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.


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 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 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;
        printf("Memory allocation failed!");

// 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,
    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);
        printf("Mirror of Node %d is NULL!\n", target);


# 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__':


Mirror of node 4 is node 6

Time Complexity: O(n)

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