SDE - 2

You have been given an array/list 'HEIGHTS' of length ‘N. 'HEIGHTS' represents the histogram and each element of 'HEIGHTS' represents the height of the histogram bar. Consider that the width of each histogram is 1.

You are supposed to return the area of the largest rectangle possible in the given histogram.

For example :

In the below histogram where array/list elements are {2, 1, 5, 6, 2, 3}.

The area of largest rectangle possible in the given histogram is 10.

You are given an integer array 'ARR' of size 'N' and an integer 'S'. Your task is to return the list of all pairs of elements such that each sum of elements of each pair equals 'S'.

Note:

Each pair should be sorted i.e the first value should be less than or equals to the second value. 

Return the list of pairs sorted in non-decreasing order of their first value. In case if two pairs have the same first value, the pair with a smaller second value should come first.

Given an unsorted array of integers, you have to move the array elements in a way such that all the zeroes are transferred to the end, and all the non-zero elements are moved to the front. The non-zero elements must be ordered in their order of appearance.

For example, if the input array is: [0, 1, -2, 3, 4, 0, 5, -27, 9, 0], then the output array must be:

[1, -2, 3, 4, 5, -27, 9, 0, 0, 0].

Expected Complexity: Try doing it in O(n) time complexity and O(1) space complexity. Here, ‘n’ is the size of the array.

You have been given a board where there are '2' rows and 'N' columns. You have an infinite supply of 2x1 tiles, and you can place a tile in the following ways:

1. Horizontally as 1x2 tile
2. Vertically as 2x1 tile

Count the number of ways to tile the given board using the available tiles.

Note :

The number of ways might be large so output your answer modulo 10^9 + 7.

Here an example of tile and board for 'N' = 4 :

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