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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 are given an array “arr'' of integers. Your task is to find the contiguous subarray within the array which has the largest product of its elements. You have to report this maximum product.

An array c is a subarray of array d if c can be obtained from d by deletion of several elements from the beginning and several elements from the end.

For e.g.- The non-empty subarrays of an array [1,2,3] will be- [1],[2],[3],[1,2],[2,3],[1,2,3]. 

For Example:

If arr = {-3,4,5}.
All the possible non-empty contiguous subarrays of “arr” are {-3}, {4}, {5}, {-3,4}, {4,5} and {-3,4,5}.
The product of these subarrays are -3, 4, 5, -12, 20 and -60 respectively.
The maximum product is 20. Hence, the answer is 20.

Follow Up:

Can you solve this in linear time and constant space complexity?

You are given an array/list ‘ARR’ of ‘N’ positive integers and an integer ‘K’. Your task is to check if there exists a subset in ‘ARR’ with a sum equal to ‘K’.

Note: Return true if there exists a subset with sum equal to ‘K’. Otherwise, return false.

For Example :

If ‘ARR’ is {1,2,3,4} and ‘K’ = 4, then there exists 2 subsets with sum = 4. These are {1,3} and {4}. Hence, return true.

What is CRUD operation

You are given an array 'ARR' of integers of length N. Your task is to find the next smaller element for each of the array elements.

Next Smaller Element for an array element is the first element to the right of that element which has a value strictly smaller than that element.

If for any array element the next smaller element does not exist, you should print -1 for that array element.

For Example:

If the given array is [ 2, 3, 1], we need to return [1, 1, -1]. Because for  2, 1 is the Next Smaller element. For 3, 1 is the Next Smaller element and for 1, there is no next smaller element hence the answer for this element is -1.

ACID properties, joins, indexing

You are given an array ‘arr’ of ‘N’ distinct integers. Your task is to print all the non-empty subsets of the array.

Note: elements inside each subset should be sorted in increasing order. But you can print the subsets in any order, you don’t have to specifically sort them.

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