Module:JI ratios: Difference between revisions

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 	return ratios
+end
+-- Go back to having a find-products function
+function p.find_products(factors, max_product)
+	local factors = factors or { 2, 3, 5, 7, 11, 13, 17, 19 }
+	local max_product = max_product or 10000
+	-- Perform a breadth-first-search
+	-- Starting with the number 1 at the root node of a (simulated) search tree,
+	-- explore the possible products (child nodes) of multiplying that number
+	-- with exactly one each of the given factors. Any products that are less
+	-- than the max product are added to the search tree, and the search
+	-- recurses for each child node by finding its children produced by multi-
+	-- plying by one of each factor. The search on any one branch stops if the
+	-- resulting products exceed that of the max product.
+	local products = {{1}}
+	local new_products_found = true
+	while new_products_found do
+		local new_products = {}
+		for i = 1, #factors do
+			for j = 1, #products[#products] do
+				local new_product = products[#products][j] * factors[i]
+				if new_product <= max_product then
+					-- Check whether the product already exists; if not, add it
+					-- to the table of new products.
+					local product_already_added = false
+					for k = 1, #new_products do
+						product_already_added = product_already_added or new_product == new_products[k]
+						if product_already_added then break end
+					end
+					if not product_already_added then
+						table.insert(new_products, new_product)
+					end
+				end
+			end
+		end
+		if #new_products == 0 then
+			new_products_found = false
+		else
+			table.insert(products, new_products)
+		end
+	end
+	-- Consolidate and sort products
+	local consolidated_products = {}
+	for i = 1, #products do
+		for j = 1, #products[i] do
+			table.insert(consolidated_products, products[i][j])
+		end
+	end
+	products = consolidated_products
+	table.sort(products)
+	return products
 end