Permutations of English Alphabet of a given length

Question

So I have this code. Not sure if it works because the runtime for the program is still continuing.

void permute(std::vector<std::string>& wordsVector, std::string prefix, int     length, std::string alphabet) {
if (length == 0) {
    //end the recursion
    wordsVector.push_back(prefix);
}
else {
    for (int i = 0; i < alphabet.length(); ++i) {
        permute(wordsVector, prefix + alphabet.at(i), length - 1, alphabet);
    }
}}

where I'm trying to get all combinations of characters in the English alphabet of a given length. I'm not sure if the approach is correct at the moment.

Alphabet consists of A-Z in a string of length 26. WordsVectors holds all the different combinations of words. prefix is meant to pass through recursively until a word is made and length is self explanatory.

Example, if I give the length of 7 to the function, I expect a size of 26 x 25 x 24 x 23 x 22 x 21 x 20 = 3315312000 if I'm correct, following the formula for permutations. I don't think programs are meant to run this long so either I'm hitting an infinite loop or something is wrong with my approach. Please advise. Thanks.

Answer 1

Surely the stack would overflow but concentrating on your question even if you write an iterative program it will take a long time ( not an infinite loop just very long )

[26L, 650L, 15600L, 358800L, 7893600L, 165765600L, 3315312000L, 62990928000L, 1133836704000L, 19275223968000L, 308403583488000L, 4626053752320000L, 64764752532480000L, 841941782922240000L, 10103301395066880000L, 111136315345735680000L, 1111363153457356800000L, 10002268381116211200000L, 80018147048929689600000L, 560127029342507827200000L, 3360762176055046963200000L, 16803810880275234816000000L, 67215243521100939264000000L, 201645730563302817792000000L, 403291461126605635584000000L, 403291461126605635584000000L]

The above list is the number of possibilities for 1<=n<=26. You can see as n increases number of possibilities increases tremendously. Say you have 1GHz processor that does 10^9 operations per second. Say consider number of possibilities for n=26 its 403291461126605635584000000L. Its evident that if you sit down to list all possibilities its so so long ( so so many years ) that you will feel it has hit an infinite loop. Finally I have not looked that closely into your code , but in nutshell even if you write it correctly,iteratively and don't store (again can't have this much memory) and just print all possibilities its going to take long time for larger values of n.

EDIT

As jaromax and others said if you just want to write it for smaller values of n, say less than 10-12 you can write an iterative program to list/print them. It will run quite fast for small values. But if you also want to store them them then n will have to be say less than 5 say. (Really depends on how much RAM is available or you could find some permutations write them to disk, then depends on how much disk memory you can spare, again refer the number of possibilities list I posted above. It gives a rough idea of both time and space complexity).