Algorithm for series

Question

A, B, C,…. Z, AA, AB, ….AZ, BA,BB,…. , ZZ,AAA, …., write a function that takes a integer n and returns the string presentation. Can somebody tell me the algorithm to find the nth value in the series?

Answer 1

Treat those strings as numbers in base 26 with A=0. It's not quite an exact translation because in real base 26 A=AA=AAA=0, so you have to make some adjustments as necessary.

Here's a Java implementation:

static String convert(int n) {
    int digits = 1;
    for (int j = 26; j <= n; j *= 26) {
        digits++;
        n -= j;
    }
    String s = "";
    for (; digits --> 0 ;) {
        s = (char) ('A' + (n % 26)) + s;
        n /= 26;
    }
    return s;
}

This converts 0=A, 26=AA, 702=AAA as required.

Answer 2

Without giving away too much (since this question seems to be a homework problem), what you're doing is close to the same as translating that integer n into base 26. Good luck!

Answer 3

If, as others suspect, this is homework, then this answer probably won't be much help. If this is for a real-world project though, it might make sense to do make a generator instead, which is an easy and idiomatic thing to do in some languages, such as Python. Something like this:

def letterPattern():
    pattern = [0]
    while True:
        yield pattern
        pattern[0] += 1

        # iterate through all numbers in the list *except* the last one
        for i in range(0,len(pattern)-1):
            if pattern[i] == 26:
                pattern[i] = 0
                pattern[i+1] += 1

        # now if the last number is 26, set it to zero, and append another zero to the end
        if pattern[-1] == 26:
            pattern[-1] = 0
            pattern.append(0)

Except instead of yielding pattern itself you would reverse it, and map 0 to A, 1 to B, etc. then yield the string. I've run the code above and it seems to work, but I haven't tested it extensively at all.

I hope you'll find this readable enough to implement, even if you don't know Python. (For the Pythonistas out there, yes the "for i in range(...)" loop is ugly and unpythonic, but off the top of my head, I don't know any other way to do what I'm doing here)