Algorithm to generate all variants of a word - algorithm

Question

i would like to explain my problem by the following example.
assume the word: abc
a has variants: ä, à
b has no variants.
c has variants: ç
so the possible words are:
abc
äbc
àbc
abç
äbç
àbç
now i am looking for the algorithm that prints all word variantions for abritray words with arbitray lettervariants.

Answer 1

I would recommend you to solve this recursively. Here's some Java code for you to get started:
static Map<Character, char[]> variants = new HashMap<Character, char[]>() {{
put('a', new char[] {'ä', 'à'});
put('b', new char[] { });
put('c', new char[] { 'ç' });
}};
public static Set<String> variation(String str) {
Set<String> result = new HashSet<String>();
if (str.isEmpty()) {
result.add("");
return result;
}
char c = str.charAt(0);
for (String tailVariant : variation(str.substring(1))) {
result.add(c + tailVariant);
for (char variant : variants.get(c))
result.add(variant + tailVariant);
}
return result;
}
Test:
public static void main(String[] args) {
for (String str : variation("abc"))
System.out.println(str);
}
Output:
abc
àbç
äbc
àbc
äbç
abç

Answer 2

A quickly hacked solution in Python:
def word_variants(variants):
print_variants("", 1, variants);
def print_variants(word, i, variants):
if i > len(variants):
print word
else:
for variant in variants[i]:
print_variants(word + variant, i + 1, variants)
variants = dict()
variants[1] = ['a0', 'a1', 'a2']
variants[2] = ['b0']
variants[3] = ['c0', 'c1']
word_variants(variants)

Answer 3

Common part:
string[] letterEquiv = { "aäà", "b", "cç", "d", "eèé" };
// Here we make a dictionary where the key is the "base" letter and the value is an array of alternatives
var lookup = letterEquiv
.Select(p => p.ToCharArray())
.SelectMany(p => p, (p, q) => new { key = q, values = p }).ToDictionary(p => p.key, p => p.values);
A recursive variation written in C#.
List<string> resultsRecursive = new List<string>();
// I'm using an anonymous method that "closes" around resultsRecursive and lookup. You could make it a standard method that accepts as a parameter the two.
// Recursive anonymous methods must be declared in this way in C#. Nothing to see.
Action<string, int, char[]> recursive = null;
recursive = (str, ix, str2) =>
{
// In the first loop str2 is null, so we create the place where the string will be built.
if (str2 == null)
{
str2 = new char[str.Length];
}
// The possible variations for the current character
var equivs = lookup[str[ix]];
// For each variation
foreach (var eq in equivs)
{
// We save the current variation for the current character
str2[ix] = eq;
// If we haven't reached the end of the string
if (ix < str.Length - 1)
{
// We recurse, increasing the index
recursive(str, ix + 1, str2);
}
else
{
// We save the string
resultsRecursive.Add(new string(str2));
}
}
};
// We launch our function
recursive("abcdeabcde", 0, null);
// The results are in resultsRecursive
A non-recursive version
List<string> resultsNonRecursive = new List<string>();
// I'm using an anonymous method that "closes" around resultsNonRecursive and lookup. You could make it a standard method that accepts as a parameter the two.
Action<string> nonRecursive = (str) =>
{
// We will have two arrays, of the same length of the string. One will contain
// the possible variations for that letter, the other will contain the "current"
// "chosen" variation of that letter
char[][] equivs = new char[str.Length][];
int[] ixes = new int[str.Length];
for (int i = 0; i < ixes.Length; i++)
{
// We start with index -1 so that the first increase will bring it to 0
equivs[i] = lookup[str[i]];
ixes[i] = -1;
}
// The current "workin" index of the original string
int ix = 0;
// The place where the string will be built.
char[] str2 = new char[str.Length];
// The loop will break when we will have to increment the letter with index -1
while (ix >= 0)
{
// We select the next possible variation for the current character
ixes[ix]++;
// If we have exausted the possible variations of the current character
if (ixes[ix] == equivs[ix].Length)
{
// Reset the current character to -1
ixes[ix] = -1;
// And loop back to the previous character
ix--;
continue;
}
// We save the current variation for the current character
str2[ix] = equivs[ix][ixes[ix]];
// If we are setting the last character of the string, then the string
// is complete
if (ix == str.Length - 1)
{
// And we save it
resultsNonRecursive.Add(new string(str2));
}
else
{
// Otherwise we have to do everything for the next character
ix++;
}
}
};
// We launch our function
nonRecursive("abcdeabcde");
// The results are in resultsNonRecursive
Both heavily commented.