insideoutclub's solution

to Alphametics in the C# Track

Published at Jul 13 2018 · 0 comments
Instructions
Test suite
Solution

Note:

This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

Write a function to solve alphametics puzzles.

Alphametics is a puzzle where letters in words are replaced with numbers.

For example `SEND + MORE = MONEY`:

``````  S E N D
M O R E +
-----------
M O N E Y
``````

Replacing these with valid numbers gives:

``````  9 5 6 7
1 0 8 5 +
-----------
1 0 6 5 2
``````

This is correct because every letter is replaced by a different number and the words, translated into numbers, then make a valid sum.

Each letter must represent a different digit, and the leading digit of a multi-digit number must not be zero.

Write a function to solve alphametics puzzles.

Hints

• To parse the text, you could try to use the Sprache library. You can also find a good tutorial here.
• You can solve this exercise with a brute force algorithm, but this will possibly have a poor runtime performance. Try to find a more sophisticated solution.
• Hint: You could try the column-wise addition algorithm that is usually taught in school.

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

AlphameticsTest.cs

``````// This file was auto-generated based on version 1.2.0 of the canonical data.

using Xunit;
using System;
using System.Collections.Generic;

public class AlphameticsTest
{
[Fact]
public void Puzzle_with_three_letters()
{
var actual = Alphametics.Solve("I + BB == ILL");
var expected = new Dictionary<char, int>
{
['I'] = 1,
['B'] = 9,
['L'] = 0
};
Assert.Equal(expected, actual);
}

[Fact(Skip = "Remove to run test")]
public void Solution_must_have_unique_value_for_each_letter()
{
Assert.Throws<ArgumentException>(() => Alphametics.Solve("A == B"));
}

[Fact(Skip = "Remove to run test")]
{
Assert.Throws<ArgumentException>(() => Alphametics.Solve("ACA + DD == BD"));
}

[Fact(Skip = "Remove to run test")]
public void Puzzle_with_four_letters()
{
var actual = Alphametics.Solve("AS + A == MOM");
var expected = new Dictionary<char, int>
{
['A'] = 9,
['S'] = 2,
['M'] = 1,
['O'] = 0
};
Assert.Equal(expected, actual);
}

[Fact(Skip = "Remove to run test")]
public void Puzzle_with_six_letters()
{
var actual = Alphametics.Solve("NO + NO + TOO == LATE");
var expected = new Dictionary<char, int>
{
['N'] = 7,
['O'] = 4,
['T'] = 9,
['L'] = 1,
['A'] = 0,
['E'] = 2
};
Assert.Equal(expected, actual);
}

[Fact(Skip = "Remove to run test")]
public void Puzzle_with_seven_letters()
{
var actual = Alphametics.Solve("HE + SEES + THE == LIGHT");
var expected = new Dictionary<char, int>
{
['E'] = 4,
['G'] = 2,
['H'] = 5,
['I'] = 0,
['L'] = 1,
['S'] = 9,
['T'] = 7
};
Assert.Equal(expected, actual);
}

[Fact(Skip = "Remove to run test")]
public void Puzzle_with_eight_letters()
{
var actual = Alphametics.Solve("SEND + MORE == MONEY");
var expected = new Dictionary<char, int>
{
['S'] = 9,
['E'] = 5,
['N'] = 6,
['D'] = 7,
['M'] = 1,
['O'] = 0,
['R'] = 8,
['Y'] = 2
};
Assert.Equal(expected, actual);
}

[Fact(Skip = "Remove to run test")]
public void Puzzle_with_ten_letters()
{
var actual = Alphametics.Solve("AND + A + STRONG + OFFENSE + AS + A + GOOD == DEFENSE");
var expected = new Dictionary<char, int>
{
['A'] = 5,
['D'] = 3,
['E'] = 4,
['F'] = 7,
['G'] = 8,
['N'] = 0,
['O'] = 2,
['R'] = 1,
['S'] = 6,
['T'] = 9
};
Assert.Equal(expected, actual);
}

[Fact(Skip = "Remove to run test")]
{
var actual = Alphametics.Solve("THIS + A + FIRE + THEREFORE + FOR + ALL + HISTORIES + I + TELL + A + TALE + THAT + FALSIFIES + ITS + TITLE + TIS + A + LIE + THE + TALE + OF + THE + LAST + FIRE + HORSES + LATE + AFTER + THE + FIRST + FATHERS + FORESEE + THE + HORRORS + THE + LAST + FREE + TROLL + TERRIFIES + THE + HORSES + OF + FIRE + THE + TROLL + RESTS + AT + THE + HOLE + OF + LOSSES + IT + IS + THERE + THAT + SHE + STORES + ROLES + OF + LEATHERS + AFTER + SHE + SATISFIES + HER + HATE + OFF + THOSE + FEARS + A + TASTE + RISES + AS + SHE + HEARS + THE + LEAST + FAR + HORSE + THOSE + FAST + HORSES + THAT + FIRST + HEAR + THE + TROLL + FLEE + OFF + TO + THE + FOREST + THE + HORSES + THAT + ALERTS + RAISE + THE + STARES + OF + THE + OTHERS + AS + THE + TROLL + ASSAILS + AT + THE + TOTAL + SHIFT + HER + TEETH + TEAR + HOOF + OFF + TORSO + AS + THE + LAST + HORSE + FORFEITS + ITS + LIFE + THE + FIRST + FATHERS + HEAR + OF + THE + HORRORS + THEIR + FEARS + THAT + THE + FIRES + FOR + THEIR + FEASTS + ARREST + AS + THE + FIRST + FATHERS + RESETTLE + THE + LAST + OF + THE + FIRE + HORSES + THE + LAST + TROLL + HARASSES + THE + FOREST + HEART + FREE + AT + LAST + OF + THE + LAST + TROLL + ALL + OFFER + THEIR + FIRE + HEAT + TO + THE + ASSISTERS + FAR + OFF + THE + TROLL + FASTS + ITS + LIFE + SHORTER + AS + STARS + RISE + THE + HORSES + REST + SAFE + AFTER + ALL + SHARE + HOT + FISH + AS + THEIR + AFFILIATES + TAILOR + A + ROOFS + FOR + THEIR + SAFE == FORTRESSES");
var expected = new Dictionary<char, int>
{
['A'] = 1,
['E'] = 0,
['F'] = 5,
['H'] = 8,
['I'] = 7,
['L'] = 2,
['O'] = 6,
['R'] = 3,
['S'] = 4,
['T'] = 9
};
Assert.Equal(expected, actual);
}
}``````
``````using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Sprache;

public static class Alphametics
{
private static void iter_swap<T>(IList<T> list, int a, int b) => (list[a], list[b]) = (list[b], list[a]);

private static void reverse<T>(IList<T> list, int first, int last)
{
while (first != last && first != --last)
iter_swap(list, first++, last);
}

private static bool next_permutation<T>(IList<T> list, int first, int last) where T : IComparable<T>
{
if (first == last) return false;
var i = last;
if (first == --i) return false;

while (true)
{
var i1 = i;
if (list[--i].CompareTo(list[i1]) < 0)
{
var i2 = last;
while (!(list[i].CompareTo(list[--i2]) < 0))
;
iter_swap(list, i, i2);
reverse(list, i1, last);
return true;
}
if (i == first)
{
reverse(list, first, last);
return false;
}
}
}

public static IDictionary<char, int> Solve(string equation)
{
var wordParser = Parse.Upper.AtLeastOnce().Token().Text();
var plusWordParser = from _ in Parse.Char('+').Token()
from word in wordParser
select word;
var parser = from x in wordParser
from xs in plusWordParser.Many()
from _ in Parse.String("==").Token()
from y in wordParser
select xs.Prepend(x).Append(y);
var letters = addends.SelectMany(x => x).Distinct().ToArray();
var indices = addends.Select(word => word.Select(c => Array.IndexOf(letters, c)).ToArray()).ToArray();
var numbers = Enumerable.Range(0, 10).ToArray();

// Partial permutations adapted from https://stackoverflow.com/a/30872882/7606550
do
{
if (indices.Any(index => numbers[index[0]] == 0))
continue;
var result = indices.Select(word => word.Select(index => numbers[index]).Aggregate(0, (acc, digit) => 10 * acc + digit)).ToArray();
if (result.Sum() == result[result.Length - 1] + result[result.Length - 1])
return letters.Zip(numbers, (c, x) => (key: c, value: x)).ToDictionary(pair => pair.key, pair => pair.value);
reverse(numbers, letters.Length, numbers.Length);
} while (next_permutation(numbers, 0, numbers.Length));

throw new ArgumentException();
}
}``````