Isomorphic Strings

Given two strings s and t, determine if they are isomorphic.
Given "egg", "add", return true.
Given "foo", "bar", return false.

• Time: O(n)
• Space: O(n)

public boolean isIsomorphic(String s, String t) {
    if (s.length() != t.length()) {
        return false;
    }
    Map<Character, Character> map = new HashMap<>();
    for(int i = 0; i < s.length(); i ++) {
        if (map.containsKey(s.charAt(i))) {
            if (!map.get(s.charAt(i)).equals(t.charAt(i))) {
                return false;
            }
        } else {
            if (map.values().contains(t.charAt(i))) {
                return false;
            }
            map.put(s.charAt(i), t.charAt(i));
        }
    }
    return true;
}