Google Kickstart 2019 Round A: Training Solution

Problem Statement 

Problem

As the football coach at your local school, you have been tasked with picking a team of exactly P students to represent your school. There are N students for you to pick from. The i-th student has a skill rating S_i, which is a positive integer indicating how skilled they are.

You have decided that a team is fair if it has exactly P students on it and they all have the same skill rating. That way, everyone plays as a team. Initially, it might not be possible to pick a fair team, so you will give some of the students one-on-one coaching. It takes one hour of coaching to increase the skill rating of any student by 1.

The competition season is starting very soon (in fact, the first match has already started!), so you'd like to find the minimum number of hours of coaching you need to give before you are able to pick a fair team.

Input

The first line of the input gives the number of test cases, T. T test cases follow. Each test case starts with a line containing the two integers N and P, the number of students and the number of students you need to pick, respectively. Then, another line follows containing N integers S_i; the i-th of these is the skill of the i-th student.

Output

For each test case, output one line containing Case #x: y, where x is the test case number (starting from 1) and y is the minimum number of hours of coaching needed, before you can pick a fair team of P students.

Limits

Time limit: 15 seconds per test set.
Memory limit: 1 GB.
1 ≤ T ≤ 100.
1 ≤ S_i ≤ 10000, for all i.
2 ≤ P ≤ N.

Test set 1 (Visible)

2 ≤ N ≤ 1000.

Test set 2 (Hidden)

2 ≤ N ≤ 10⁵.

Sample

Input	Output
3 4 3 3 1 9 100 6 2 5 5 1 2 3 4 5 5 7 7 1 7 7	Case #1: 14 Case #2: 0 Case #3: 6

In Sample Case #1, you can spend a total of 6 hours training the first student and 8 hours training the second one. This gives the first, second and third students a skill level of 9. This is the minimum time you can spend, so the answer is 14.

In Sample Case #2, you can already pick a fair team (the first and second student) without having to do any coaching, so the answer is 0.

In Sample Case #3, P = N, so every student will be on your team. You have to spend 6 hours training the third student, so that they have a skill of 7, like everyone else. This is the minimum time you can spend, so the answer is 6.

Problem link

 

Video Tutorial

You can find the detailed video tutorial here

• Youtube
• B站

 

Thought Process

Start with brute force approach, get all different combos of picking P students over N. O(Cn^p), which is factorial.

Sort definitely comes into mind. After sort,we have to go through the sorted array once, assuming if the highest score element is picked, the rest elements should be close to it. We can keep a rolling sum to avoid computing the sum over and over again.

Solutions

Sort and rolling sum solution

Time Complexity: O(N)
Space Complexity: O(N)

References

• Google kickstart official solution