September 2017 Update

Task/Ordered-Partitions/Jq/ordered-partitions-1.jq

@@ -0,0 +1,20 @@
+# Generate a stream of the distinct combinations of r items taken from the input array.
+def combination(r):
+  if r > length or r < 0 then empty
+  elif r == length then .
+  else  ( [.[0]] + (.[1:]|combination(r-1))),
+        ( .[1:]|combination(r))
+  end;
+
+# Input: a mask, that is, an array of lengths.
+# Output: a stream of the distinct partitions defined by the mask.
+def partition:
+
+  # partition an array of entities, s, according to a mask presented as input:
+  def p(s):
+    if length == 0 then []
+    else . as $mask
+    | (s | combination($mask[0])) as $c
+    | [$c] + ($mask[1:] | p(s - $c))
+    end;
+ . as $mask | p( [range(1; 1 + ($mask|add))] );

Task/Ordered-Partitions/Jq/ordered-partitions-2.jq

@@ -0,0 +1,3 @@
+([],[0,0,0],[1,1,1],[2,0,2])
+  | . as $test_case
+  |  "partitions \($test_case):" , ($test_case | partition), ""

Task/Ordered-Partitions/Jq/ordered-partitions-3.jq

@@ -0,0 +1,23 @@
+$ jq -M -n -c -r -f Ordered_partitions.jq
+
+partitions []:
+[]
+
+partitions [0,0,0]:
+[[],[],[]]
+
+partitions [1,1,1]:
+[[1],[2],[3]]
+[[1],[3],[2]]
+[[2],[1],[3]]
+[[2],[3],[1]]
+[[3],[1],[2]]
+[[3],[2],[1]]
+
+partitions [2,0,2]:
+[[1,2],[],[3,4]]
+[[1,3],[],[2,4]]
+[[1,4],[],[2,3]]
+[[2,3],[],[1,4]]
+[[2,4],[],[1,3]]
+[[3,4],[],[1,2]]