Task 3 Appointment Slots

Task 3

There are N patients (numbered from 0 to N-1) who want to visit the doctor. The doctor has S possible appointment slots, numbered from 1 to S. Each of the patients has two preferences. Patient K would like to visit the doctor during either slot A[K] or slot B[K]. The doctor can treat only one patient during each slot.

Is it possible to assign every patient to one of their preferred slots so that there will be at most one patient assigned to each slot?

Write a function:

    class Solution { public boolean solution(int[] A, int[] B, int S); } 

that, given two arrays A and B, both of N integers, and an integer S, returns true if it is possible to assign every patient to one of their preferred slots, one patient to one slot, and false otherwise.

Examples:

1. Given A = [1, 1, 3], B = [2, 2, 1] and S = 3, the function should return true. We could assign patients in the following way: [1, 2, 3], where the K-th element of the array represents the number of the slot to which patient K was assigned. Another correct assignment would be [2, 1, 3]. On the other hand, [2, 2, 1] would be an incorrect assignment as two patients would be assigned to slot 2.
2. Given A = [3, 2, 3, 1], B = [1, 3, 1, 2] and S = 3, the function should return false. There are only three slots available, but there are four patients who want to visit the doctor. It is therefore not possible to assign the patients to the slots so that only one patient at a time would visit the doctor.
3. Given A = [2, 5, 6, 5], B = [5, 4, 2, 2] and S = 8, the function should return true. For example, we could assign patients in the following way: [5, 4, 6, 2].
4. Given A = [1, 2, 1, 6, 8, 7, 8], B = [2, 3, 4, 7, 7, 8, 7] and S = 10, the function should return false. It is not possible to assign all of the patients to one of their preferred slots so that only one patient will visit the doctor during one slot.

Write an efficient algorithm for the following assumptions:

• N is an integer within the range [1…100,000];
• S is an integer within the range [2…100,000];
• each element of array A and B is an integer within the range [1…S];
• no patient has two preferences for the same slot, L.e. A[1] != B[i].