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Carpet and Boxes
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Carpet and Boxes

Contributed by
Amit Shaw
Medium
yellow-spark
0/80
Avg time to solve 20 mins
Success Rate 70 %
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Problem Statement

You are given 'N' boxes of width 1 unit. You are also given an array 'POSITION' which denotes the positions of the boxes, e.g POSITION[ i ] denotes the position of the ith box. You need to cover any 'K' boxes with a carpet.

Find the minimum length of the carpet to cover any 'K' boxes.

Example:
Input: ‘N’ = 3, ‘K’ = 2, 'POSITION' = [2, 3, 6] 

Output: 2

 There are two possible ways to cover exactly two boxes. One covers the boxes at positions 2 and 3 and the other at positions 3 and 6. The carpet lengths required for both ways are 2 ( Since boxes are at positions 2 and 3 each having width 1) and 4, respectively. So the minimum length of the carpet is 2.
Detailed explanation ( Input/output format, Notes, Constraints, Images )
Sample Input 1 :
2
4 3
4 9 2 6
2 1
1 2
Sample Output 1 :
5
1
Explanation Of Sample Input 1 :
For the first case:
There are two possible ways to cover exactly three boxes. One covers the boxes at positions 2, 4 and 6 and the other at positions 4, 6 and 9. The carpet lengths required for both ways are 5 and 6, respectively. So the minimum length of the carpet is 5. 

For the second case:
Since we need to cover only one box, the minimum length of the carpet is 1.
Sample Input 2 :
2
5 2
100 2 95 145 47 
1 1
100
Sample Output 2 :
6
1
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