SDE - 1

We are given a sorted doubly-linked list which contains distinct positive integers, and an integer ‘X’. Print all such unique pairs from the given list so that their sum is equal to ‘X’.

There are ‘N’ people at a party. Each person has been assigned a unique id between 0 to 'N' - 1(both inclusive). A celebrity is a person who is known to everyone but does not know anyone at the party.

Given a helper function ‘knows(A, B)’, It will returns "true" if the person having id ‘A’ know the person having id ‘B’ in the party, "false" otherwise. Your task is to find out the celebrity at the party. Print the id of the celebrity, if there is no celebrity at the party then print -1.

Note:

1. The helper function ‘knows’ is already implemented for you.
2. ‘knows(A, B)’ returns "false", if A doesn't know B.
3. You should not implement helper function ‘knows’, or speculate about its implementation.
4. You should minimize the number of calls to function ‘knows(A, B)’.
5. There are at least 2 people at the party.
6. At most one celebrity will exist.

You are given the number ‘N’. The task is to find the number of ways to represent ‘N’ as a sum of two or more consecutive natural numbers.

Example:

N = 9
‘9’ can be represented as:
2 + 3 + 4 = 9
4 + 5 = 9
The number of ways to represent ‘9’ as a sum of consecutive natural numbers is ‘2’. So, the answer is ‘2’.

Note:

1. The numbers used to represent ‘N’ should be natural numbers (Integers greater than equal to 1).

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.