Find the area of the smallest rectangle to contain squares of sizes up to n

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Find the area of the smallest rectangle to contain squares of sizes up to n

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4

$begingroup$

This is a sequence question of the usual type, as applied to OEIS sequence A038666. That is, do either of the following:

• Accept no or any input, and output A038666 until the heat death of the universe.


• Accept a positive integer as input, and output the nth term of A038666 or its first n terms. (If using 0- instead of 1-indexing, then of course you also have to output 1 on 0 input.)

The nth term of A038666 is the least area among rectangles that contain nonoverlapping squares of sizes 1×1, 2×2,… n×n if you're using 1-indexing.

Example:

The smallest rectangle which can contain non-overlapping squares of $1times1$ to $4times4$ has a size of $7times5$:

4 4 4 4 3 3 3
4 4 4 4 3 3 3
4 4 4 4 3 3 3
4 4 4 4 2 2 1
x x x x 2 2 x

Therefore, $a(4)=7times5=35$ (1-indexed).

code-golf packing

share|improve this question

edited 5 hours ago

Arnauld

83k798340

asked 6 hours ago

msh210msh210

2,3871231

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  For some reason my browser appears to be broken and I can't go to the linked website. Could you please post some examples of expected input and output? Thanks!
  $endgroup$
  – ElPedro
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I've added an example. But feel free to either rollback or edit further.
  $endgroup$
  – Arnauld
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  A couple more test cases including an odd number and a large(r) number would be useful.
  $endgroup$
  – Shaggy
  5 hours ago
  

  
  
  
  

add a comment | 

4

$begingroup$

This is a sequence question of the usual type, as applied to OEIS sequence A038666. That is, do either of the following:

• Accept no or any input, and output A038666 until the heat death of the universe.


• Accept a positive integer as input, and output the nth term of A038666 or its first n terms. (If using 0- instead of 1-indexing, then of course you also have to output 1 on 0 input.)

The nth term of A038666 is the least area among rectangles that contain nonoverlapping squares of sizes 1×1, 2×2,… n×n if you're using 1-indexing.

Example:

The smallest rectangle which can contain non-overlapping squares of $1times1$ to $4times4$ has a size of $7times5$:

4 4 4 4 3 3 3
4 4 4 4 3 3 3
4 4 4 4 3 3 3
4 4 4 4 2 2 1
x x x x 2 2 x

Therefore, $a(4)=7times5=35$ (1-indexed).

code-golf packing

share|improve this question

edited 5 hours ago

Arnauld

83k798340

asked 6 hours ago

msh210msh210

2,3871231

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  For some reason my browser appears to be broken and I can't go to the linked website. Could you please post some examples of expected input and output? Thanks!
  $endgroup$
  – ElPedro
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I've added an example. But feel free to either rollback or edit further.
  $endgroup$
  – Arnauld
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  A couple more test cases including an odd number and a large(r) number would be useful.
  $endgroup$
  – Shaggy
  5 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

This is a sequence question of the usual type, as applied to OEIS sequence A038666. That is, do either of the following:

• Accept no or any input, and output A038666 until the heat death of the universe.


• Accept a positive integer as input, and output the nth term of A038666 or its first n terms. (If using 0- instead of 1-indexing, then of course you also have to output 1 on 0 input.)

The nth term of A038666 is the least area among rectangles that contain nonoverlapping squares of sizes 1×1, 2×2,… n×n if you're using 1-indexing.

Example:

The smallest rectangle which can contain non-overlapping squares of $1times1$ to $4times4$ has a size of $7times5$:

4 4 4 4 3 3 3
4 4 4 4 3 3 3
4 4 4 4 3 3 3
4 4 4 4 2 2 1
x x x x 2 2 x

Therefore, $a(4)=7times5=35$ (1-indexed).

code-golf packing

share|improve this question

edited 5 hours ago

Arnauld

83k798340

asked 6 hours ago

msh210msh210

2,3871231

$endgroup$

4 4 4 4 3 3 3
4 4 4 4 3 3 3
4 4 4 4 3 3 3
4 4 4 4 2 2 1
x x x x 2 2 x

share|improve this question

edited 5 hours ago

Arnauld

83k798340

asked 6 hours ago

msh210msh210

2,3871231

share|improve this question

edited 5 hours ago

Arnauld

83k798340

asked 6 hours ago

msh210msh210

2,3871231

edited 5 hours ago

Arnauld

83k798340

edited 5 hours ago

Arnauld

83k798340

asked 6 hours ago

msh210msh210

2,3871231

asked 6 hours ago

msh210msh210

2,3871231

1 Answer
1

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oldest

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3

$begingroup$

JavaScript (ES6),  209  183 bytes

1-indexed.

f=(n,a,S=(n,c)=>n?c(--n)||S(n,c):0)=>S(a+1,w=>a%w?0:(F=(l,n)=>n?S(w,x=>S(h=a/w,y=>x+n>w|y+n>h|l.some(([X,Y,W])=>X<x+n&X+W>x&Y<y+n&Y+W>y)?0:F([...l,[x,y,n]],n-1))):1)([],n))?a:f(n,-~a)

Try it online!

share|improve this answer

edited 2 hours ago

answered 2 hours ago

ArnauldArnauld

83k798340

$endgroup$

add a comment | 

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3

$begingroup$

JavaScript (ES6),  209  183 bytes

1-indexed.

f=(n,a,S=(n,c)=>n?c(--n)||S(n,c):0)=>S(a+1,w=>a%w?0:(F=(l,n)=>n?S(w,x=>S(h=a/w,y=>x+n>w|y+n>h|l.some(([X,Y,W])=>X<x+n&X+W>x&Y<y+n&Y+W>y)?0:F([...l,[x,y,n]],n-1))):1)([],n))?a:f(n,-~a)

Try it online!

share|improve this answer

edited 2 hours ago

answered 2 hours ago

ArnauldArnauld

83k798340

$endgroup$

add a comment | 

3

$begingroup$

JavaScript (ES6),  209  183 bytes

1-indexed.

f=(n,a,S=(n,c)=>n?c(--n)||S(n,c):0)=>S(a+1,w=>a%w?0:(F=(l,n)=>n?S(w,x=>S(h=a/w,y=>x+n>w|y+n>h|l.some(([X,Y,W])=>X<x+n&X+W>x&Y<y+n&Y+W>y)?0:F([...l,[x,y,n]],n-1))):1)([],n))?a:f(n,-~a)

Try it online!

share|improve this answer

edited 2 hours ago

answered 2 hours ago

ArnauldArnauld

83k798340

$endgroup$

add a comment | 

$begingroup$

JavaScript (ES6),  209  183 bytes

1-indexed.

f=(n,a,S=(n,c)=>n?c(--n)||S(n,c):0)=>S(a+1,w=>a%w?0:(F=(l,n)=>n?S(w,x=>S(h=a/w,y=>x+n>w|y+n>h|l.some(([X,Y,W])=>X<x+n&X+W>x&Y<y+n&Y+W>y)?0:F([...l,[x,y,n]],n-1))):1)([],n))?a:f(n,-~a)

Try it online!

share|improve this answer

edited 2 hours ago

answered 2 hours ago

ArnauldArnauld

83k798340

$endgroup$

f=(n,a,S=(n,c)=>n?c(--n)||S(n,c):0)=>S(a+1,w=>a%w?0:(F=(l,n)=>n?S(w,x=>S(h=a/w,y=>x+n>w|y+n>h|l.some(([X,Y,W])=>X<x+n&X+W>x&Y<y+n&Y+W>y)?0:F([...l,[x,y,n]],n-1))):1)([],n))?a:f(n,-~a)

share|improve this answer

edited 2 hours ago

answered 2 hours ago

ArnauldArnauld

83k798340

answered 2 hours ago

ArnauldArnauld

83k798340

answered 2 hours ago

ArnauldArnauld

83k798340