CrossProduct.cs

/*-----------------------------
The MIT License (MIT)

Copyright (c) 2013 Avi Levin

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
-------------------------------*/

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Arithmomaniac.CsTools
{
    /// <summary>
    /// The cross product library
    /// </summary>
    public static class CrossProductFunctions
    {


        /// <summary>
        /// Gets a multiple-cross-product of all of the numbers from [0,0,0] to [i1, i2, ...]
        /// </summary>
        /// <param name="maxIndices">A list of the maximum indices to iterate in each position (eg [2,4,1]</param>
        /// <returns>An iterator of cross-products ([0,0,0], [0,0,1], [0,1,0], etc)</returns>
        public static IEnumerable<List<int>> IndexCrossProduct(IReadOnlyList<int> maxIndices)
        {
            //don't do anything to an empty lsit
            if (maxIndices == null || maxIndices.Count == 0)
                yield break;

            //we repeatedly make reference to what's the index of the last digit in the enumeration
            var lastIndex = maxIndices.Count - 1;

            //initialize the iterable return value. Start with [0,0,0, etc]
            List<int> currentIndices = Enumerable.Repeat(0, maxIndices.Count).ToList();

            //increment the iteration by repeatedly adding one to the next index.
            for (; true; currentIndices[lastIndex]++)
            {
                //This could result in a value for the last place outside of the allowed range.
                //If so, we repeately "carry" the value over to the previous index, in a fasion similar to adding 1 to 099
                
                //for reach index in the set, working right to left
                for (int incrementIndex = lastIndex; true; incrementIndex--)
                {
                    //if no overflow, we can directly return the enumerator value
                    if (currentIndices[incrementIndex] <= maxIndices[incrementIndex])
                    {
                        yield return currentIndices.Select(i => i).ToList(); //copy the list
                        break;
                    }

                    //If addition would completely break range, exit
                    if (incrementIndex == 0)
                        yield break;

                    //else, carry the increment to the next index
                    currentIndices[incrementIndex] = 0;
                    currentIndices[incrementIndex - 1]++;
                }

                


            }

        }

        /// <summary>
        /// Finds the multi-cross-product of an list of object lists
        /// </summary>
        /// <typeparam name="T">The type of the object being enumerated</typeparam>
        /// <param name="possibleValueArrays">The list of object lists to cross-product over</param>
        /// <returns>An iterator of the cross products</returns>
        public static IEnumerable<List<T>> CrossProduct<T> (IReadOnlyList<IReadOnlyList<T>> possibleValueArrays)
        {


            //The technique is to iterate over the possible index values, then use each generated
            //integer cross product as indices for the possibleValueArrays
            var maxIndices = possibleValueArrays.Select(arr => arr.Count - 1).ToList();

            //convert each generated possible index to the underlying values
            foreach (var indexList in IndexCrossProduct(maxIndices))
            {
                yield return possibleValueArrays.Select((values, i) => values[indexList[i]]).ToList();

            }            
            yield break;
        }

    }


    /// <summary>
    /// A simple example to use the CrossProductFunctions library. Takes a set of digits from a phone
    /// number and generates the possible words
    /// </summary>
    static class PhoneParser
    {
        private static List<List<char>> phoneWords = new List<List<char>>(10){
            null,
            null,
            new List<char>() { 'A', 'B', 'C' }, //the 2 digit
            new List<char>() { 'D', 'E', 'F' },
            new List<char>() { 'G', 'H', 'I' },
            new List<char>() { 'J', 'K', 'L' },
            new List<char>() { 'M', 'N', 'O' },
            new List<char>() { 'P', 'Q', 'R', 'S' },
            new List<char>() { 'T', 'U', 'V' },
            new List<char>() { 'W', 'X', 'Y', 'Z' },
        };

        /// <summary>
        /// Gets the phone number strings from a set of numbers.
        /// </summary>
        /// <param name="numbers">The numbers.</param>
        internal static IEnumerable<string> GetPhoneStrings(IList<short> numbers)
        {
            //get the arrays that we will cross product
            var characterSets = numbers.Select(i => phoneWords[i]).ToList();
            
            //get the cross products and turn into strings
            return CrossProductFunctions.CrossProduct(characterSets)
                .Select(chars => String.Join("", chars));
        }

        /// <summary>
        /// Gets the phone number strings from a numeric string.
        /// </summary>
        /// <param name="phonestring">The phone  number digit string.</param>
        internal static IEnumerable<string> GetPhoneStrings(string phonestring)
        {
            return GetPhoneStrings(
                phonestring.ToCharArray().Select(c => Int16.Parse(c.ToString())).ToList()
            );
        }

    }

    class Program
    {

        static void Main(string[] args)
        {
            foreach (var str in PhoneParser.GetPhoneStrings("3868"))
            {
                Console.WriteLine(str);
            }
            Console.ReadLine();

        }
    }
}