You have a range of consecutive numbers, from 1 to n (inclusive). e.g. [1,2,3,4,...,n]. We would like to calculate a sum of a function across the entire range, where the function returns the product of the preceding C elements. If there are less than C previous elements, just use the available numbers. i.e. if you are processing the fourth number in the range, but C is greater than 3, then you will calculate the product using only the 3 available preceding numbers. In this situation as you move further along in this range more preceding numbers become available. A worked example follows: if n=5 and C=2, the correct products and final sum for each element of the range are: 0 + 1 + 2 + 6 + 12 = 21 The solution should be implemented in Java. Initially calculate the value where n=100 and C=10, and let us know the answer Please additionally tell us the values where n=1000000 and C=200, but only include the first 10 digits of the result in your answer. What is the algorithmic complexity of your solution? What if you needed to calculate n=10,000,000 and C=200

To test the logic run the file: ProductSumTest.java It runs the puzzle with different inputs to check the efficiency of the logic. Algorithmic complexity is O(n) in all the cases. We can also add some validation logic which is missing in this solution.

Output of the file:

sum of productElements for n = 5 and c = 2 is 21 Total time taken for n = 5 and c = 2 is 0 seconds

sum of productElements for n = 100 and c = 10 is 5139462350 Total time taken for n = 100 and c = 10 is 0 seconds

sum of productElements for n = 1000000 and c = 200 is 4876116127 Total time taken for n = 1000000 and c = 200 is 3 seconds

sum of productElements for n = 10000000 and c = 200 is 4965134354 Total time taken for n = 10000000 and c = 200 is 33 seconds