SDE - 1

Given an unsorted array ‘arr’ of distinct integers and an integer ‘k’, your task is to find the ‘k-th’ smallest element in the array.

Example:

n = 5, k = 2 and arr[] = {6, 5, 4, 8, 7}
The array elements in sorted order are [4, 5, 6, 7, 8]. The ‘2-nd’ smallest element in the array is 5, so the answer is 5.

Note:

1. Don’t print anything. Return the value of ‘k-th’ smallest element.
2. ‘k’ is a positive integer and not greater than the size of the array.
3. The array ‘arr’ is unsorted, and all the elements of the array are distinct.

You are given an array Arr consisting of N integers. You need to find the equilibrium index of the array.

An index is considered as an equilibrium index if the sum of elements of the array to the left of that index is equal to the sum of elements to the right of it.

Note:

1. The array follows 0-based indexing, so you need to return the 0-based index of the element.
2. Note that the element at the equilibrium index won’t be considered for either left sum or right sum.
3. If there are multiple indices which satisfy the given condition, then return the left-most index i.e if there are indices i,j,k…. which are equilibrium indices, return the minimum among them
4. If no such index is present in the array, return -1.

You are given three arrays 'A', 'B' and 'C' of length 'N', 'M' and 'K' respectively. All the three arrays are sorted in non-decreasing order. Your task is to find all such elements which are present in all the three given arrays.

Note:

1. The output array should have the same ordering of elements as the original arrays.
2. Even if a particular element appears more than once in each of the three arrays, it should still be present only once in the output array.
3. If there are no common elements in the arrays, return an empty array.

For example:

Consider the three arrays A = [ 2, 3, 4, 7 ] , B = [ 0, 0, 3, 5 ] , C = [ 1, 3, 8, 9 ]
The output array should be [ 3 ] as 3 is the only element which is present in all the three arrays.

A Derangement is a permutation of ‘N’ elements, such that no element appears in its original position. For example, an instance of derangement of {0, 1, 2, 3} is {2, 3, 1, 0}, because 2 present at index 0 is not at its initial position which is 2 and similarly for other elements of the sequence.

Given a number ‘N’, find the total number of derangements possible of a set of 'N’ elements.

Note:

The answer could be very large, output answer %(10 ^ 9 + 7).

Given a maze in the form of a binary rectangular matrix of size M*N, where each element can either be 0 or 1, the task is to find the length of the shortest path in a maze from a given source cell to a destination cell.

The path can only be created out of a cell if its value is 1 and at any given moment, we can only move one step in one of the four directions. The valid moves are:

Up: (x, y) -> (x - 1, y)
Left: (x, y) -> (x, y - 1)
Down: (x, y) -> (x + 1, y)
Right: (x, y) -> (x, y + 1)

If there is no path from a given source cell to a destination cell, return -1.

For example :

consider the binary matrix below. If source = (0, 0) and destination = (3, 4), the shortest path from source to destination has length 11.

Consider all numbers from 1 to ‘N’, your task is to find the sum of gcd of all pairs (i, j) such that 1 <= i < j <= N.

For example for N = 3, all pairs are { (1, 2), (1, 3), (2, 3) }.

Note :

Gcd of two numbers (X, Y) is defined as the largest integer that divides both ‘X’ and ‘Y’.