palindrome.py

def ingest(s):
    counts = {}
    for c in s:
        if not c in counts:
            counts[c] = 0
        counts[c] += 1
    return counts

import math

def run(count_dict, middle_char = ""):
    # Sort by count
    item_list = list(count_dict.items())
    item_list.sort(key=lambda a: a[1], reverse=True)

    # Starting from the lowest ordered (most common) pair,
    # build the rest of the palindrome
    output = ""
    for char,count in item_list:
        # Less than 2 of this char left
        if count < 2:
            continue
        
        output += char * math.floor(count / 2) 

    # Assemble the two halves
    return output[::-1] + middle_char + output

count_dict = ingest("sexytimes")

# Find the highest ordered (least common) single
# to start with as the middle character
singles = [(char,count) for (char,count) in count_dict.items() if count % 2 == 1]
singles.sort(key=lambda a: a[1])

if len(singles) > 0:
    result = run(count_dict, middle_char=singles[0][0])
else:
    result = run(count_dict)

result