How to check if two words are anagrams

If you sort either array, the solution becomes O(n log n). but if you use a hashmap, it's O(n). tested and working.

char[] word1 = "test".toCharArray();
char[] word2 = "tes".toCharArray();

Map<Character, Integer> lettersInWord1 = new HashMap<Character, Integer>();

for (char c : word1) {
    int count = 1;
    if (lettersInWord1.containsKey(c)) {
        count = lettersInWord1.get(c) + 1;
    }
    lettersInWord1.put(c, count);
}

for (char c : word2) {
    int count = -1;
    if (lettersInWord1.containsKey(c)) {
        count = lettersInWord1.get(c) - 1;
    }
    lettersInWord1.put(c, count);
}

for (char c : lettersInWord1.keySet()) {
    if (lettersInWord1.get(c) != 0) {
        return false;
    }
}

return true;

Fastest algorithm would be to map each of the 26 English characters to a unique prime number. Then calculate the product of the string. By the fundamental theorem of arithmetic, 2 strings are anagrams if and only if their products are the same.

Two words are anagrams of each other if they contain the same number of characters and the same characters. You should only need to sort the characters in lexicographic order, and determine if all the characters in one string are equal to and in the same order as all of the characters in the other string.

Here's a code example. Look into Arrays in the API to understand what's going on here.

public boolean isAnagram(String firstWord, String secondWord) {
     char[] word1 = firstWord.replaceAll("[\\s]", "").toCharArray();
     char[] word2 = secondWord.replaceAll("[\\s]", "").toCharArray();
     Arrays.sort(word1);
     Arrays.sort(word2);
     return Arrays.equals(word1, word2);
}