Telephone Words

Write a function that takes a seven-digit telephone number and prints out all of the possible "words" or combinations of letters that can represent the give number. 

Recursive Solution

• If we've passed 7 digits, print out our current number. Other wise, loop through each letter associated with the current digit, save the current digit in position, and then recurse.

If you want to instead return the values instead of merely printing them, you would want to maintain a running list of all the numbers that grows as the functions "unwind". 

Iterative Solutions

1. Just use 7 for loops :)

for ...

    for ...

        for ...

            :(

1. If you write out a bunch of combinations for a number by going from left to right, you'll notice that as the last digit cycles, the digit to its left also cycles. 

For example, lets say we're only dealing with three sets of characters: [[a,b,c],[d,e,f],[g,h,j]]. Our pattern will be as follows:

a,d,g

a,d,h

a,d,j

a,e,g

a,e,h

a,e,j

a,f,g

a,f,h

a,f,j

b,d,g

...

As you can see, after we go through [g,h,j] at the end once, the previous numbers letter changes from a higher value to a lower value (d to e). We can take advantage of this simply by starting out with a word, say "a,d,g". Then we'll change "g" to "h" and print. Then change "h" to "j" and print. And then since we've gone through a full cycle, we'll reset it back to zero and then change our neighbor to be a higher value ("e"). The trick here is updating the counters for each position correctly (like when [d,e,f] is cycled through, its neighbor is updated.