2016 Update

Task/N-queens-problem/Lua/n-queens-problem.lua

@@ -1,46 +1,35 @@
 N = 8
 
-board = {}
-for i = 1, N do
-    board[i] = {}
-    for j = 1, N do
-	board[i][j] = false
-    end
+-- We'll use nil to indicate no queen is present.
+grid = {}
+for i = 0, N do
+  grid[i] = {}
 end
 
-function Allowed( x, y )
-    for i = 1, x-1 do
-	if ( board[i][y] ) or ( i <= y and board[x-i][y-i] ) or ( y+i <= N and board[x-i][y+i] ) then
-  	    return false
-	end
-    end		
-    return true
+function can_find_solution(x0, y0)
+  local x0, y0 = x0 or 0, y0 or 1  -- Set default vals (0, 1).
+  for x = 1, x0 - 1 do
+    if grid[x][y0] or grid[x][y0 - x0 + x] or grid[x][y0 + x0 - x] then
+      return false
+    end
+  end
+  grid[x0][y0] = true
+  if x0 == N then return true end
+  for y0 = 1, N do
+    if can_find_solution(x0 + 1, y0) then return true end
+  end
+  grid[x0][y0] = nil
+  return false
 end
 
-function Find_Solution( x )
-    for y = 1, N do
-	if Allowed( x, y ) then
-  	    board[x][y] = true
-	    if x == N or Find_Solution( x+1 ) then
-		return true
-	    end
-	    board[x][y] = false			
-	end		
-    end
-    return false
-end
-		
-if Find_Solution( 1 ) then
-    for i = 1, N do
- 	for j = 1, N do
-  	    if board[i][j] then
-		io.write( "|Q" )
-	    else
-		io.write( "| " )
-	    end
-	end
-	print( "|" )
+if can_find_solution() then
+  for y = 1, N do
+    for x = 1, N do
+      -- Print "|Q" if grid[x][y] is true; "|_" otherwise.
+      io.write(grid[x][y] and "|Q" or "|_")
     end
+    print("|")
+  end
 else
-    print( string.format( "No solution for %d queens.\n", N ) )
+  print(string.format("No solution for %d queens.\n", N))
 end