Partition a square grid into parts of equal area












5












$begingroup$


This challenge is based on the following puzzle: You are given an n by n grid with n cells marked. Your job is to the partition the grid into n parts where each part consists of exactly n cells.



Example



Here is a puzzle on the left and its (unique) solution on the right:



puzzlesolution



Challenge



You will be given a set of n zero-indexed coordinates in any reasonable format.



[(0,0), (0,3), (1,0), (1,1), (2,2)]


And your job is to write a program that returns any valid parition (again, in any reasonable format).



[

  [(0,0), (0,1), (0,2), (1,2), (1,3)],

  [(0,3), (0,4), (1,4), (2,4), (3,4)],

  [(1,0), (2,0), (3,0), (4,0), (4,1)],

  [(1,1), (2,1), (3,1), (3,2), (4,2)],

  [(2,2), (2,3), (3,3), (4,3), (4,4)]

]


If the puzzle has no solution, the program should indicate that by throwing an error or returning an empty solution.



Input/Output Examples



[(0,0)]               => [[(0,0)]]



[(0,0), (1,1)]        => [

                          [(0,0), (1,0)], 

                          [(0,1), (1,1)]

                         ]



[(0,0), (0,1), (1,0)] =>  (no solution)



[(0,0), (0,1), (0,2)] => [

                          [(0,0), (1,0), (2,0)], 

                          [(0,1), (1,1), (2,1)],

                          [(0,2), (1,2), (2,2)],

                         ]



[(0,0), (0,2), (1,2)] => [

                          [(0,0), (1,0), (2,0)], 

                          [(0,1), (0,2), (1,1)],

                          [(1,2), (2,1), (2,2)],

                         ]


Scoring



This is code-golf, so shortest code wins.






code-golf combinatorics grid set-partitions







share|improve this question









$endgroup$












  • $begingroup$
    This was inspired by this Math Stack Exchange question.
    $endgroup$
    – Peter Kagey
    5 hours ago










  • $begingroup$
    @Arnauld, it looks like for Shikaku puzzles, "the objective is to divide the grid into rectangular and square pieces". In this case, there is no such constraint.
    $endgroup$
    – Peter Kagey
    5 hours ago










  • $begingroup$
    Sorry for the confusion. I think there might be a Shikaku challenge somewhere in the sandbox, or maybe I was planning to make one myself at some point -- I can't remember for sure. Either way, I thought it was the same thing at first glance.
    $endgroup$
    – Arnauld
    5 hours ago
















5












$begingroup$


This challenge is based on the following puzzle: You are given an n by n grid with n cells marked. Your job is to the partition the grid into n parts where each part consists of exactly n cells.



Example



Here is a puzzle on the left and its (unique) solution on the right:



puzzlesolution



Challenge



You will be given a set of n zero-indexed coordinates in any reasonable format.



[(0,0), (0,3), (1,0), (1,1), (2,2)]


And your job is to write a program that returns any valid parition (again, in any reasonable format).



[

  [(0,0), (0,1), (0,2), (1,2), (1,3)],

  [(0,3), (0,4), (1,4), (2,4), (3,4)],

  [(1,0), (2,0), (3,0), (4,0), (4,1)],

  [(1,1), (2,1), (3,1), (3,2), (4,2)],

  [(2,2), (2,3), (3,3), (4,3), (4,4)]

]


If the puzzle has no solution, the program should indicate that by throwing an error or returning an empty solution.



Input/Output Examples



[(0,0)]               => [[(0,0)]]



[(0,0), (1,1)]        => [

                          [(0,0), (1,0)], 

                          [(0,1), (1,1)]

                         ]



[(0,0), (0,1), (1,0)] =>  (no solution)



[(0,0), (0,1), (0,2)] => [

                          [(0,0), (1,0), (2,0)], 

                          [(0,1), (1,1), (2,1)],

                          [(0,2), (1,2), (2,2)],

                         ]



[(0,0), (0,2), (1,2)] => [

                          [(0,0), (1,0), (2,0)], 

                          [(0,1), (0,2), (1,1)],

                          [(1,2), (2,1), (2,2)],

                         ]


Scoring



This is code-golf, so shortest code wins.






code-golf combinatorics grid set-partitions







share|improve this question









$endgroup$












  • $begingroup$
    This was inspired by this Math Stack Exchange question.
    $endgroup$
    – Peter Kagey
    5 hours ago










  • $begingroup$
    @Arnauld, it looks like for Shikaku puzzles, "the objective is to divide the grid into rectangular and square pieces". In this case, there is no such constraint.
    $endgroup$
    – Peter Kagey
    5 hours ago










  • $begingroup$
    Sorry for the confusion. I think there might be a Shikaku challenge somewhere in the sandbox, or maybe I was planning to make one myself at some point -- I can't remember for sure. Either way, I thought it was the same thing at first glance.
    $endgroup$
    – Arnauld
    5 hours ago














5












5








5


1



$begingroup$


This challenge is based on the following puzzle: You are given an n by n grid with n cells marked. Your job is to the partition the grid into n parts where each part consists of exactly n cells.



Example



Here is a puzzle on the left and its (unique) solution on the right:



puzzlesolution



Challenge



You will be given a set of n zero-indexed coordinates in any reasonable format.



[(0,0), (0,3), (1,0), (1,1), (2,2)]


And your job is to write a program that returns any valid parition (again, in any reasonable format).



[

  [(0,0), (0,1), (0,2), (1,2), (1,3)],

  [(0,3), (0,4), (1,4), (2,4), (3,4)],

  [(1,0), (2,0), (3,0), (4,0), (4,1)],

  [(1,1), (2,1), (3,1), (3,2), (4,2)],

  [(2,2), (2,3), (3,3), (4,3), (4,4)]

]


If the puzzle has no solution, the program should indicate that by throwing an error or returning an empty solution.



Input/Output Examples



[(0,0)]               => [[(0,0)]]



[(0,0), (1,1)]        => [

                          [(0,0), (1,0)], 

                          [(0,1), (1,1)]

                         ]



[(0,0), (0,1), (1,0)] =>  (no solution)



[(0,0), (0,1), (0,2)] => [

                          [(0,0), (1,0), (2,0)], 

                          [(0,1), (1,1), (2,1)],

                          [(0,2), (1,2), (2,2)],

                         ]



[(0,0), (0,2), (1,2)] => [

                          [(0,0), (1,0), (2,0)], 

                          [(0,1), (0,2), (1,1)],

                          [(1,2), (2,1), (2,2)],

                         ]


Scoring



This is code-golf, so shortest code wins.






code-golf combinatorics grid set-partitions







share|improve this question









$endgroup$




This challenge is based on the following puzzle: You are given an n by n grid with n cells marked. Your job is to the partition the grid into n parts where each part consists of exactly n cells.



Example



Here is a puzzle on the left and its (unique) solution on the right:



puzzlesolution



Challenge



You will be given a set of n zero-indexed coordinates in any reasonable format.



[(0,0), (0,3), (1,0), (1,1), (2,2)]


And your job is to write a program that returns any valid parition (again, in any reasonable format).



[

  [(0,0), (0,1), (0,2), (1,2), (1,3)],

  [(0,3), (0,4), (1,4), (2,4), (3,4)],

  [(1,0), (2,0), (3,0), (4,0), (4,1)],

  [(1,1), (2,1), (3,1), (3,2), (4,2)],

  [(2,2), (2,3), (3,3), (4,3), (4,4)]

]


If the puzzle has no solution, the program should indicate that by throwing an error or returning an empty solution.



Input/Output Examples



[(0,0)]               => [[(0,0)]]



[(0,0), (1,1)]        => [

                          [(0,0), (1,0)], 

                          [(0,1), (1,1)]

                         ]



[(0,0), (0,1), (1,0)] =>  (no solution)



[(0,0), (0,1), (0,2)] => [

                          [(0,0), (1,0), (2,0)], 

                          [(0,1), (1,1), (2,1)],

                          [(0,2), (1,2), (2,2)],

                         ]



[(0,0), (0,2), (1,2)] => [

                          [(0,0), (1,0), (2,0)], 

                          [(0,1), (0,2), (1,1)],

                          [(1,2), (2,1), (2,2)],

                         ]


Scoring



This is code-golf, so shortest code wins.






code-golf combinatorics grid set-partitions




code-golf combinatorics grid set-partitions






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 5 hours ago









Peter KageyPeter Kagey

773517




773517












  • $begingroup$
    This was inspired by this Math Stack Exchange question.
    $endgroup$
    – Peter Kagey
    5 hours ago










  • $begingroup$
    @Arnauld, it looks like for Shikaku puzzles, "the objective is to divide the grid into rectangular and square pieces". In this case, there is no such constraint.
    $endgroup$
    – Peter Kagey
    5 hours ago










  • $begingroup$
    Sorry for the confusion. I think there might be a Shikaku challenge somewhere in the sandbox, or maybe I was planning to make one myself at some point -- I can't remember for sure. Either way, I thought it was the same thing at first glance.
    $endgroup$
    – Arnauld
    5 hours ago


















  • $begingroup$
    This was inspired by this Math Stack Exchange question.
    $endgroup$
    – Peter Kagey
    5 hours ago










  • $begingroup$
    @Arnauld, it looks like for Shikaku puzzles, "the objective is to divide the grid into rectangular and square pieces". In this case, there is no such constraint.
    $endgroup$
    – Peter Kagey
    5 hours ago










  • $begingroup$
    Sorry for the confusion. I think there might be a Shikaku challenge somewhere in the sandbox, or maybe I was planning to make one myself at some point -- I can't remember for sure. Either way, I thought it was the same thing at first glance.
    $endgroup$
    – Arnauld
    5 hours ago
















$begingroup$
This was inspired by this Math Stack Exchange question.
$endgroup$
– Peter Kagey
5 hours ago




$begingroup$
This was inspired by this Math Stack Exchange question.
$endgroup$
– Peter Kagey
5 hours ago












$begingroup$
@Arnauld, it looks like for Shikaku puzzles, "the objective is to divide the grid into rectangular and square pieces". In this case, there is no such constraint.
$endgroup$
– Peter Kagey
5 hours ago




$begingroup$
@Arnauld, it looks like for Shikaku puzzles, "the objective is to divide the grid into rectangular and square pieces". In this case, there is no such constraint.
$endgroup$
– Peter Kagey
5 hours ago












$begingroup$
Sorry for the confusion. I think there might be a Shikaku challenge somewhere in the sandbox, or maybe I was planning to make one myself at some point -- I can't remember for sure. Either way, I thought it was the same thing at first glance.
$endgroup$
– Arnauld
5 hours ago




$begingroup$
Sorry for the confusion. I think there might be a Shikaku challenge somewhere in the sandbox, or maybe I was planning to make one myself at some point -- I can't remember for sure. Either way, I thought it was the same thing at first glance.
$endgroup$
– Arnauld
5 hours ago










1 Answer
1






active

oldest

votes


















3












$begingroup$

JavaScript (ES6), 163 bytes



Prints all possible solutions as matrices containing 1-indexed values that describe the partition. (Or prints nothing if there's no solution.)





a=>(m=a.map(_=>[...a]),g=(n,[X,Y]=a[n++],j=0)=>a[j]?m.map((r,y)=>r.map((v,x)=>++v|(X-x)**2+(Y-y)**2-!!j?0:r[g(r[x]=n,[x,y],j+1),x]=v)):a[n]?g(n):console.log(m))(0)


Try it online!






share|improve this answer









$endgroup$













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    $begingroup$

    JavaScript (ES6), 163 bytes



    Prints all possible solutions as matrices containing 1-indexed values that describe the partition. (Or prints nothing if there's no solution.)





    a=>(m=a.map(_=>[...a]),g=(n,[X,Y]=a[n++],j=0)=>a[j]?m.map((r,y)=>r.map((v,x)=>++v|(X-x)**2+(Y-y)**2-!!j?0:r[g(r[x]=n,[x,y],j+1),x]=v)):a[n]?g(n):console.log(m))(0)


    Try it online!






    share|improve this answer









    $endgroup$


















      3












      $begingroup$

      JavaScript (ES6), 163 bytes



      Prints all possible solutions as matrices containing 1-indexed values that describe the partition. (Or prints nothing if there's no solution.)





      a=>(m=a.map(_=>[...a]),g=(n,[X,Y]=a[n++],j=0)=>a[j]?m.map((r,y)=>r.map((v,x)=>++v|(X-x)**2+(Y-y)**2-!!j?0:r[g(r[x]=n,[x,y],j+1),x]=v)):a[n]?g(n):console.log(m))(0)


      Try it online!






      share|improve this answer









      $endgroup$
















        3












        3








        3





        $begingroup$

        JavaScript (ES6), 163 bytes



        Prints all possible solutions as matrices containing 1-indexed values that describe the partition. (Or prints nothing if there's no solution.)





        a=>(m=a.map(_=>[...a]),g=(n,[X,Y]=a[n++],j=0)=>a[j]?m.map((r,y)=>r.map((v,x)=>++v|(X-x)**2+(Y-y)**2-!!j?0:r[g(r[x]=n,[x,y],j+1),x]=v)):a[n]?g(n):console.log(m))(0)


        Try it online!






        share|improve this answer









        $endgroup$



        JavaScript (ES6), 163 bytes



        Prints all possible solutions as matrices containing 1-indexed values that describe the partition. (Or prints nothing if there's no solution.)





        a=>(m=a.map(_=>[...a]),g=(n,[X,Y]=a[n++],j=0)=>a[j]?m.map((r,y)=>r.map((v,x)=>++v|(X-x)**2+(Y-y)**2-!!j?0:r[g(r[x]=n,[x,y],j+1),x]=v)):a[n]?g(n):console.log(m))(0)


        Try it online!







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 4 hours ago









        ArnauldArnauld

        73.9k690310




        73.9k690310






























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