Write a recursive program for the fake coin problem (Chapter 4 Slide 20) using a decrease by factor 3 algorithm. Make sure your program runs for all n>2. Analyze its time and space complexity. Include details/comments to explain your code/approach as I did in Quiz 2 solution (posted under Week 6 on Blackboard).

Specifically, the program will read “input.txt” that contains the weights of coins. All the weights will be identical except one of them, which is the lighter coin that is fake. The program will find the index of that coin and output it. The challenge here is to simulate a balance scale used to find the fake coin (Chapter 4 Slide 20).