SDE - 1

You are given an integer ‘N’, which denotes there are ‘N’ friends. You are supposed to form some pairs them satisfying the following conditions:

1. Each friend can be paired with some other friend or remain single.

2. Each friend can be a part of at most one pair.

You are supposed to find the total number of ways in which the pairing can be done satisfying both conditions. Since the number of ways can be quite large, you should find the answer modulo 1000000007(10^9+7).

Note:

1. Return the final answer by doing a mod with 10^9 + 7.
2. Pairs {A, B} and {B, A} are considered the same.

Given a binary tree, return the vertical order traversal of the values of the nodes of the given tree.

For each node at position (X, Y), (X-1, Y-1) will be its left child position while (X+1, Y-1) will be the right child position.

Running a vertical line from X = -infinity to X = +infinity, now whenever this vertical line touches some nodes, we need to add those values of the nodes in order starting from top to bottom with the decreasing ‘Y’ coordinates.

Note:

If two nodes have the same position, then the value of the node that is added first will be the value that is on the left side.

For example:

For the binary tree in the image below.

The vertical order traversal will be {2, 7, 5, 2, 6, 5, 11, 4, 9}.

You are given two integers, ‘dividend’ and ‘divisor’.

You are required to divide the integers without using multiplication, division, and modular operators.

Your task is to return the quotient after dividing ‘dividend’ by ‘divisor’.

Note :

In cases where the dividend is not perfectly divisible by the divisor, you are required to return the integer value of the quotient which is closer to zero.

For example - If the answer is '8.34', we return the integer part, i.e., '8'. Also, If the answer is '-2.67', we return the integer part, i.e., '-2'.

Assume we're dealing with a system that can only store integers in the 32-bit signed integer range: [2^31, 2^31-1]. If the quotient is higher than 2^31 - 1, return 2^31 - 1; if it is less than -2^31, return -2^31. 

For example :

If the answer is ‘9.333’, then return ‘9’, or if the answer is ‘-8.123’, then return ‘-8’.