21
3
Input is an r by c matrix of non-negative integers (you may input r and c as other parameters if this helps with golf). This may be inputted as a 2D array or, if you prefer, a 1D array (though taking in r this time is necessary). Strings separated by spaces to distinguish rows and newlines to distinguish columns are also fine (below, the test cases have multiple spaces to distinguish rows for clarity -- you do not have to do this).
Consider a matrix of zeros. A move consists of replacing a rectangle of numbers with a rectangle of some positive integer (not zero). For example, these are all valid first moves:
0 0 0 0
0 2 0 0
0 0 0 0
0 0 0 0
0 3 0 0
0 3 0 0
0 3 0 0
0 3 0 0
1 1 1 0
1 1 1 0
0 0 0 0
0 0 0 0
These are not valid first moves:
0 0 0 0
0 2 0 0
0 0 0 0
0 2 0 0
0 1 0 0
0 2 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
Make golfed code to answer the following the question:
Given an r by c matrix, what is the smallest possible number of turns taken to construct this?
Test Cases:
1 1 1 1
1 2 2 2
1 2 3 3
1 2 3 4
1 2 3 4
> 4
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
> 15
3 3 3 3 3 3
3 2 2 2 2 3
3 2 1 1 2 3
3 2 1 1 2 3
3 2 2 2 2 3
3 3 3 3 3 3
> 3
1 1 1 1 1 1
1 2 2 2 2 1
1 2 0 0 2 1
1 2 0 0 2 1
1 2 2 2 2 1
1 1 1 1 1 1
> 8
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
> 0
1 1 1 1
1 3 3 1
2 3 3 2
2 2 2 4
> 4
8This seems like a very, very hard problem to compute efficiently to me. – orlp – 2018-01-27T15:03:03.530
This is a harder variation of this challenge.
– Arnauld – 2018-01-29T09:26:13.637Based on your examples of first moves I guess the numbers aren't inputted in order? None of your test cases reflect that, though. The test cases all go from 1 upwards (first test case four movies:
1,2,3,4
; second test case 15 moves:1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
; third test case 3 moves:1,2,3
; fourth test case 8 moves:1,1,1,1,2,2,2,2
). (It does make the challenge easier if only the same or next numbers can be inputted in that order. But if that's not your intention, you could for example swap the1
s and3
s in the third test case to reflect this.) – Kevin Cruijssen – 2018-03-02T08:18:27.780@KevinCruijssen That's not my intention. Fixed. – 0WJYxW9FMN – 2018-03-02T23:01:45.920
2What is the answer for [[1,1,1,1], [1,3,3,1], [2,3,3,2], [2,2,2,3]]? (In other words, can a rectangle be placed over different numbers?) – Peter Kagey – 2019-03-23T17:06:25.973
2Can you add a test case where the optimal solution requires multiple rectangles with the same number for a reason other than interfering zeros? For example, [[1,1,2,2],[1,1,2,2],[2,2,1,1],[2,2,1,1]] should take 3 rectangles. – Hiatsu – 2019-08-24T22:35:38.790