SDE - 1

You are given a positive integer 'N'. You have to generate all possible sequences of balanced parentheses using 'N' pairs of parentheses.

A sequence of brackets is called balanced if one can turn it into a valid math expression by adding characters ‘+’ and ‘1’. For example, sequences ‘(())()’, ‘()’ and ‘(()(()))’ are balanced, while ‘)(‘, ‘(()’ and ‘(()))(‘ are not.

For example :

For N = 1, there is only one sequence of balanced parentheses,  ‘()’.

For N = 2, all sequences of balanced parentheses are ‘()()’, ‘(())’.

Ninja has created his own encryption technique to encrypt a number. He makes use of the logic behind factorial. In a factorial, we multiply the number by its previous number and so on but if we want to encrypt a number we don’t multiply in every step like in the case of factorial but multiply, divide, add and subtract and repeat in the same order.

So your task is to find the encrypted form of a number using the ninja encryption technique and you were being provided with the number.

You are given a string 'S' containing only digits. Your task is to find all possible IP addresses that can be obtained from string 'S' in lexicographical order.

Note:

A valid IP address consists of exactly four integers, each integer is between 0 and 255 separated by single dots, and cannot have leading zeros except in the case of zero itself.

For example:

The following are valid IP addresses:
0.1.24.255
18.5.244.1

Following are invalid IP addresses:
0.01.24.255  (as  01  contains one leading zero).
18.312.244.1 (as 312 not lies between 0 and 255).

Aahad and Harshit always have fun by solving problems. Harshit took a sorted array consisting of distinct integers and rotated it clockwise by an unknown amount. For example, he took a sorted array = [1, 2, 3, 4, 5] and if he rotates it by 2, then the array becomes: [4, 5, 1, 2, 3].

After rotating a sorted array, Aahad needs to answer Q queries asked by Harshit, each of them is described by one integer Q[i]. which Harshit wanted him to search in the array. For each query, if he found it, he had to shout the index of the number, otherwise, he had to shout -1.

For each query, you have to complete the given method where 'key' denotes Q[i]. If the key exists in the array, return the index of the 'key', otherwise, return -1.

Note:

Can you solve each query in O(logN) ?

You are given an integer ‘N’. Your task is to find all palindromic numbers from 1 to ‘N’.

Palindromic integers are those integers that read the same backward or forwards.

Note:

Order of numbers should be in the non-decreasing matter.

For example:

You are given ‘N’ as 12, so the output should be [1, 2, 3, 4, 5, 6, 7, 8, 9, 11], as all single-digit numbers are palindromic, and 11 is also a palindromic number.

You have been given a long type array/list 'arr’ of size 'n’.

It represents an elevation map wherein 'arr[i]’ denotes the elevation of the 'ith' bar.

Print the total amount of rainwater that can be trapped in these elevations.

Note :

The width of each bar is the same and is equal to 1.

Example:

Input: ‘n’ = 6, ‘arr’ = [3, 0, 0, 2, 0, 4].

Output: 10

Explanation: Refer to the image for better comprehension:

Note :

You don't need to print anything. It has already been taken care of. Just implement the given function.