SDE - 1

Given a sequence of ‘N’ space-separated non-negative integers A[1],A[2],A[3],......A[i]…...A[n]. Where each number of the sequence represents the height of the line drawn at point 'i'. Hence on the cartesian plane, each line is drawn from coordinate ('i',0) to coordinate ('i', 'A[i]'), here ‘i’ ranges from 1 to ‘N’. Find two lines, which, together with the x-axis forms a container, such that the container contains the most area of water.

Note :

1. You can not slant the container i.e. the height of the water is equal to the minimum height of the two lines which define the container.

2. Do not print anything, you just need to return the area of the container with maximum water.

Example

For the above Diagram, the first red marked line is formed between coordinates (2,0) and (2,10), and the second red-marked line is formed between coordinates (5,0) and (5,9). The area of water contained between these two lines is (height* width) = (5-2)* 9 = 27, which is the maximum area contained between any two lines present on the plane. So in this case, we will return 3* 9=27.

Ninjaland is a country having 'N' states numbered from 1 to 'N'. These 'N' states are connected by 'M' bidirectional roads. Each road connects to different states and has some cost to travel from one state to another. Now, the chief wants you to select 'N' - 1 roads in such a way that the tourist bus can travel to every state at least once at minimum 'COST'.

For example :

Consider a country having 4 states numbered from 1 to 4. These 4 states are connected by 5 bidirectional roads given as :
1 --- 2 with cost = 8
2 --- 3 with cost = 6
3 --- 4 with cost = 5
1 --- 4 with cost = 2
1 --- 3 with cost = 4

The map of the country can be represented as:

Now, the best way to choose 3 roads is:

The cost of travelling from any state to all other states is  2 + 4 + 6 i.e. 12.

You are given an array 'ARR' of integers of length N. Your task is to find the first missing positive integer in linear time and constant space. In other words, find the lowest positive integer that does not exist in the array. The array can have negative numbers as well.

For example, the input [3, 4, -1, 1] should give output 2 because it is the smallest positive number that is missing in the input array.

You are given a path to a file/directory in Unix-style of length N, In a Unix-style file system, a dot(.) refers to the current directory. A double dot(..) refers to the previous directory in reference to the current directory. If there are multiple slashes between two directories you should consider it as a single slash.

Now, for a given directory path as a string, you are required to simplify the same and tell the final destination in the directory structure or the path.

The simplified path should always begin with a slash(/) and there must be a single slash between two directory names. There should not be a trailing slash.

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.

You are given a sorted array 'ARR' and a number 'X'. Your task is to count the number of occurrences of 'X' in 'ARR'.

Note :

1. If 'X' is not found in the array, return 0.
2. The given array is sorted in non-decreasing order.