telephoneWords problem
Given a list of integers, print out all possible words that can be spelled by using the telephone letter mapping.
For example, telephoneWords([2,5]) would print out: AJ, AK, AL, BJ, BK, BL, CJ, CK, CL
I've written a step by step guide below to my solution below.
I found it helpful to think of all letter combinations in a tree like structure.
Steps
The solution is written in JavaScript. I've used the Mocha and Chai testing suites.
Step 1: Create a 'library' object that associates phone digits to their letters
var library = { "1": [], "2": ['A','B','C'], "3": ['D', 'E', 'F'], "4": ['G', 'H', 'I'], "5": ['J', 'K', 'L'], "6": ['M', 'N', 'O'], "7": ['P', 'Q', 'R', 'S'], "8": ['T', 'U', 'V'], "9": ['W', 'X', 'Y', 'Z'] };
Step 2: Add letters associated with the first input integer straight away.
var output = library[integerArray[0].toString()];
Step 3: Iterate through input array of integers.
- for each of the letters arrays (correspondingLettersArray)
- make a copy of where the output array is up to (oldOutput)
- iterate through oldOutput array
- add the letter we are up to in correspondingLettersArray to the end of each block in oldOutput array
- push the new block to a new array called newOutput
- set output to newOutput
- return output
Time Complexity Discussion
The time complexity of the telephoneWords algorithm is kind of weird to consider.
- We iterate through the input array once.
- Inside this loop we iterate through the output array which grows as the program runs. The output array triples (or 4x if the button pressed is 7 or 9) in length every time we increment in the outer loop.
This makes the time complexity of the algorithm exponential.
Get in touch
If you can spot any bugs in the code, or untrue statements in the read me, please make an issue on this repo.