Data update

Task/Padovan-sequence/Lua/padovan-sequence.lua

@@ -0,0 +1,72 @@
+-- Define the constants
+local p = 1.32471795724474602596
+local s = 1.0453567932525329623
+
+
+-- Generator for the Padovan sequence using coroutines
+function pad_recur_gen(n)
+    local co = coroutine.create(function ()
+        local p = {1, 1, 1, 2}
+        for i = 1, n do
+            local next_val = p[2] + p[3]
+            coroutine.yield(p[1])
+            table.remove(p, 1)
+            table.insert(p, next_val)
+        end
+    end)
+    return function ()   -- iterator
+        local status, value = coroutine.resume(co)
+        return value
+    end
+end
+
+-- Padovan floor function
+function pad_floor(index)
+    if index < 3 then
+        return math.floor(1/2 + p)
+    else
+        return math.floor(1/2 + p^(index - 2) / s)
+    end
+end
+
+local l, m, n = 10, 20, 32
+
+local pr = {}
+local pad_recur = pad_recur_gen(n)
+for i = 1, n do
+    pr[i] = pad_recur()
+end
+for i = 1, m do
+    io.write(pr[i] .. ' ')
+end
+io.write('\n')
+
+local pf = {}
+for i = 1, n do
+    pf[i] = pad_floor(i)
+end
+for i = 1, m do
+    io.write(pf[i] .. ' ')
+end
+io.write('\n')
+
+local L = {'A'}
+local rules = { A = 'B', B = 'C', C = 'AB' }
+for i = 1, n do
+    local next_str = ''
+    for char in L[#L]:gmatch('.') do
+        next_str = next_str .. rules[char]
+    end
+    table.insert(L, next_str)
+end
+for i = 1, l do
+    io.write(L[i] .. ' ')
+end
+io.write('\n')
+
+for i = 1, n do
+    assert(pr[i] == pf[i] and pr[i] == #L[i],
+           "Uh oh, n=" .. i .. ": " .. pr[i] .. " vs " .. pf[i] .. " vs " .. #L[i])
+end
+
+print('100% agreement among all 3 methods.')