How to Check if Two Strings Are Anagrams

Given an input of two strings, determine if they are anagrams of each other.
A first approach to this involves sorting the two strings by their characters. Then, a simple equality check can be done to see if the sorted strings match.
Approach 2: Use char[256]

public boolean areAnagrams(String first, String second) {
  if(first.length() != second.length()) return false;

  int alphabet1[] = new int[26];
  int alphabet2[] = new int[26];

  for(int x = 0; x < first.length(); x++) {
    if(Character.isLetter(first.charAt(x)) && Character.isLetter(second.charAt(x))) {
      alphabet1[first.charAt(x) - 'a']++;
      alphabet2[second.charAt(x) - 'a']++;
    }   
    else
      return false;
  }

  for(int x = 0; x < 26; x++) {
    if(alphabet1[x] != alphabet2[x])
      return false;
  }
  return true;
}

From Coding Interviews: Questions, Analysis & Solutions
boolean areAnagrams(String str1, String str2) {
    if(str1.length() != str2.length())
        return false;

    Map<Character, Integer> times = new HashMap<Character, Integer>();    for(int i = 0; i < str1.length(); ++i) {
        Character ch = str1.charAt(i);
        if(times.containsKey(ch))
            times.put(ch, times.get(ch) + 1);
        else
            times.put(ch, 1);
    }

    for(int i = 0; i < str2.length(); ++i) {
        Character ch = str2.charAt(i);
        if(!times.containsKey(ch))
            return false;

        if(times.get(ch) == 0)
            return false;

        times.put(ch, times.get(ch) - 1);
    }

    return true;
}
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