# Backtracking to get all Letter Combinations of a Phone Number

I am currently practicing for my interview. The question that I am working on is getting all Letter Combinations of a Phone Number.

Given a string containing digits from 2-9 inclusive, return all possible letter combinations that the number could represent. A mapping of digit to letters (just like on the telephone buttons) is given below. Note that 1 does not map to any letters.

Is the problem, and the map for the digit-letter pair looks like:

nums = {
'2':'abc',
'3':'def',
'4':'ghi',
'5':'jkl',
'6':'mno',
'7':'pqrs',
'8':'tuv',
'9':'wxyz'
}

My solution to this problem looks like:

def letterCombinations(self, digits):
"""
:type digits: str
:rtype: List[str]
"""

letters = {'2':'abc', '3':'def','4':'ghi', '5':'jkl', '6':'mno', '7':'pqrs','8':'tuv', '9':'wxyz'}

def backtrack(digits, path, res):
if digits == '':
res.append(path)
return
for n in digits:
for letter in letters[n]:
path += letter
backtrack(digits[1:], path, res)
path = path[:-1]

res = []
backtrack(digits, '', res)
return res

The correct answer for the input "23" is supposed to be ["ad","ae","af","bd","be","bf","cd","ce","cf"] However, my answer looks like