SDE - 1

You are given an integer 'N', your task is to generate all combinations of well-formed parenthesis having ‘N’ pairs.

A parenthesis is called well-formed if it is balanced i.e. each left parenthesis has a matching right parenthesis and the matched pairs are well nested.

For Example:

For ‘N’ = 3,
All possible combinations are: 
((()))
(()())
(())()
()(())
()()()

You are given an array/list 'prices' where the elements of the array represent the prices of the stock as they were yesterday and indices of the array represent minutes. Your task is to find and return the maximum profit you can make by buying and selling the stock. You can buy and sell the stock only once.

Note:

You can’t sell without buying first.

For Example:

For the given array [ 2, 100, 150, 120],
The maximum profit can be achieved by buying the stock at minute 0 when its price is Rs. 2 and selling it at minute 2 when its price is Rs. 150.
So, the output will be 148.

Your friend Ninja has been learning about binary numbers lately. In order to understand binary numbers with perfection, Ninja asks you to generate a list of binary numbers from 1 to ‘N’, which he can use later for reference.

For every integer Ninja gives, your task is to generate all the binary numbers from 1 to ‘N’.

Example:

Consider N = 5,
All the binary numbers from 1 to 5 are: 1, 10, 11, 100, 101.

Given two binary trees T and S, check whether tree S has exactly the same structure and node values with a subtree of T, i.e., check if tree S is a subtree of the tree T.

A subtree of a tree T is a tree S consisting of a node in T and all of its descendants in T. The subtree corresponding to the root node is the entire tree; the subtree corresponding to any other node is called a proper subtree.

A few days back, Ninja encountered a string containing characters from ‘A’ to ‘Z’ which indicated a secret message. For security purposes he encoded each character of the string to its numeric value, that is, A = 1, B = 2, C = 3, till Z = 26 and combined them as a single sequence (SEQ) of digits of length N. Let's say the message was "LA", Ninja encoded it as 121 for L=12 and A=1.

Today, when he read the encoded secret message, he realised that he was not able to decode the original string. So, the Ninja is wondering in how many ways he can decode the numeric sequence to some valid string.

A valid string is a string with characters from A to Z and no other characters.

Example:

Let the encoded sequence be 121,

The first way to decode 121 is:
1 = A
2 = B
1 = A
Thus, the decoded string will be ABA.

The second way to decode 121 is:
12 = L
1 = A
Thus, the decoded string will be LA.

The third way to decode 121 is:
1 = A
21 = U
Thus, the decoded string will be AU.

So, there will be 3 ways to decode the sequence 121 i.e. [(ABA), (LA), (AU)].

Note:

The input sequence will always have at least 1 possible way to decode.    

As the answer can be large, return your answer modulo 10^9  + 7.

Follow Up:

Can you solve this using constant extra space?

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