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Task/Permutations-by-swapping/Nim/permutations-by-swapping.nim

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+# iterative Boothroyd method
+iterator permutations*[T](ys: openarray[T]): tuple[perm: seq[T], sign: int] =
+  var
+    d = 1
+    c = newSeq[int](ys.len)
+    xs = newSeq[T](ys.len)
+    sign = 1
+
+  for i, y in ys: xs[i] = y
+  yield (xs, sign)
+
+  block outter:
+    while true:
+      while d > 1:
+        dec d
+        c[d] = 0
+      while c[d] >= d:
+        inc d
+        if d >= ys.len: break outter
+
+      let i = if (d and 1) == 1: c[d] else: 0
+      swap xs[i], xs[d]
+      sign *= -1
+      yield (xs, sign)
+      inc c[d]
+
+if isMainModule:
+  for i in permutations([0,1,2]):
+    echo i
+
+  echo ""
+
+  for i in permutations([0,1,2,3]):
+    echo i