Check Permutation: Given two strings, write a method to decide if one is a permutation of the other.

StringsPermutation.cs

using System;
using System.Diagnostics;

namespace StringsPermutation
{
    /// <summary>
    /// Check Permutation: Given two strings,
    /// write a method to decide if one is a permutation of the other.
    /// Let's assume that strings are ASCII, case-insensitive
    /// </summary>
    public class Program
    {
        /// <summary>
        /// Simple hash
        /// </summary>
        /// <param name="x"></param>
        /// <returns></returns>
        public uint Hash(uint x)
        {
            x = ((x >> 16) ^ x) * 0x45d9f3b;
            x = ((x >> 16) ^ x) * 0x45d9f3b;
            x = (x >> 16) ^ x;
            return x;
        }

        /// <summary>
        /// Sum (xor) of hashes of each character in the string
        /// (order doesnt matter)
        /// </summary>
        /// <param name="plain"></param>
        /// <returns></returns>
        public uint Hash(string plain)
        {
            uint hash = 0;
            foreach (var c in plain)
            {
                hash ^= Hash(c);
            }
            return hash;
        }

        /// <summary>
        /// Check if one string is a permutation of the other
        /// Let's assume that strings are ASCII
        /// </summary>
        /// <param name="a"></param>
        /// <param name="b"></param>
        /// <returns></returns>
        public bool IsPermutation(string a, string b)
        {
            return a.Length == b.Length && Hash(a) == Hash(b);
        }

        public static void Main(string[] args)
        {
            var p = new Program();

            Debug.Assert(p.IsPermutation("dog","god"));
            Debug.Assert(!p.IsPermutation("dag", "god"));
            Debug.Assert(p.IsPermutation("abcdefgh", "hgfedcba"));
            Debug.Assert(p.IsPermutation("a", "a"));
            Debug.Assert(p.IsPermutation("ba", "ba"));
            Debug.Assert(p.IsPermutation("ba", "ab"));
            Debug.Assert(!p.IsPermutation("ba", "aa"));
            Debug.Assert(p.IsPermutation("aa", "aa"));
            Debug.Assert(!p.IsPermutation("aa", "aaa"));
            Debug.Assert(p.IsPermutation("aba", "baa"));
            Debug.Assert(!p.IsPermutation("aba", "bab"));
            Debug.Assert(p.IsPermutation("abc", "abc"));
            Debug.Assert(p.IsPermutation("abc", "acb"));
            Debug.Assert(p.IsPermutation("abc", "cab"));
            Debug.Assert(p.IsPermutation("abc", "cba"));
        }
    }
}