SDE - Intern

You are given three positive integers: L, R, and G.

Your task is to count the number of ordered pairs (x, y) that satisfy two conditions:

1) Both x and y must be within the inclusive range [L, R].

2) The Greatest Common Divisor (GCD) of x and y must be exactly G.

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Design and implement a data structure for Least Recently Used (LRU) cache to support the following operations:

1. get(key) - Return the value of the key if the key exists in the cache, otherwise return -1.

2. put(key, value), Insert the value in the cache if the key is not already present or update the value of the given key if the key is already present. When the cache reaches its capacity, it should invalidate the least recently used item before inserting the new item.

You will be given ‘Q’ queries. Each query will belong to one of these two types:

Type 0: for get(key) operation.
Type 1: for put(key, value) operation.

Note :

1. The cache is initialized with a capacity (the maximum number of unique keys it can hold at a time).

2. Access to an item or key is defined as a get or a put operation on the key. The least recently used key is the one with the oldest access time.

A number is given which is greater than 10^18 so you can't store this number in any data type. Find the last digit of its square.

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You are given a 'Binary Tree'.

Return the bottom view of the binary tree.

Note :

1. A node will be in the bottom-view if it is the bottom-most node at its horizontal distance from the root. 

2. The horizontal distance of the root from itself is 0. The horizontal distance of the right child of the root node is 1 and the horizontal distance of the left child of the root node is -1. 

3. The horizontal distance of node 'n' from root = horizontal distance of its parent from root + 1, if node 'n' is the right child of its parent.

4. The horizontal distance of node 'n' from root = horizontal distance of its parent from the root - 1, if node 'n' is the left child of its parent.

5. If more than one node is at the same horizontal distance and is the bottom-most node for that horizontal distance, including the one which is more towards the right.

Example:

Input: Consider the given Binary Tree:

Output: 4 2 6 3 7

Explanation:
Below is the bottom view of the binary tree.

1 is the root node, so its horizontal distance = 0.
Since 2 lies to the left of 0, its horizontal distance = 0-1= -1
3 lies to the right of 0, its horizontal distance = 0+1 = 1
Similarly, horizontal distance of 4 = Horizontal distance of 2 - 1= -1-1=-2
Horizontal distance of 5 = Horizontal distance of 2 + 1=  -1+1 = 0
Horizontal distance of 6 = 1-1 =0
Horizontal distance of 7 = 1+1 = 2

The bottom-most node at a horizontal distance of -2 is 4.
The bottom-most node at a horizontal distance of -1 is 2.
The bottom-most node at a horizontal distance of 0 is 5 and 6. However, 6 is more towards the right, so 6 is included.
The bottom-most node at a horizontal distance of 1 is 3.
The bottom-most node at a horizontal distance of 2 is 7.

Hence, the bottom view would be 4 2 6 3 7

You are given a Binary Tree.

Return the length of the diameter of the tree.

Note :

The diameter of a binary tree is the length of the longest path between any two end nodes in a tree.

The number of edges between two nodes represents the length of the path between them.

Example :

Input: Consider the given binary tree:

Output: 6

Explanation:
Nodes in the diameter are highlighted. The length of the diameter, i.e., the path length, is 6.

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Given two strings, 'S' and 'T' with lengths 'M' and 'N', find the length of the 'Longest Common Subsequence'.

For a string 'str'(per se) of length K, the subsequences are the strings containing characters in the same relative order as they are present in 'str,' but not necessarily contiguous. Subsequences contain all the strings of length varying from 0 to K.

Example :

Subsequences of string "abc" are:  ""(empty string), a, b, c, ab, bc, ac, abc.

Given a string input of length n, find the length of the longest substring without repeating characters i.e return a substring that does not have any repeating characters.

Substring is the continuous sub-part of the string formed by removing zero or more characters from both ends.