September 2017 Update

Task/Evaluate-binomial-coefficients/Lua/evaluate-binomial-coefficients-2.lua

@@ -0,0 +1,30 @@
+local Binomial = setmetatable({},{
+ __call = function(self,n,k)
+   local hash = (n<<32) | (k & 0xffffffff)
+   local ans = self[hash]
+   if not ans then
+    if n<0 or k>n then
+      return 0 -- not save
+    elseif n<=1 or k==0 or k==n then
+      ans = 1
+    else
+      if 2*k > n then
+        ans = self(n, n - k)
+      else
+        local lhs = self(n-1,k)
+        local rhs = self(n-1,k-1)
+        local sum = lhs + rhs
+        if sum<0 or not math.tointeger(sum)then
+          -- switch to double
+          ans = lhs/1.0 + rhs/1.0 -- approximate
+        else
+          ans = sum
+        end
+      end
+    end
+    rawset(self,hash,ans)
+   end
+   return ans
+ end
+})
+print( Binomial(100,50)) -- 1.0089134454556e+029