September 2017 Update

Task/Set/Jq/set-1.jq

@@ -0,0 +1,2 @@
+{"a":true, "b":true } == {"b":true, "a":true}.
+{"a":true} + {"b":true } == { "a":true, "b":true}

Task/Set/Jq/set-10.jq

@@ -0,0 +1,19 @@
+# If A and B are sets, then A-B is emitted
+def difference(A;B):
+  (A|length) as $al
+  | (B|length) as $bl
+  | if $al == 0 then [] elif $bl == 0 then A
+    else
+      reduce range(0; $al + $bl) as $k
+        ( [0, 0, []];
+          .[0] as $i | .[1] as $j
+          | if $i < $al and $j < $bl then
+              if A[$i] == B[$j] then [ $i+1, $j+1,  .[2] ]
+              elif  A[$i] < B[$j] then [ $i+1, $j, .[2] + [A[$i]] ]
+              else [ $i , $j+1, .[2] ]
+              end
+            elif $i < $al then [ $i+1, $j,  .[2] + [A[$i]] ]
+            else .
+            end
+         ) | .[2]
+    end ;

Task/Set/Jq/set-11.jq

@@ -0,0 +1,22 @@
+# merge input array with array x by comparing the heads of the arrays in turn;
+# if both arrays are sorted, the result will be sorted:
+def merge(x):
+  length as $length
+  | (x|length) as $xl
+  | if $length == 0 then x
+    elif $xl == 0 then .
+    else
+      . as $in
+      | reduce range(0; $xl + $length) as $z
+         # state [ix, xix, ans]
+         ( [0, 0, []];
+           if .[0] < $length and ((.[1] < $xl and $in[.[0]] <= x[.[1]]) or .[1] == $xl)
+           then [(.[0] + 1), .[1], (.[2] + [$in[.[0]]]) ]
+           else [.[0], (.[1] + 1), (.[2] + [x[.[1]]]) ]
+           end
+         ) | .[2]
+    end ;
+
+def union(A;B):
+  A|merge(B)
+  | reduce .[] as $m ([]; if length == 0 or .[length-1] != $m then . + [$m] else . end);

Task/Set/Jq/set-12.jq

@@ -0,0 +1,10 @@
+def subset(A;B):
+  # TCO
+  def _subset:
+    if .[0]|length == 0 then true
+    elif .[1]|length == 0 then false
+    elif .[0][0] == .[1][0] then [.[0][1:], .[1][1:]] | _subset
+    elif .[0][0] < .[1][0] then false
+    else [ .[0], .[1][1:] ] | _subset
+    end;
+  [A,B] | _subset;

Task/Set/Jq/set-13.jq

@@ -0,0 +1,11 @@
+def intersect:
+ .[0] as $A  | .[1] as $B
+ | ($A|length) as $al
+  | ($B|length) as $bl
+  | if $al == 0 or $bl == 0 then false
+    else
+      ($B | bsearch($A[0])) as $b
+      | if $b >= 0 then true
+        else [$A[1:], $B[- (1 + $b) :]] | intersect
+        end
+    end;

Task/Set/Jq/set-2.jq

@@ -0,0 +1,2 @@
+def is_stringset:
+  . as $in | type == "object" and reduce keys[] as $key (true; . and $in[$key] == true);

Task/Set/Jq/set-3.jq

@@ -0,0 +1 @@
+T | has(m)

Task/Set/Jq/set-4.jq

@@ -0,0 +1,4 @@
+# Set-intersection: A ∩ B
+def stringset_intersection(A;B):
+  reduce (A|keys)[] as $k
+    ({}; if (B|has($k)) then . + {($k):true} else . end);

Task/Set/Jq/set-5.jq

@@ -0,0 +1,4 @@
+# stringset_difference: A \ B
+def stringset_difference(A;B):
+  reduce (A|keys)[] as $k
+    ({}; if (B|has($k)) then . else . + {($k):true} end);

Task/Set/Jq/set-6.jq

@@ -0,0 +1,4 @@
+# A ⊆ B iff string_subset(A;B)
+def stringset_subset(A;B):
+  reduce (A|keys)[] as $k
+    (true; . and (B|has($k)));

Task/Set/Jq/set-7.jq

@@ -0,0 +1,5 @@
+def is_set:
+  . as $in
+  | type == "array" and
+    reduce range(0;length-1) as $i
+      (true; if . then $in[$i] < $in[$i+1] else false end);

Task/Set/Jq/set-8.jq

@@ -0,0 +1 @@
+def is_member(m):  bsearch(m) > -1;

Task/Set/Jq/set-9.jq

@@ -0,0 +1,18 @@
+# If A and B are sets, then intersection(A;B) emits their intersection:
+def intersection(A;B):
+  (A|length) as $al
+  | (B|length) as $bl
+  | if $al == 0 or $bl == 0 then []
+    else
+      reduce range(0; $al + $bl) as $k
+        ( [0, 0, []];
+          .[0] as $i | .[1] as $j
+          | if $i < $al and $j < $bl then
+              if A[$i] == B[$j] then [ $i+1 , $j+1,  .[2] + [A[$i]]]
+              elif  A[$i] < B[$j] then [ $i+1 , $j,  .[2] ]
+              else [ $i , $j+1,  .[2] ]
+              end
+            else .
+            end
+         ) | .[2]
+    end ;