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While learning DSA, Ninja found two N-ary trees and wants to check whether they are mirror images of each other or not. But, he can’t find a suitable method to check the same. Can you help Ninja to solve this problem?

You are given two N-ary trees, ‘TREEA’ and ‘TREEB’ having ‘N’ vertices labeled from 0 to ‘N’-1, and both the trees are rooted at node 0. Your task is to find whether the trees are mirror images of each other or not. Edges of the tree are in order from left to right.

For Example:

For the given example below, the trees are mirror images of each other.

You are given an array 'nums' consisting of first N positive integers. But from the N integers, one of the integers occurs twice in the array, and one of the integers is missing. You need to determine the repeating and the missing integer.

Example:

Let the array be [1, 2, 3, 4, 4, 5]. In the given array ‘4’ occurs twice and the number ‘6’ is missing.

You are given a sequence of only digits in the form of a string 'DIGIT_PATTERN', your task is to find the first repeating digit. If no digit is repeating you should return -1.

Example:

Given string of digits is 123456325. Now starting from the left, the first digit which is repeating is 3 as till 2nd 3 every digit is encountered 1st time and thus our answer for this input will be 3.

Given a sequence of numbers ‘ARR’. Your task is to return a sorted sequence of ‘ARR’ in non-descending order with help of the merge sort algorithm.

Example :

Merge Sort Algorithm -

Merge sort is a Divide and Conquer based Algorithm. It divides the input array into two-parts, until the size of the input array is not ‘1’. In the return part, it will merge two sorted arrays a return a whole merged sorted array.

The above illustrates shows how merge sort works.

Note :

It is compulsory to use the ‘Merge Sort’ algorithm.

You are given an array 'ARR' of 'N' positive integers. You need to find the minimum number of operations needed to make all elements of the array equal. You can perform addition, multiplication, subtraction or division with any element on an array element.

Addition, Subtraction, Multiplication or Division on any element of the array will be considered as a single operation.

Example:

If the given array is [1,2,3] then the answer would be 2. One of the ways to make all the elements of the given array equal is by adding 1 to the array element with value 1 and subtracting 1 from the array element with value 3. So that final array would become [2,2,2]. 

Given an adjacency list representation of a directed graph with ‘n’ vertices and ‘m’ edges. Your task is to return a list consisting of Breadth-First Traversal (BFS) starting from vertex 0.

In this traversal, one can move from vertex 'u' to vertex 'v' only if there is an edge from 'u' to 'v'. The BFS traversal should include all nodes directly or indirectly connected to vertex 0.

Note:

The traversal should proceed from left to right according to the input adjacency list.

Example:

Adjacency list: { {1,2,3},{4}, {5}, {},{},{}}

The interpretation of this adjacency list is as follows:
Vertex 0 has directed edges towards vertices 1, 2, and 3.
Vertex 1 has a directed edge towards vertex 4.
Vertex 2 has a directed edge towards vertex 5.
Vertices 3, 4, and 5 have no outgoing edges.

We can also see this in the diagram below.

BFS traversal: 0 1 2 3 4 5