Given two n-ary trees, the task is to check if they are mirror of each other or not. Print “Yes” if they are mirror of each other else “No”.

Examples:

Input : Node = 3, Edges = 2 Edge 1 of first N-ary: 1 2 Edge 2 of first N-ary: 1 3 Edge 1 of second N-ary: 1 2 Edge 2 of second N-ary: 1 3 Output : Yes Input : Node = 3, Edges = 2 Edge 1 of first N-ary: 1 2 Edge 2 of first N-ary: 1 3 Edge 1 of second N-ary: 1 2 Edge 2 of second N-ary: 1 3 Output : No

The idea is to use Queue and Stack to check if given N-ary tree are mirror of each other or not.

Let first n-ary tree be t1 and second n-ary tree is t2. For each node in t1, make stack and push its connected node in it. Now, for each node in t2, make queue and push its connected node in it.

Now, for each corresponding node do following:

While stack and Queue is not empty. a = top element of stack; b = front of stack; if (a != b) return false; pop element from stack and queue.

// C++ program to check if two n-ary trees are // mirror. #include <bits/stdc++.h> using namespace std; // First vector stores all nodes and adjacent of every // node in a stack. // Second vector stores all nodes and adjacent of every // node in a queue. bool mirrorUtil(vector<stack<int> >& tree1, vector<queue<int> >& tree2) { // Traversing each node in tree. for (int i = 1; i < tree1.size(); ++i) { stack<int>& s = tree1[i]; queue<int>& q = tree2[i]; // While stack is not empty && Queue is not empty while (!s.empty() && !q.empty()) { // checking top element of stack and front // of queue. if (s.top() != q.front()) return false; s.pop(); q.pop(); } // If queue or stack is not empty, return false. if (!s.empty() || !q.empty()) return false; } return true; } // Returns true if given two trees are mirrors. // A tree is represented as two arrays to store // all tree edges. void areMirrors(int m, int n, int u1[], int v1[], int u2[], int v2[]) { vector<stack<int> > tree1(m + 1); vector<queue<int> > tree2(m + 1); // Pushing node in the stack of first tree. for (int i = 0; i < n; i++) tree1[u1[i]].push(v1[i]); // Pushing node in the queue of second tree. for (int i = 0; i < n; i++) tree2[u2[i]].push(v2[i]); mirrorUtil(tree1, tree2) ? (cout << "Yes" << endl) : (cout << "No" << endl); } // Driver code int main() { int M = 3, N = 2; int u1[] = { 1, 1 }; int v1[] = { 2, 3 }; int u2[] = { 1, 1 }; int v2[] = { 3, 2 }; areMirrors(M, N, u1, v1, u2, v2); return 0; }

Output:

Yes

Reference: https://practice.geeksforgeeks.org/problems/check-mirror-in-n-ary-tree/0

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