calculate-fibonacci-return-count-of-digit-occurrences

Calculate Fibonacci return count of digit occurrences

Fibonacci numbers are generated by setting F₀ = 0, F₁ = 1, and then using the formula:

F_n = F_n-1 + F_n-2

Your task is to efficiently calculate the nth element in the Fibonacci sequence and then count the occurrence of each digit in the number. Return a list of integer pairs sorted in descending order.

10 ≤ n ≤ 100000

Examples

f(10) = 55  # returns [(2, 5)], as there are two occurances of digit 5

f(10000)    # returns:
  [(254, 3),
   (228, 2),
   (217, 6),
   (217, 0),
   (202, 5),
   (199, 1),
   (198, 7),
   (197, 8),
   (194, 4),
   (184, 9)]

If two integers have the same count, sort them in descending order.

Your algorithm must be efficient.