find smallest number whose digits_product is equal to given number

Author: ahsankamal

beginners/digits_product.rb

@@ -0,0 +1,23 @@
+
+# Given an integer product, find the smallest positive integer the product of whose digits is equal to given product. If there is no such integer, return -1 instead.
+
+def digits_product(product)
+    digits=[]
+    if product<10
+    	return product+10
+    end
+	9.downto(2).each do |i| #find all factors starting from 9 down to 2 and then reverse them to get the smallest positive integer whose digit's product is equal to the given number
+	while product%i == 0
+		digits<<i
+		product=product/i
+	end
+end
+	if product > 10 #means given number has a prime factor greater than 10. 
+		return -1
+	end	
+	digits.reverse.join
+end
+	
+	print digits_product(100)
+	puts ""
+	print digits_product(1000)