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# http://rosettacode.org/wiki/N-queens_problem
# port of the Arc solution at http://arclanguage.org/item?id=19743
# run with tracing turned on:
# ./mu --trace nqueens.mu
container square [
rank:num
file:num
]
def nqueens n:num, queens:&:list:square -> result:num, queens:&:list:square [
local-scope
load-ingredients
# if 'queens' is already long enough, print it and return
added-so-far:num <- length queens
{
done?:bool <- greater-or-equal added-so-far, n
break-unless done?
stash queens
return 1
}
# still work to do
next-rank:num <- copy 0
{
break-unless queens
first:square <- first queens
existing-rank:num <- get first, rank:offset
next-rank <- add existing-rank, 1
}
result <- copy 0
next-file:num <- copy 0
{
done?:bool <- greater-or-equal next-file, n
break-if done?
curr:square <- merge next-rank, next-file
{
curr-conflicts?:bool <- conflict? curr, queens
break-if curr-conflicts?
new-queens:&:list:square <- push curr, queens
sub-result:num <- nqueens n, new-queens
result <- add result, sub-result
}
next-file <- add next-file, 1
loop
}
]
# check if putting a queen on 'curr' conflicts with any of the existing
# queens
# assumes that 'curr' is on a non-conflicting rank, and checks for conflict
# only in files and diagonals
def conflict? curr:square, queens:&:list:square -> result:bool [
local-scope
load-ingredients
result <- conflicting-file? curr, queens
return-if result
result <- conflicting-diagonal? curr, queens
]
def conflicting-file? curr:square, queens:&:list:square -> result:bool [
local-scope
load-ingredients
curr-file:num <- get curr, file:offset
{
break-unless queens
q:square <- first queens
qfile:num <- get q, file:offset
file-match?:bool <- equal curr-file, qfile
return-if file-match?, 1/conflict-found
queens <- rest queens
loop
}
return 0/no-conflict-found
]
def conflicting-diagonal? curr:square, queens:&:list:square -> result:bool [
local-scope
load-ingredients
curr-rank:num <- get curr, rank:offset
curr-file:num <- get curr, file:offset
{
break-unless queens
q:square <- first queens
qrank:num <- get q, rank:offset
qfile:num <- get q, file:offset
rank-delta:num <- subtract qrank, curr-rank
file-delta:num <- subtract qfile, curr-file
rank-delta <- abs rank-delta
file-delta <- abs file-delta
diagonal-match?:bool <- equal rank-delta, file-delta
return-if diagonal-match?, 1/conflict-found
queens <- rest queens
loop
}
return 0/no-conflict-found
]
def main [
nqueens 4
$dump-trace [app]
]
|