1 # http://rosettacode.org/wiki/N-queens_problem
  2 # port of the Arc solution at http://arclanguage.org/item?id=19743
  3 # run with tracing turned on:
  4 #   ./mu --trace nqueens.mu
  5 
  6 container square [
  7   rank:num
  8   file:num
  9 ]
 10 
 11 def nqueens n:num, queens:&:list:square -> result:num, queens:&:list:square [
 12   local-scope
 13   load-ingredients
 14   # if 'queens' is already long enough, print it and return
 15   added-so-far:num <- length queens
 16   {
 17   ¦ done?:bool <- greater-or-equal added-so-far, n
 18   ¦ break-unless done?
 19   ¦ stash queens
 20   ¦ return 1
 21   }
 22   # still work to do
 23   next-rank:num <- copy 0
 24   {
 25   ¦ break-unless queens
 26   ¦ first:square <- first queens
 27   ¦ existing-rank:num <- get first, rank:offset
 28   ¦ next-rank <- add existing-rank, 1
 29   }
 30   result <- copy 0
 31   next-file:num <- copy 0
 32   {
 33   ¦ done?:bool <- greater-or-equal next-file, n
 34   ¦ break-if done?
 35   ¦ curr:square <- merge next-rank, next-file
 36   ¦ {
 37   ¦ ¦ curr-conflicts?:bool <- conflict? curr, queens
 38   ¦ ¦ break-if curr-conflicts?
 39   ¦ ¦ new-queens:&:list:square <- push curr, queens
 40   ¦ ¦ sub-result:num <- nqueens n, new-queens
 41   ¦ ¦ result <- add result, sub-result
 42   ¦ }
 43   ¦ next-file <- add next-file, 1
 44   ¦ loop
 45   }
 46 ]
 47 
 48 # check if putting a queen on 'curr' conflicts with any of the existing
 49 # queens
 50 # assumes that 'curr' is on a non-conflicting rank, and checks for conflict
 51 # only in files and diagonals
 52 def conflict? curr:square, queens:&:list:square -> result:bool [
 53   local-scope
 54   load-ingredients
 55   result <- conflicting-file? curr, queens
 56   return-if result
 57   result <- conflicting-diagonal? curr, queens
 58 ]
 59 
 60 def conflicting-file? curr:square, queens:&:list:square -> result:bool [
 61   local-scope
 62   load-ingredients
 63   curr-file:num <- get curr, file:offset
 64   {
 65   ¦ break-unless queens
 66   ¦ q:square <- first queens
 67   ¦ qfile:num <- get q, file:offset
 68   ¦ file-match?:bool <- equal curr-file, qfile
 69   ¦ return-if file-match?, 1/conflict-found
 70   ¦ queens <- rest queens
 71   ¦ loop
 72   }
 73   return 0/no-conflict-found
 74 ]
 75 
 76 def conflicting-diagonal? curr:square, queens:&:list:square -> result:bool [
 77   local-scope
 78   load-ingredients
 79   curr-rank:num <- get curr, rank:offset
 80   curr-file:num <- get curr, file:offset
 81   {
 82   ¦ break-unless queens
 83   ¦ q:square <- first queens
 84   ¦ qrank:num <- get q, rank:offset
 85   ¦ qfile:num <- get q, file:offset
 86   ¦ rank-delta:num <- subtract qrank, curr-rank
 87   ¦ file-delta:num <- subtract qfile, curr-file
 88   ¦ rank-delta <- abs rank-delta
 89   ¦ file-delta <- abs file-delta
 90   ¦ diagonal-match?:bool <- equal rank-delta, file-delta
 91   ¦ return-if diagonal-match?, 1/conflict-found
 92   ¦ queens <- rest queens
 93   ¦ loop
 94   }
 95   return 0/no-conflict-found
 96 ]
 97 
 98 def main [
 99   nqueens 4
100   $dump-trace [app]
101 ]