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Fraction reduction: Difference between revisions
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%%%mzn-stat: nSolutions=5087
</pre>
=={{header|Nim}}==
{{trans|Phix}}
<lang Nim>
# Fraction reduction.
import strformat
import times
type Result = tuple[n: int, nine: array[1..9, int]]
template find[T; N: static int](a: array[1..N, T]; value: T): int =
## Return the one-based index of a value in an array.
## This is needed as "system.find" returns a 0-based index even if the
## array lower bound is not null.
system.find(a, value) + 1
func toNumber(digits: seq[int]; removeDigit: int = 0): int =
## Convert a list of digits into a number.
var digits = digits
if removeDigit != 0:
let idx = digits.find(removeDigit)
digits.delete(idx)
for d in digits:
result = 10 * result + d
func nDigits(n: int): seq[Result] =
var digits = newSeq[int](n + 1) # Allocating one more to work with one-based indexes.
var used: array[1..9, bool]
for i in 1..n:
digits[i] = i
used[i] = true
var terminated = false
while not terminated:
var nine: array[1..9, int]
for i in 1..9:
if used[i]:
nine[i] = digits.toNumber(i)
result &= (n: digits.toNumber(), nine: nine)
block searchLoop:
terminated = true
for i in countdown(n, 1):
let d = digits[i]
doAssert(used[d], "Encountered an inconsistency with 'used' array")
used[d] = false
for j in (d + 1)..9:
if not used[j]:
used[j] = true
digits[i] = j
for k in (i + 1)..n:
digits[k] = used.find(false)
used[digits[k]] = true
terminated = false
break searchLoop
let start = gettime()
for n in 2..6:
let rs = nDigits(n)
var count = 0
var omitted: array[1..9, int]
for i in 1..<rs.high:
let (xn, rn) = rs[i]
for j in (i + 1)..rs.high:
let (xd, rd) = rs[j]
for k in 1..9:
let yn = rn[k]
let yd = rd[k]
if yn != 0 and yd != 0 and xn * yd == yn * xd:
inc count
inc omitted[k]
if count <= 12:
echo &"{xn}/{xd} => {yn}/{yd} (removed {k})"
echo &"{n}-digit fractions found: {count}, omitted {omitted}\n"
echo &"Took {gettime() - start}"
</lang>
=={{header|Pascal}}==
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