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.

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 inmirrorvariable. 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 andmirroris none, recur internal nodes.

## C

// C program to find the mirror Node in Binary tree #include <stdio.h> #include <stdlib.h> /* 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\n", target, mirror); else printf("Mirror of Node %d is NULL!\n", target); }

## Python

# 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()

Output:

Mirror of node 4 is node 6

**Time Complexity:**

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