Recursive Python Program to Merge Three Sorted Lists

Question

Write a purely recursive Python function called Merge3 that takes three lists of numbers each sorted in increasing order as input and outputs a single sorted list by merging elements from the three lists in proper increasing order. For example, Merge3([1,2,72,108],[3,4,94,103],[45,67,456]) should return a list [1,2,3,4,45,67,72,94,103,108,456] .

I was able to write a version for two lists, but I'm struggling to come up with a compact way to do this for three lists. See my example below:

def Merge2(A, B):
  if A == []:
    return B
  if B == []:
    return A
  if A != [] and B != []:
    if A[0] > B[0]:
      return [B[0]] + Merge(A, B[1:])
    else:
      return [A[0]] + Merge(A[1:], B)

print(Merge2([1, 2, 6, 7],[3, 4, 8, 9]))

Is there an easy way to do this for three lists that I'm missing? I feel like it's going to require a lot of additional checking that will make the program fairly long. Can you come up with a concise way to do this for three lists?

Answer 1

An easy way to solve this is to reuse Merge2 that you already have:

def Merge3(A, B, C):
    return Merge2(Merge2(A, B), C)

Answer 2

janos's answer for Merge3 is perfect. I did want to offer you an improvement on Merge2 however -

def Merge2(A, B):
  if not A:
    return B
  elif not B:
    return A
  elif A[0] > B[0]:
    return [B[0]] + Merge2(A, B[1:])
  else:
    return [A[0]] + Merge2(A[1:], B)

print(Merge2([1, 2, 6, 7],[3, 4, 8, 9, 11, 13]))
# [1, 2, 3, 4, 6, 7, 8, 9, 11, 13]