SDE - Intern

You are given D dice, each having F faces numbered 1 to F, both inclusive. The task is to find the possible number of ways to roll the dice together such that the sum of face-up numbers equal the given target S.

Note :

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

Follow Up :

Can you solve this using not more than O(S) extra space?

You are given a positive integer ‘N’. Your task is to find the total number of ‘1’ in the binary representation of all the numbers from 1 to N.

Since the count of ‘1’ can be huge, you are required to return it modulo 1e9+7.

Note:

Do not print anything, just return the number of set bits in the binary representation of all integers between 1 and ‘N’.

You have been given a Binary Tree of 'n' nodes, where the nodes have integer values. Your task is to return its postorder traversal.

For Example:

For the given tree below,
Postorder traversal for the given tree will be [4, 5, 2, 3, 1]. Hence, the answer is [4, 5, 2, 3, 1].

For a given array with N elements, you need to find the length of the longest subsequence from the array such that all the elements of the subsequence are sorted in strictly increasing order.

Strictly Increasing Sequence is when each term in the sequence is larger than the preceding term.

For example:

[1, 2, 3, 4] is a strictly increasing array, while [2, 1, 4, 3] is not.

You have been given an unsorted array ‘ARR’.

Your task is to sort the array in such a way that the array looks like a wave array.

Example:

If the given sequence ‘ARR’ has ‘N’ elements then the sorted wave array looks like - 
‘ARR[0] >= ARR[1]’ and ‘ARR[1] <= ARR[2]’
‘ARR[2] >= ARR[3]’ and ‘ARR[3] <= ARR[4]’
‘ARR[4] >= ARR[5]’ and ‘ARR[5] <= ARR[6]’  And so on.

Note:

1. ‘ARR[0]’ must be greater than or equal to ‘ARR[1]’.

2. There can be multiple arrays that look like a wave array but you have to return only one.

3. We have an internal function that will check your solution and return 'True' in case your array is one of the solutions otherwise return 'False'.

Explanation

The given array ‘ ARR = { 4, 3, 5, 2, 3, 1, 2 } ’
The below figure is a visual representation of the given ‘ARR’ and you can see we can express ‘ARR’ in a waveform array because 
4>3 and 3<5 
5>2 and 2<3
3>1 and 1<2
And it follows the condition of wave array.

Follow up:

Try to solve this problem in linear time complexity.

Implement a data structure for implementing the feature of showing three last watched movies on Amazon Prime.

Design and implement a data structure which supports the following operations:

insert(X): Inserts an element X in the data structure and returns true if the element was not present, and false otherwise.

remove(X): Removes the element X from the data structure, if present. Returns true if the element was present and false otherwise.

search(X): Search the element X in the data structure. Returns true if the element was present and false otherwise.

getRandom(): Return a random element present in the data structure.

Four types of queries denote these operations:

Type 1: for insert(X) operation.
Type 2: for remove(X) operation.
Type 3: for search(X) operation.
Type 4: for getRandom() operation.

Note:

It is guaranteed that at least one element will be present in the data structure when getRandom() operation is performed.

Follow Up:

Can you implement every operation such that it works in O(1) time?