Create a complement of list preserving duplicate values

Question

Given list a = [1, 2, 2, 3] and its sublist b = [1, 2] find a list complementing b in such a way that sorted(a) == sorted(b + complement)

Answer 1

O(n log n)

a = [1, 2, 2, 3]
b = [1, 2]
a.sort()
b.sort()

L = []
i = j = 0
while i < len(a) and j < len(b):
    if a[i] < b[j]:
        L.append(a[i])
        i += 1
    elif a[i] > b[j]:
        L.append(b[j])
        j += 1
    else:
        i += 1
        j += 1

while i < len(a):
    L.append(a[i])
    i += 1

while j < len(b):
    L.append(b[j])
    j += 1

print(L)