Isomorphic strings

Can every character of one string be swapped for a fixed character in another, with the swap working both ways?

The idea

Isomorphic means every character in s can be swapped for a fixed character in t, and the swap has to work in both directions. One dictionary remembers s -> t; a second remembers t -> s. If either direction would ever need to send the same character to two different partners, the strings are not isomorphic.

Code

public static bool IsIsomorphic(string s, string t) {
    if (s.Length != t.Length) return false;
    var mapST = new Dictionary<char, char>();
    var mapTS = new Dictionary<char, char>();
    for (int i = 0; i < s.Length; i++) {
        char a = s[i], b = t[i];
        if (mapST.TryGetValue(a, out char mb) && mb != b) return false;
        if (mapTS.TryGetValue(b, out char ma) && ma != a) return false;
        mapST[a] = b; mapTS[b] = a;
    }
    return true;
}

Tips

• Checking only s -> t misses cases like s = "ab", t = "aa": a maps to a and b maps to a, which breaks going backwards from t.
• Equal lengths are required first - without that check the index loop could run past the shorter string.

In the .NET library

This is the same "remember what has been paired so far" idea as Two Sum, just applied twice, once per direction, so a many-to-one mapping in either direction gets caught.