SDE - 1

You have been given a Binary Tree of distinct integers and two nodes ‘X’ and ‘Y’. You are supposed to return the LCA (Lowest Common Ancestor) of ‘X’ and ‘Y’.

The LCA of ‘X’ and ‘Y’ in the binary tree is the shared ancestor of ‘X’ and ‘Y’ that is located farthest from the root.

Note :

You may assume that given ‘X’ and ‘Y’ definitely exist in the given binary tree.

For example :

For the given binary tree

LCA of ‘X’ and ‘Y’ is highlighted in yellow colour.

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.

Given two sorted arrays 'a' and 'b' of size 'n' and 'm' respectively.

Find the median of the two sorted arrays.

Median is defined as the middle value of a sorted list of numbers. In case the length of list is even, median is the average of the two middle elements.

The expected time complexity is O(min(logn, logm)), where 'n' and 'm' are the sizes of arrays 'a' and 'b', respectively, and the expected space complexity is O(1).

Example:

Input: 'a' = [2, 4, 6] and 'b' = [1, 3, 5]

Output: 3.5

Explanation: The array after merging 'a' and 'b' will be { 1, 2, 3, 4, 5, 6 }. Here two medians are 3 and 4. So the median will be the average of 3 and 4, which is 3.5.

After years of research, Ninja is finally able to invent the time machine, and now he is back to the good old days when T9 keypads were being used in mobile phones.

Being a curious person, Ninja wants to find out all possible strings that can be formed by pressing the keys of the phone.

Formally, you are given a string S, that consists of digits from 2-9 (both inclusive), your task is to find out all the possible strings that can be formed from the input string by mapping the digits to the letters as in a T9 keypad. Then, print the strings in a lexicographically sorted order.

For Example:

If S = “34”, then all the possible letters that can be formed from string S are {“dg”, “dh”, “di”, “eg”, “eh”, “ei”, “fg”, “fh”, “fi”}.