `    ``/* A binary tree Node has data,  ` `        ``pointer to left child and a ` `        ``pointer to right child */` `    ``class` `Node  ` `    ``{  ` `        ``public` `int` `key;  ` `        ``public` `Node left, right;  ` `    ``} ` ` `  `    ``// create new Node and initialize it  ` `    ``static` `Node newNode(``int` `key)  ` `    ``{  ` `        ``Node n = ``new` `Node();  ` ` `  `            ``n.key = key;  ` `            ``n.left = ``null``;  ` `            ``n.right = ``null``;  ` `            ``return` `n;  ` `    ``}  ` ` `  `    ``// recursive function to find mirror of Node  ` `    ``static` `int` `findMirrorRec(``int` `target, Node left, ` `                                        ``Node right)  ` `    ``{  ` `        ``/* if any of the Node is none then Node itself  ` `        ``and decendent have no mirror, so return  ` `        ``none, no need to further explore! */` `        ``if` `(left==``null` `|| right==``null``)  ` `            ``return` `0;  ` ` `  `        ``/* if left Node is target Node, then return  ` `        ``right's key (that is mirror) and vice  ` `        ``versa */` `        ``if` `(left.key == target)  ` `            ``return` `right.key;  ` ` `  `        ``if` `(right.key == target)  ` `            ``return` `left.key;  ` ` `  `        ``// first recur external Nodes  ` `        ``int` `mirror_val = findMirrorRec(target,  ` `                        ``left.left, right.right);  ` `        ``if` `(mirror_val != 0)  ` `            ``return` `mirror_val;  ` ` `  `        ``// if no mirror found, recur internal Nodes  ` `        ``return` `findMirrorRec(target,  ` `                ``left.right, right.left);  ` `    ``}  ` ` `  `    ``// interface for mirror search  ` `    ``static` `int` `findMirror(Node root, ``int` `target)  ` `    ``{  ` `        ``if` `(root == ``null``)  ` `            ``return` `0;  ` `        ``if` `(root.key == target)  ` `            ``return` `target;  ` `        ``return` `findMirrorRec(target, ` `                ``root.left, root.right);  ` `    ``}  ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main(String[] args)  ` `    ``{  ` `        ``Node root = newNode(1);  ` `        ``root.left = newNode(2);  ` `        ``root.left.left = newNode(4);  ` `        ``root.left.left.right = newNode(7);  ` `        ``root.right = newNode(3);  ` `        ``root.right.left = newNode(5);  ` `        ``root.right.right = newNode(6);  ` `        ``root.right.left.left = newNode(8);  ` `        ``root.right.left.right = newNode(9);  ` ` `  `        ``// target Node whose mirror have to be searched  ` `        ``int` `target = root.left.left.key;  ` ` `  `        ``int` `mirror = findMirror(root, target);  ` ` `  `        ``if` `(mirror != 0)  ` `            ``Console.WriteLine(``"Mirror of Node "` `+  ` `                                ``target + ``" is Node "` `+ ` `                                            ``mirror); ` `        ``else` `            ``Console.WriteLine(``"Mirror of Node "` `+ target + ` `                                            ``" is null "``); ` `    ``}  ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```Mirror of node 4 is node 6
```

Time Complexity:

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