Given a collection of amount values $($A$)$ and a target sum $($S$),$ find all unique combinations in$$ A where the amount values sum up to S$.$ Return these combinations in the form of a list. Each amount value may be used only the number of times it occurs in list A$.$ The solution set$$ should not contain duplicate combinations. Amounts will be positive numbers. Return an empty list if no possible solution exists.$$

Example: A $=[11,1,3,2,6,1,5]$; Target Sum $=8$

Result $=[[3,5],[2,6],[1,2,5],[1,1,6]]$

a$.$ Describe a backtracking algorithm to solve this problem.$$

b$.$ Implement the solution in a function amount$($A$,$ S$).$ Name your file Amount.py c$.$ What is the time complexity of your implementation, you may find time complexity in$$ detailed or state whether it is linear$/$polynomial$/$exponential$.$ etc.?