Isomorphic Strings

Given two strings s and t, determine if they are isomorphic.
Two strings are isomorphic if the characters in s can be replaced to get t.
All occurrences of a character must be replaced with another character while preserving the order of characters. No two characters may map to the same character but a character may map to itself.
For example,
Given "egg", "add", return true.
Given "foo", "bar", return false.
Given "paper", "title", return true.

Naive Way: Use a HashMap to note down the mapping. Also use .containsKey and .containsValue function to check duplicates. The point being easily ignored is the value also needs to be uniquely mapped. No two characters can map to the same value.

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