SDE - 1

Ninja is learning the bitwise operations to score well in his class test. He found an interesting question on bitwise XOR. The problem statement is as follows:

An array ‘ARR’ consists of ‘N’ numbers. The task is to find pair having the minimum XOR value.No, need to print the values of the element. Just print the minimum XOR value. Can you help Ninja to solve this problem?

For Example

If the array ‘ARR’ is [13,5,11,1], the answer will be 4, corresponding to the XOR value of 1 and 5.

Ninja has a 'GRID' of size 'R' X 'C'. Each cell of the grid contains some chocolates. Ninja has two friends Alice and Bob, and he wants to collect as many chocolates as possible with the help of his friends.

Initially, Alice is in the top-left position i.e. (0, 0), and Bob is in the top-right place i.e. (0, ‘C’ - 1) in the grid. Each of them can move from their current cell to the cells just below them. When anyone passes from any cell, he will pick all chocolates in it, and then the number of chocolates in that cell will become zero. If both stay in the same cell, only one of them will pick the chocolates in it.

If Alice or Bob is at (i, j) then they can move to (i + 1, j), (i + 1, j - 1) or (i + 1, j + 1). They will always stay inside the ‘GRID’.

Your task is to find the maximum number of chocolates Ninja can collect with the help of his friends by following the above rules.

Example:

Input: ‘R’ = 3, ‘C’ = 4
       ‘GRID’ = [[2, 3, 1, 2], [3, 4, 2, 2], [5, 6, 3, 5]]
Output: 21

Initially Alice is at the position (0,0) he can follow the path (0,0) -> (1,1) -> (2,1) and will collect 2 + 4 + 6 = 12 chocolates.

Initially Bob is at the position (0, 3) and he can follow the path (0, 3) -> (1,3) -> (2, 3) and will colllect 2 + 2 + 5 = 9 chocolates.

Hence the total number of chocolates collected will be 12 + 9 = 21. there is no other possible way to collect a greater number of chocolates than 21.

You are given an integer ‘N’. You need to find an array of size 2*N that satisfies the following two conditions.

1. All numbers from 1 to N should appear exactly twice in the array.

2. The distance between the second occurrence and the first occurrence of any number should exactly be equal to the value of that number.

The distance between two numbers at indices ‘i’ and ‘j’ is defined as (j-i-1) where i < j.

If no such array exists, then you should return an empty array.

For example :

For N = 3 one valid array is [3,1,2,1,3,2].

You are given a tree(root 0) with N vertex having N - 1 edges. You are also given an array ‘QUERY’ of size ‘Q’, where each query consists of an integer that denotes a node. You have to print the xor of all the values of nodes in the sub-tree of the given node.

Note:

Here XOR denotes the bitwise operator (^).

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’.

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