Isomorphic Strings leetcode

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.

题目很简单，也很容易想到方法，就是记录遍历s的每一个字母，并且记录s[i]到t[i]的映射，当发现与已有的映射不同时，说明无法同构，直接return false。但是这样只能保证从s到t的映射，不能保证从t到s的映射，所以交换s与t的位置再重来一遍上述的遍历就OK了。

举一个例子为什么需要两次映射

如果是 "ega"和"add" 那么g和a都会映射到d，如何要保证一一对应，需要双向映射关系

bool check(string s, string t)
{
    unordered_map<char, char> map;
    for (int i = 0; i < s.length(); ++i)
    {
        char c1 = s[i];
        char c2 = t[i];
        if (map.find(c1) == map.end())
            map[c1] = c2;
        else if (map[c1] != c2)
            return false;
    }
    return true;
}

bool isIsomorphic(string s, string t) {
    return check(s, t) && check(t, s);
}