Data commit

Task/N-queens-problem/Jq/n-queens-problem-1.jq

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+def single_solution_queens(n):
+  def q: "♛";
+  def init(k): reduce range(0;k) as $i ([]; . + ["."]);
+  def matrix(k): init(k) as $row | reduce range(0;k) as $i ([]; . + [$row]);
+  def place(stream; i; j):
+    # jq indexing is based on offsets but we are using the 1-based formulae:
+    reduce stream as $s (.; setpath([-1+($s|i), -1+($s|j)]; q) );
+  def even(k):
+    if ((k-2) % 6) != 0 then
+         place( range(1; 1+(k/2));         .; 2*. )
+       | place( range(1; 1+(k/2)); (k/2) + .; 2*. -1 )
+    else place( range(1; 1+(k/2));         .; 1 + ((2*. + (k/2) - 3) % k))
+       | place( range(1; 1+(n/2)); n + 1 - .; n - ((2*. + (n/2) - 3) % n))
+    end;
+
+  matrix(n)                          # the chess board
+  | if (n % 2) == 0 then even(n)
+    else even(n-1) | .[n-1][n-1] = q
+    end;
+
+# Example:
+def pp: reduce .[] as $row
+  ("";  reduce $row[] as $x (.; . + $x) + "\n");
+
+single_solution_queens(8) | pp

Task/N-queens-problem/Jq/n-queens-problem-2.jq

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+...♛....
+.....♛..
+.......♛
+.♛......
+......♛.
+♛.......
+..♛.....
+....♛...

Task/N-queens-problem/Jq/n-queens-problem-3.jq

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+# permutations of 0 .. (n-1)
+def permutations(n):
+  # Given a single array, generate a stream by inserting n at different positions:
+  def insert(m;n):
+     if m >= 0 then (.[0:m] + [n] + .[m:]), insert(m-1;n) else empty end;
+
+  if n==0 then []
+  elif n == 1 then [1]
+  else
+    permutations(n-1) | insert(n-1; n)
+  end;
+
+def count(g): reduce g as $i (0; .+1);

Task/N-queens-problem/Jq/n-queens-problem-4.jq

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+def queens(n):
+  def sums:
+  . as $board
+  | [ range(0;length) | . + $board[.]]
+  | unique | length;
+
+  def differences:
+  . as $board
+  | [ range(0;length) | . - $board[.]]
+  | unique | length;
+
+  def allowable:
+    length as $n
+    | sums == $n and differences == $n;
+
+  count( permutations(n) | select(allowable) );

Task/N-queens-problem/Jq/n-queens-problem-5.jq

@@ -0,0 +1 @@
+queens(8)