SDE - 1

You are given an array/list 'ARR' consisting of N integers, which contains elements only in the range 0 to N - 1. Some of the elements may be repeated in 'ARR'. Your task is to find all such duplicate elements.

Note:

1. All the elements are in the range 0 to N - 1.
2. The elements may not be in sorted order.
3. You can return the duplicate elements in any order.
4. If there are no duplicates present then return an empty array.

You have been given a non-empty grid ‘MAT’ consisting of only 0s and 1s. Your task is to find the area of maximum size square sub-matrix with all 1s.

If there is no such sub-matrix, print 0.

For example, for the following grid:

The area of the largest square submatrix with all 1s is 4.

There is a one-dimensional garden of length 'N'. On each of the positions from 0 to 'N', there is a fountain, and this fountain’s water can reach up to a certain range as explained further. In other words, there are 'N' + 1 fountains located at positions 0, 1, 2, 3, …. 'N' which can be activated in the garden.

You are given an integer 'N' and an array/list 'ARR' of length 'N' + 1, where each index of the array denotes the coverage limit of a particular fountain.

A fountain at index 'i' can water the area ranging from the position 'i' - 'ARR'['i'] to 'i' + 'ARR'['i'].

Your task is to find the minimum number of fountains that have to be activated such that the whole garden from position 0 to 'N' has access to the water from at least some fountain.

Note:

1. 0-based indexing is used in the array.
2. We only care about the garden from 0 to 'N' only. So if i - 'ARR'['i'] < 0 or i + 'ARR'['i'] > 'N', you may ignore the exceeding area.
3. If some fountain covers the garden from position 'A' to position 'B', it means that the water from this fountain will spread to the whole line segment with endpoints 'A' and 'B'.

You are given 2D array/list 'POINTS' containing N distinct points on a 2D coordinate system where 'POINTS[i] = [Xi, Yi]. You have to find the maximum area of the triangle that can be formed by using any 3 points out of these N points.

Example

Let 'N' = 5, and the 'POINTS' = [ [0, 0], [2, 1], [0, 4], [0, 2], [5, 0] ].

Here, the maximum area triangle will be formed by using the points [0, 0], [0, 4], [5, 0] as shown below.

Hence, the area will be 10 units.

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