Software Engineer

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.

Ninja is traveling to a Happy city where ‘N’ people reside. In the city, the happiness of each person is represented as a number ‘H’ where ‘H’ ranges from -20,000,000 to 20,000,000 (both inclusive). The happiness of each person in the city is given in an array/list ‘HAPPINESS’ where ‘HAPPINESS[i]’ represents the happiness of the i’th person.

Ninja wants to make a group of people such that the overall happiness of the group (sum of happiness value of all the people in the group) ranges between ‘A’ and ‘B’ where -500,000,000 ≤ A ≤ B ≤ 500,000,000. Ninja wants to know in how many ways he can make this group.

For example :

For the given ‘HAPPINESS[]’ = ‘[-1, 0, 3]’ and ‘A’ = 0 , ‘B’ = 2. Following are the ways to group people such that the overall happiness of the group is between ‘A’ and ‘B’:

[-1, 0, 3], the sum of all the happiness values of this group is 2.

[-1, 3], the sum of all the happiness values of this group is 2.

[0], the sum of all the happiness values of this group is 0.

[ ], the sum of all the happiness values of this empty group is 0.

So the number of ways is 4.

As Ninja is busy with some other task so he asks you for help. Can you help Ninja to find out the number of ways in which he can pick groups so that the overall happiness of the group must be in the range between ‘A’ and ‘B’?