Constructing the largest number possible by rearranging a list

Question

Say I have an array of positive whole integers; I\'d like to manipulate the order so that the concatenation of the resultant array is the largest number possible. For exampl

Answer 1

You can do this with some clever sorting.

If two strings are the same length, choose the larger of the two to come first. Easy.

If they're not the same length, figure out what would be the result if the best possible combination were appended to the shorter one. Since everything that follows the shorter one must be equal to or less than it, you can determine this by appending the short one to itself until it's the same size as the longer one. Once they're the same length you do a direct comparison as before.

If the second comparison is equal, you've proven that the shorter string can't possibly be better than the longer one. Depending on what it's paired with it could still come out worse, so the longer one should come first.

def compare(s1, s2):
    if len(s1) == len(s2):
        return -1 if s1 > s2 else int(s2 > s1)
    s1x, s2x = s1, s2
    m = max(len(s1), len(s2))
    while len(s1x) < m:
        s1x = s1x + s1
    s1x = s1x[:m]
    while len(s2x) < m:
        s2x = s2x + s2
    s2x = s2x[:m]
    return -1 if s1x > s2x or (s1x == s2x and len(s1) > len(s2)) else 1

def solve_puzzle(seq):
    return ''.join(sorted([str(x) for x in seq], cmp=compare))

>>> solve_puzzle([9, 1, 95, 17, 5])
'9955171'
>>> solve_puzzle([97, 9, 13])
'99713'
>>> solve_puzzle([936, 21, 212])
'93621221'
>>> solve_puzzle([87, 17, 878])
'8788717'
>>> solve_puzzle([97, 9, 13, 979])
'99799713'

This should be much more efficient than running through all the permutations.