SDE - 1

You are given an array 'ARR' of positive integers, each of which represents the number of liters of water in that particular bucket, we have to make the liters of water in every bucket equal.

We are allowed to do two types of operations any number of times:

1. We can altogether remove a bucket from the sequence

2. We can draw some water from a bucket

We have to tell the minimum number of liters removed to make all buckets have the same amount of water.

For example:

Given ‘N’ = 4 and ‘ARR’ = [1, 1, 2, 2].
The answer will be 2, i.e., if we chose that all buckets should have 1 unit of water, we will have to throw 1 unit of water from buckets 3 and 4. Hence 2.

You are given a starting position for a rat which is stuck in a maze at an initial point (0, 0) (the maze can be thought of as a 2-dimensional plane). The maze would be given in the form of a square matrix of order 'N' * 'N' where the cells with value 0 represent the maze’s blocked locations while value 1 is the open/available path that the rat can take to reach its destination. The rat's destination is at ('N' - 1, 'N' - 1). Your task is to find all the possible paths that the rat can take to reach from source to destination in the maze. The possible directions that it can take to move in the maze are 'U'(up) i.e. (x, y - 1) , 'D'(down) i.e. (x, y + 1) , 'L' (left) i.e. (x - 1, y), 'R' (right) i.e. (x + 1, y).

Note:

Here, sorted paths mean that the expected output should be in alphabetical order.

For Example:

Given a square matrix of size 4*4 (i.e. here 'N' = 4):
1 0 0 0
1 1 0 0
1 1 0 0
0 1 1 1 
Expected Output:
DDRDRR DRDDRR 
i.e. Path-1: DDRDRR and Path-2: DRDDRR

The rat can reach the destination at (3, 3) from (0, 0) by two paths, i.e. DRDDRR and DDRDRR when printed in sorted order, we get DDRDRR DRDDRR.

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 a list of ‘transactions’ between ‘n’ number of friends. who have to give each other money. The list consists of data of receiver, sender, and transaction.

Your task is to minimize the cash flow and the total number of transactions should also be minimum.

For example :

In figure 1 : friend-1 has to pay 2000$ to friend-2, and 4000$ to friend-3 and friend-2 has to pay 3000$ to friend-3.

In figure 2 : so we can minimize the flow between friend-1 to friend-2 by direct pay to friend-1 to friend-3

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