Write a script to identify an anagram

Peter Kim Frank on February 01, 2018

Inspired by this tweet from the always awesome Fermat's Library. Fermat's Library @fermatslibrary Clever algorithm to find out whether or... [Read Full]
 

I'd think sorting the characters of the string and comparing them would be a fine solution.

In Ruby:

def is_anagram?(first_word, second_word)
    first_word.chars.sort.join == first_word.chars.sort.join
end

We might want to refactor into two functions

def is_anagram?(first_word, second_word)
    sort_alphabetically(first_word) == sort_alphabetically(second_word)
end

def sort_alphabetically(string)
    string.chars.sort.join
end

The ? in Ruby is just another character, but it's commonly used in naming comparison methods like this.

 

Actually, the join step is unnecessary given that the arrays will match or not at that point, but it still seems like an ergonomic step if we are thinking in words. 🙂

 

If we wanted the comparison to work for n words, we might take an approach like this:

    def are_anagrams?(words)
        words.map { |w| sort_alphabetically(w) }.uniq.size == 1
    end

This would check if the "unique" array of sorted words is a length of one, indicating they are all the same.

In true Ruby style, we could monkey patch the Array class, like such:

class Array
  def are_anagrams?
    self.map { |w| sort_alphabetically(w) }.uniq.size == 1
  end
end

So then we could call:

["pots", "post", "stop"].are_anagrams? # true
["pots", "post", "ghost"].are_anagrams? # false

Looking up methods on the Array class, I see that I can refactor the above to:

def are_anagrams?
    self.map { |w| sort_alphabetically(w) }.uniq.one?
end

This may be less clear to non-Rubyists, but that method is there for a reason for Ruby folks.

Very cool
i'm learning ruby currently and the refactor steps are very clear and easy to follow.
At then end only one line method!
i would have written this in 20 lines probably and in a couple of hours :)

Cool stuff.

 

Hi Ben,

seems to have a small typo in your code (first part).
After "==" should be second_word, no?

 

Full blown Java implementation of the Prime Product method mentioned in the tweet (Gist for full viewing):

package testing;

import java.math.BigInteger;
import java.util.List;
import java.util.stream.Collectors;
import java.util.stream.Stream;

public class IsAnagramDemo
{
    /* Get the primes we need */
    private static final List<BigInteger> alphaPrimes = primes()
            .limit(26)
            .collect(Collectors.toList());

    /* Int encoding of lowercase a in unicode */
    private static final int A_INT_ENCODING = 97;

    /* Int encoding of lowercase z in unicode */
    private static final int Z_INT_ENCODING = 122;

    /*
        Main method to demonstrate success
     */
    public static void main(String[] args) throws Exception
    {
        assert isAnagram("stressed", "desserts");

        assert !isAnagram("happy", "sad");
    }

    /**
     * Determines if two strings are anagrams using the prime product method
     *
     * @param s1 First input string
     * @param s2 Second input string
     * @return Boolean indicating anagram-ness
     * @throws IllegalArgumentException Thrown when at least one of the input strings is invalid
     */
    public static boolean isAnagram(String s1, String s2) throws IllegalArgumentException
    {
        return primeProduct(s1).equals(primeProduct(s2));
    }

    /**
     * Converts a string to the corresponding product of prime values
     *
     * @param s Input string
     * @return Big integer product of primes
     * @throws IllegalArgumentException Thrown when strong contains chars outside of A-z
     */
    private static BigInteger primeProduct(String s) throws IllegalArgumentException
    {
        /* Convert to lowercase char array */
        char[] chars = s.toLowerCase().toCharArray();

        BigInteger product = BigInteger.ONE;

        for (char c : chars)
        {
            /* Cast char to int */
            int cInt = (int)c;

            /* If the char is out of bounds we must throw an exception */
            if (cInt < A_INT_ENCODING || cInt > Z_INT_ENCODING)
            {
                throw new IllegalArgumentException("Character \"" + c + "\" not valid");
            }
            /* Otherwise we can do the prime lookup */
            else
            {
                /* Prime value corresponding to this char */
                BigInteger primeVal = alphaPrimes.get(cInt % A_INT_ENCODING);

                /* Add this prime to our product */
                product = product.multiply(primeVal);
            }
        }

        /* Return the product */
        return product;
    }

    /**
     * @return Infinite stream of primes
     */
    private static Stream<BigInteger> primes()
    {
        return Stream.iterate(BigInteger.valueOf(2L), n -> n.add(BigInteger
                .ONE)).filter(n -> n.isProbablePrime(10));
    }
}
 

The common way, written in Scala:

scala> def isAnagram(s1: String, s2: String): Boolean = s1.sorted.equalsIgnoreCase(s2.sorted)
isAnagram: (s1: String, s2: String)Boolean                                                   

scala> isAnagram("stressed", "desserts")                                                     
res1: Boolean = true                                                                         

scala> isAnagram("sad", "happy")                                                             
res2: Boolean = false
 

Always happy to provide Clojure answers ;)

(defn anagram? [w1 w2]
  (= (sort w1) (sort w2)))

And of course I snooped the algorithm from all the other answers here.

 

You don't need sort or multiply or any fancy stuff

int[26] wordcount; //array containing encounter count of each character.

for each char:
    charnum <- ConvertCharToNum(char)
    wordcount[charnum]++

return wordcount

Check if the wordcount array of the two strings.

Computation
Does not require to sort, which is nlogn. This only requires a single pass to create wordcount array, thus n.
You can also optimize on aborting upon first index mismatch with this solution (You could also do this with the prime hashing, by aborting on first division yielding a decimal number).

Memory
The 26th prime is 97. Assume it's 100, 6 'z's would be 1006 = 1012. It would take 39 bits, or 5 bytes to store (1012 /log2). This is much less efficient to store a hash. If you want to be stricter, you could store only 1 wordcount, and have the second string count down instead of up.

Feature extension
If I want to accept numbers, the 36th prime is 367 (See Memory). With the array, it's just allocating another 10 index. It is also possible to add this feature without redeploying code, by replacing a specifically allocated array with a map of char to count

 

This is good. I adapted it to Haskell, recording letter frequencies in Maps/dictionaries. The Map data structure is already an instance of the Eq typeclass, so it was a one-liner to add the equality check:

import qualified Data.Map.Strict as M

-- incrementor for Map entries (used by Map's alter function)

inc Nothing = Just 1
inc (Just x) = Just (x+1)

-- produces a Map containing frequencies of elements in a given list (or Foldable)
-- e.g. a Map of frequencies of characters in a given word

frequencies :: (Foldable t, Ord k, Num a) => t k -> M.Map k a
frequencies = foldr (M.alter inc) M.empty

-- equality is already defined for Maps :)

isAnagram word1 word2 = frequencies word1 == frequencies word2
 

Best answer here. The prime trick is nice but as you said it gets way too expensive very fast.

 

In Python, I've always used the builtin Counter collection!

from collections import Counter

def isAnagram(word, check_word):
    return Counter(word) == Counter(check_word)
 

I stick with mappings to prime numbers. Haskell, without considerations of performance:

import Data.Char(toLower)
import Data.List(lookup)

primes = sieve [2..]
  where sieve (p:xs) = p : sieve [x | x <- xs, x `mod` p /= 0]

charToPrime c = lookup c $ zip ['a'..'z'] primes

eval word = product <$> sequence (map (charToPrime . toLower) word)

isAnagram word1 word2 = eval word1 == eval word2

lookup and charToPrime return a Maybe value, without catching the eye. Umlauts or digits result in a Nothing value for the character and in a product of 1 for the word. The handling of those cases could be improved.

 

My quick PHP one

<?php

function isAnagram($word1, $word2) {
  $word1Array = str_split($word1);
  $word2Array = str_split($word2);
  sort($word1Array);
  sort($word2Array);

  return $word1Array === $word2Array;
}

var_dump (isAnagram("test","etst")); //returns bool(true)
var_dump (isAnagram("test","ftst")); //returns bool(false)

?>


 

Not super practical maybe, but using binary XOR is a sneaky way of checking for exact pairs of things (or finding an odd one out!). :) No sorting, and it works with punctuation!

# Detects whether two words are anagrams or not
def is_anagram?(word1, word2)
  (word1 + word2).chars.reduce(0) { |acc, curr| acc ^ curr.ord } == 0
end

puts "stressed is an anagram of desserts: #{is_anagram?('stressed', 'desserts')}"
# => true
puts "happy is an anagram of sad: #{is_anagram?('happy', 'sad')}"
# => false
puts "banana? is an anagram of b?naana: #{is_anagram?('banana?', 'b?naana')}"
# => true
 

Wouldn't "hello" and "hellooo" be a false positive here? I like the feel of this approach though.

 

Oh, good point. This is probably better suited to a “find the one unique letter” type problem. I like the solution that uses ‘uniq’ the best so far, I think.

 
function isAnagram(a,b) {
    const vals = [a,b].map(x => x.split('').sort());
    return vals[0].every((v,i) => v === vals[1][i]);
}

Alternatively,

function isAnagram(a,b) {
    return new Set([a,b].map(x => x.split('').sort().join(''))).size === 1;
}
 

Edit: Added sort-based solution for Elm.

import String
import List

sortLetters word =
  List.sort (String.toList word)

isAnagram word1 word2 =
  sortLetters word1 == sortLetters word2

I think the primes thing was actually harder than what I did. Here is my 15-line Elm solution where you could also reuse the breakdown of how many of which letters were used. I could have turned it into 1 long line with the 3 import statements, but I won't do that to you. :)

Read this code from the bottom up. I got used to writing it like this in F# because of its single-pass compiler. This is not a requirement of Elm, though.

import Dict exposing (Dict)
import String
import Char


updateCount countM =
  case countM of
    -- no previous count of letter, set to 1
    Nothing ->
      Just 1

    -- saw same letter again, increment
    Just i ->
      Just (i + 1)

updateAnalysis char dict =
  Dict.update (Char.toLower char) updateCount dict

analyzeWord word =
  String.foldr updateAnalysis Dict.empty word

isAnagram word1 word2 =
  -- built-in equality superpowers
  analyzeWord word1 == analyzeWord word2

Don't take my word for it.

Here is a full program with tests that you can run over at elm-lang.org/try. Paste the code below in the left window and hit the Compile button.

I included type annotations for clarity, but they are not necessary.

import Html exposing (Html, text, div, span, u)
import Html.Attributes exposing (style)
import Dict exposing (Dict)
import String
import Char


-- anagram functions

type alias WordAnalysis = Dict Char Int

updateCount : Maybe Int -> Maybe Int
updateCount countM =
  case countM of
    -- no previous count of letter, set to 1
    Nothing ->
      Just 1

    -- saw same letter again, increment
    Just i ->
      Just (i + 1)

updateAnalysis : Char -> WordAnalysis -> WordAnalysis
updateAnalysis char dict =
  Dict.update (Char.toLower char) updateCount dict

analyzeWord : String -> WordAnalysis
analyzeWord word =
  String.foldr updateAnalysis Dict.empty word

isAnagram : String -> String -> Bool
isAnagram word1 word2 =
  analyzeWord word1 == analyzeWord word2


-- test functions

anagramTests : List (String, String)
anagramTests =
  [ ("stressed", "desserts")
  , ("stressed", "deserts")
  , ("marching", "charming")
  , ("happy", "sad")
  ]

renderTest : (String, String) -> Html msg
renderTest (word1, word2) =
  div []
    [ u [] [ text word1 ]
    , text " and "
    , u [] [ text word2 ]
    , if isAnagram word1 word2 then
        span
          [ style [ ( "color", "green" ), ("font-weight", "bold") ] ]
          [ text " are anagrams" ]
      else
        span [] [ text " are not anagrams" ]
    ]

main =
  div [] ( List.map renderTest anagramTests )
 

Scheme R5RS using srfi-13:
First we define a LUT of the first 26 primes.

(define primes '(2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101))

Next we define our function:

(define (isAnagram a b) (let ((mult (lambda (l) (apply * (map (lambda (x) (list-ref primes (- (char->integer x) 97))) (string->list (string-downcase l))))))) (= (mult a) (mult b))))

To break it down, our function takes two string arguments a and b, and applies the internal function 'mult' to both.
Taking a closer look at 'mult':

(mult (lambda (l) (apply * (map (lambda (x) (list-ref primes (- (char->integer x) 97))) (string->list (string-downcase l))))))

It's a lambda expression which takes a string 'l', downcases it, converts it to a list of chars, and maps an anonymous lambda function across that list, then multiplies the resulting list of integers.
Taking a closer look at the anonymous lambda:

lambda (x) (list-ref primes (- (char->integer x) 97))

It quite simply finds the prime number corresponding to the code-point of each character in the list, minus 97 (the code-point for 'a', we can do this because of the earlier downcasing), a number which corresponds to each letter's ordinal value in the alphabet if a corresponds with 0.

 

This is close to cheating and must have terrible space and runtime complexity:

import Data.List(permutations)
isAnagram word1 word2 = word1 `elem` permutations word2

The solution based on sort:

import Data.List(sort)
isAnagram word1 word2 = sort word1 == sort word2

The library functions sort and permutations seem to be such an integral part of the solution, they should be implemented, here. :)

 

I'm surprised that no one has talked about using ord in python (It Returns the Unicode code point for a string) and comparing the sum

>>> sum(map(ord, 'stressed')) == sum(map(ord, 'desserts'))
True

It even performs better than sorting

>>> timeit.timeit("sorted('stressed') == sorted('desserts')")
1.3272779149992857
>>> timeit.timeit("sum(map(ord, 'stressed')) == sum(map(ord, 'desserts'))")
1.2404647049988853
 

It performs better but it's wrong. Comparing sums can give you false positives.

>>> sum(map(ord, 'false positive'))
1438
>>> sum(map(ord, 'farce positivo'))
1438
>>>
 

In javascript you can do something like this:

function isAnagram(s1, s2){
    return s1.split('').sort().toString() === s2.split('').sort().toString();
}

isAnagram('stressed', 'desserts');
// true
isAnagram('add', 'dad');
// true
isAnagram('happy', 'sad');
// false

 

I like the solution to "subtract" all characters of the shorter word from the (possibly) longer word, and check if there is some character left:

import Data.List(delete,sortBy)
import Data.Function(on)

-- deletes the first character of word from str
del str word = delete (head word) str

-- deletes all chars of word from str
str `without` word = foldl del str (map (:[]) word)

-- are there any remaining characters? 
isAnagram word1 word2 = null $ longer `without` shorter
  where [shorter,longer] = sortBy (compare `on` length) [word1,word2]

Ok, this is more fun, but it somehow reimplemented the library function ( \ \ ) (which can be read as the difference operation in set theory)

import Data.List((\\),sortBy)
import Data.Function(on)
isAnagram word1 word2 = null $ longer \\ shorter
  where [shorter,longer] = sortBy (compare `on` length) [word1,word2]
 

I'm sorry, it took me a dinner out to see, this was unnecessarily complicated. :) The delete functions perfectly fits a right fold. And if the words aren't of equal length, they are not anagrams.

-- deletes the first occurance of element x from a list
delete _ [] = []
delete x (y:ys) = if x == y then ys else y : delete x ys

-- deletes all elements of the second list from the first
without :: Eq a => [a] -> [a] -> [a]
without = foldr delete

-- are there any remaining characters? 
isAnagram word1 word2 = null $ word1 `without` word2

delete could also be imported from Data.List

 

So there was a perl6 version of the using this method posted on twitter. But it had a wee bug (it was summing not multiplying the value). Here's the fixed version:

sub ana(*@words) {
    state %primes = 'A'..'Z' Z=> (^Inf).grep(*.is-prime);
    [==] @words.map({ [*] %primes{$_.comb} });
}

I realise any version of Perl can look like line noise so I'll break it done.

Firstly the *@words indicates that all the arguments passed into the function should be put into an Array called @words.

state %primes state variables are defined once and then reused each time the function is called so the first time you call the ana function the primes hash is populated.

(^Inf).grep(*.is-prime) this gives a lazy list of integers from 0 to Infinity (but then only returns those that are prime).

'A'..'Z' gives the Range of characters from A to Z (inclusive).

The Z meta operator applies the infix operator on it's right (in this case the => Pair constructor) to each element in the Positional objeect on it's left and right until one is used up. (That important, don't use a Z operator on a couple of lazy lists... it won't go well).

So that gives us a hash starting { A => 2, B => 3, C => 5 ... and so on.

@words.map applies the code block inside the map call to each item in @words. Inside the block $_ is assign the current value.

$_.comb splits the word into individual characters and %primes{$_.comb} references each of the characters and gets it's value in the prime array.

[*] and [==] are cases of applying the [] meta operator to an infix operator. It acts like taking the list on the right and putting the operator between each item.

So for the string "ABC" %primes{$_.comb} returns the list (2 3 5) and then you have [*] (2 3 5) which can be thought of as 2 * 3 * 5 or 30.

The [==] takes our list of products and puts == between them. In this case it makes use of Perl6 operator chaining which allow you to write something like 30 == 30 == 30 or 5 < 10 > 7 in both the cases each individual Boolean check is made and then these are all combined into a sets of AND checks.

Hope that makes sense. Note that this function only works on uppercase strings. It would be easy enough to make it case insensitive and to also add any Unicode characters for accents found in the expected strings.

 

Rust way, could be done better.
This just compares the char vector directly after sorting them.

fn is_anagram(a: &str ,b : &str) ->  bool {
    if a.len() != b.len() {    // Length check 
        return false;
    }
    let mut a:Vec<char> = a.chars().collect();
    a.sort();
    let mut b:Vec<char> = b.chars().collect();
    b.sort();
    if a == b {
        return true
    }
    false
}
 

C++

using namespace std;
bool isAnagram(const string& s1, const string& s2)
{
    unordered_map<string::value_type, int> themap;
    if (s1.size() != s2.size())
        return false;
    for (auto c : s1)
        themap[c] += 1;
    for (auto c : s2)
        themap[c] -= 1;
    for (auto& p : themap) {
        if (p.second != 0)
            return false;
    }
    return true;
}
 

This algorithm is actually an excellent illustration of why clever algorithms aren't always better.

In fact the clever algorithm here is worse in basically every way imaginable. It's more complicated, limited in scope, error prone, can fail in unexpected ways, and possibly less efficient than the obvious solution.

  • You need to store a lookup table of letters to primes. For the 26 letters, this 26 element lookup table is already more code than it would take to iterate over the characters and increment values in a map.
  • If you typo one of the values you'll get wrong answers all the time. Or you need code to compute the first n primes which comes with its own performance penalty and extra code.
  • The list of primes gets pretty huge if you want to support any kind if i18n and you're dealing with more than just 26 letters.
  • In most languages on modern processors integers are 64 bits long. The 26th prime is 101. In the worst case you could overflow the integers in as few as 10 letters. Integer overflow is DEFINITELY an issue if you're dealing with i18n and therefore more characters and larger primes, or if you want to support phrases rather than individual words, and therefore longer input. Once you overflow and wrap around you could get false positives. Or you could use arbitrary precision arithmetic, but that's drastically less efficient.
 
 

While this happens to work for stressed and desserts this only checks for words which are reverse copies of each other, not anagrams.

add and dad are anagrams (same letters) but this check does not catch it:

>>> def isAnagram(a, b):   
...     return a == b[::-1]
...                        
>>> isAnagram("dad", "add")
False                      
 

I feel we need SPOILER warnings for the comments

 

Paging @heikodudzus , I feel like you always enjoy these challenges!

 

Hey, thank you very much! I'm glad you sent me a notice. I will look for some spare time! :)

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