Data commit

Task/Permutations-Derangements/Lua/permutations-derangements.lua

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+-- Return an iterator to produce every permutation of list
+function permute (list)
+    local function perm (list, n)
+        if n == 0 then coroutine.yield(list) end
+        for i = 1, n do
+            list[i], list[n] = list[n], list[i]
+            perm(list, n - 1)
+            list[i], list[n] = list[n], list[i]
+        end
+    end
+    return coroutine.wrap(function() perm(list, #list) end)
+end
+
+-- Return a copy of table t (wouldn't work for a table of tables)
+function copy (t)
+    if not t then return nil end
+    local new = {}
+    for k, v in pairs(t) do new[k] = v end
+    return new
+end
+
+-- Return true if no value in t1 can be found at the same index of t2
+function noMatches (t1, t2)
+    for k, v in pairs(t1) do
+        if t2[k] == v then return false end
+    end
+    return true
+end
+
+-- Return a table of all derangements of table t
+function derangements (t)
+    local orig = copy(t)
+    local nextPerm, deranged = permute(t), {}
+    local numList, keep = copy(nextPerm())
+    while numList do
+        if noMatches(numList, orig) then table.insert(deranged, numList) end
+        numList = copy(nextPerm())
+    end
+    return deranged
+end
+
+-- Return the subfactorial of n
+function subFact (n)
+    if n < 2 then
+        return 1 - n
+    else
+        return (subFact(n - 1) + subFact(n - 2)) * (n - 1)
+    end
+end
+
+-- Return a table of the numbers 1 to n
+function listOneTo (n)
+    local t = {}
+    for i = 1, n do t[i] = i end
+    return t
+end
+
+-- Main procedure
+print("Derangements of [1,2,3,4]")
+for k, v in pairs(derangements(listOneTo(4))) do print("", unpack(v)) end
+print("\n\nSubfactorial vs counted derangements\n")
+print("\tn\t| subFact(n)\t| Derangements")
+print("    " .. string.rep("-", 42))
+for i = 0, 9 do
+    io.write("\t" .. i .. "\t|  " .. subFact(i))
+    if string.len(subFact(i)) < 5 then io.write("\t") end
+    print("\t|  " .. #derangements(listOneTo(i)))
+end
+print("\n\nThe subfactorial of 20 is " .. subFact(20))