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Abelian sandpile model/Identity: Difference between revisions
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1 0 1
2 1 2
</pre>
=={{header|Nim}}==
<lang Nim>
import sequtils
import strutils
type SandPile = array[3, array[3, int]]
#---------------------------------------------------------------------------------------------------
iterator neighbors(i, j: int): tuple[a, b: int] =
## Yield the indexes of the neighbours of cell at indexes (i, j).
if i > 0:
yield (i - 1, j)
if i < 2:
yield (i + 1, j)
if j > 0:
yield (i, j - 1)
if j < 2:
yield (i, j + 1)
#---------------------------------------------------------------------------------------------------
proc print(s: openArray[SandPile]) =
## Print a list of sandpiles.
for i in 0..2:
for n, sp in s:
if n != 0:
stdout.write(if i == 1: " ⇨ " else: " ")
stdout.write(sp[i].join(" "))
stdout.write('\n')
#---------------------------------------------------------------------------------------------------
proc printSum(s1, s2, s3: SandPile) =
## Print "s1 + s2 = s3".
for i in 0..2:
stdout.write(s1[i].join(" "))
stdout.write(if i == 1: " + " else: " ", s2[i].join(" "))
stdout.write(if i == 1: " = " else: " ", s3[i].join(" "))
stdout.write('\n')
#---------------------------------------------------------------------------------------------------
func isStable(sandPile: SandPile): bool =
## Return true if the sandpile is stable, else false.
result = true
for row in sandPile:
if row.anyit(it > 3):
return false
#---------------------------------------------------------------------------------------------------
proc topple(sandPile: var SandPile) =
## Eliminate one value > 3, propagating a grain to each neighbor.
for i, row in sandPile:
for j, val in row:
if val > 3:
dec sandPile[i][j], 4
for (i, j) in neighbors(i, j):
inc sandPile[i][j]
return
#---------------------------------------------------------------------------------------------------
proc stabilize(sandPile: var SandPile) =
## Stabilize a sandpile.
while not sandPile.isStable():
sandPile.topple()
#---------------------------------------------------------------------------------------------------
proc `+`(s1, s2: SandPile): SandPile =
## Add two sandpiles, stabilizing the result.
for row in 0..2:
for col in 0..2:
result[row][col] = s1[row][col] + s2[row][col]
result.stabilize()
#---------------------------------------------------------------------------------------------------
const Separator = "\n-----\n"
echo "Avalanche\n"
var s: SandPile = [[4, 3, 3], [3, 1, 2], [0, 2, 3]]
var list = @[s]
while not s.isStable():
s.topple()
list.add(s)
list.print()
echo Separator
echo "s1 + s2 == s2 + s1\n"
let s1 = [[1, 2, 0], [2, 1, 1], [0, 1, 3]]
let s2 = [[2, 1, 3], [1, 0, 1], [0, 1, 0]]
printSum(s1, s2, s1 + s2)
echo ""
printSum(s2, s1, s2 + s1)
echo Separator
echo "s3 + s3_id == s3\n"
let s3 = [[3, 3, 3], [3, 3, 3], [3, 3, 3]]
let s3_id = [[2, 1, 2], [1, 0, 1], [2, 1, 2]]
printSum(s3, s3_id, s3 + s3_id)
echo Separator
echo "s3_id + s3_id = s3_id\n"
printSum(s3_id, s3_id, s3_id + s3_id)
</lang>
{{out}}
<pre>
Avalanche
4 3 3 0 4 3 1 0 4 1 1 0 2 1 0
3 1 2 ⇨ 4 1 2 ⇨ 4 2 2 ⇨ 4 2 3 ⇨ 0 3 3
0 2 3 0 2 3 0 2 3 0 2 3 1 2 3
-----
s1 + s2 == s2 + s1
1 2 0 2 1 3 3 3 3
2 1 1 + 1 0 1 = 3 1 2
0 1 3 0 1 0 0 2 3
2 1 3 1 2 0 3 3 3
1 0 1 + 2 1 1 = 3 1 2
0 1 0 0 1 3 0 2 3
-----
s3 + s3_id == s3
3 3 3 2 1 2 3 3 3
3 3 3 + 1 0 1 = 3 3 3
3 3 3 2 1 2 3 3 3
-----
s3_id + s3_id = s3_id
2 1 2 2 1 2 2 1 2
1 0 1 + 1 0 1 = 1 0 1
2 1 2 2 1 2 2 1 2
</pre>
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