Add alphametics exercise (#379)

config.json

@@ -19,10 +19,18 @@
     "average_run_time": 1
   },
   "files": {
-    "solution": ["%{snake_slug}.pl"],
-    "test": ["%{snake_slug}_tests.plt"],
-    "example": [".meta/%{snake_slug}.example.pl"],
-    "exemplar": [".meta/%{snake_slug}.exemplar.pl"]
+    "solution": [
+      "%{snake_slug}.pl"
+    ],
+    "test": [
+      "%{snake_slug}_tests.plt"
+    ],
+    "example": [
+      ".meta/%{snake_slug}.example.pl"
+    ],
+    "exemplar": [
+      ".meta/%{snake_slug}.exemplar.pl"
+    ]
   },
   "exercises": {
     "practice": [
@@ -65,7 +73,9 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 1,
-        "topics": ["math"]
+        "topics": [
+          "math"
+        ]
       },
       {
         "slug": "rna-transcription",
@@ -90,7 +100,9 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 1,
-        "topics": ["math"]
+        "topics": [
+          "math"
+        ]
       },
       {
         "slug": "dominoes",
@@ -107,7 +119,9 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 1,
-        "topics": ["math"]
+        "topics": [
+          "math"
+        ]
       },
       {
         "slug": "grains",
@@ -148,7 +162,11 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 1,
-        "topics": ["binary_trees", "recursion", "tree_traversals"]
+        "topics": [
+          "binary_trees",
+          "recursion",
+          "tree_traversals"
+        ]
       },
       {
         "slug": "space-age",
@@ -173,7 +191,9 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 1,
-        "topics": ["math"]
+        "topics": [
+          "math"
+        ]
       },
       {
         "slug": "wordy",
@@ -182,7 +202,9 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 1,
-        "topics": ["parsing"]
+        "topics": [
+          "parsing"
+        ]
       },
       {
         "slug": "zebra-puzzle",
@@ -663,6 +685,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 1
+      },
+      {
+        "slug": "alphametics",
+        "name": "Alphametics",
+        "uuid": "9f430940-9e6f-4f80-9ae4-0ebcc91cf055",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 1
       }
     ],
     "foregone": [

exercises/practice/alphametics/.docs/instructions.md

@@ -0,0 +1,31 @@
+# Instructions
+
+Write a function to solve alphametics puzzles.
+
+[Alphametics][alphametics] is a puzzle where letters in words are replaced with numbers.
+
+For example `SEND + MORE = MONEY`:
+
+```text
+  S E N D
+  M O R E +
+-----------
+M O N E Y
+```
+
+Replacing these with valid numbers gives:
+
+```text
+  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.
+
+[alphametics]: https://en.wikipedia.org/wiki/Alphametics

exercises/practice/alphametics/.meta/alphametics.example.pl

@@ -0,0 +1,55 @@
+:- use_module(library(dcg/basics)).
+:- use_module(library(clpfd)).
+:- set_prolog_flag(double_quotes, chars).
+
+letter(Letter) --> [Letter], { char_type(Letter, upper) }.
+operand([Letter|Letters]) --> letter(Letter), operand(Letters).
+operand([Letter]) --> letter(Letter).
+
+operands([Operand|Operands]) --> operand(Operand), " + ", operands(Operands).
+operands([Operand]) --> operand(Operand).
+
+equation(Left, Right) --> operands(Left), " == ", operands(Right).
+
+letter_map(Sign, Letters, Mapping) :- 
+    reverse(Letters, ReversedLetters),
+    findall(L-C, (nth0(I, ReversedLetters, L), C is Sign * 10 ^ I), Mapping).
+
+map_merge(Mappings, Mapping) :-
+    setof(Key, Value^member(Key-Value, Mappings), Keys),
+    findall(Key-Sum, (member(Key, Keys), aggregate(sum(Value), member(Key-Value, Mappings), Sum)), Mapping).
+
+mapping(Left, Right, Mapping) :-
+    maplist(letter_map(1), Left, LeftMappings),
+    maplist(letter_map(-1), Right, RightMappings),
+    append(LeftMappings, RightMappings, NestedMappings),
+    flatten(NestedMappings, Mappings),
+    map_merge(Mappings, Mapping).
+
+zero_letters(Left, Right, ZeroLetters) :-
+    append(Left, Right, LeftAndRight),
+    findall(ZeroChar, member([ZeroChar|_], LeftAndRight), ALlZeroLetters),
+    sort(ALlZeroLetters, ZeroLetters).
+
+parse(Equation, Mapping, Letters, ZeroLetters) :-
+    string_chars(Equation, Chars),
+    phrase(equation(Left, Right), Chars),
+    mapping(Left, Right, Mapping),
+    zero_letters(Left, Right, ZeroLetters),
+    pairs_keys(Mapping, Letters).    
+
+add_range(ZeroLetters, Letter, Digit) :-
+    (member(Letter, ZeroLetters) -> Min = 1; Min = 0),
+    Digit in Min..9.
+
+solve(Equation, Solution) :-
+    parse(Equation, Mapping, Letters, ZeroLetters),
+    length(Letters, Count),
+    length(Digits, Count),
+    all_different(Digits),
+    maplist(add_range(ZeroLetters), Letters, Digits),
+    pairs_values(Mapping, Multipliers),
+    scalar_product(Multipliers, Digits, #=, 0),
+    pairs_keys_values(Solution, Letters, Digits),
+    label(Digits),
+    !.

exercises/practice/alphametics/.meta/config.json

@@ -0,0 +1,17 @@
+{
+  "authors": [
+    "erikschierboom"
+  ],
+  "files": {
+    "solution": [
+      "alphametics.pl"
+    ],
+    "test": [
+      "alphametics_tests.plt"
+    ],
+    "example": [
+      ".meta/alphametics.example.pl"
+    ]
+  },
+  "blurb": "Write a function to solve alphametics puzzles."
+}

exercises/practice/alphametics/.meta/tests.toml

@@ -0,0 +1,40 @@
+# This is an auto-generated file.
+#
+# Regenerating this file via `configlet sync` will:
+# - Recreate every `description` key/value pair
+# - Recreate every `reimplements` key/value pair, where they exist in problem-specifications
+# - Remove any `include = true` key/value pair (an omitted `include` key implies inclusion)
+# - Preserve any other key/value pair
+#
+# As user-added comments (using the # character) will be removed when this file
+# is regenerated, comments can be added via a `comment` key.
+
+[e0c08b07-9028-4d5f-91e1-d178fead8e1a]
+description = "puzzle with three letters"
+
+[a504ee41-cb92-4ec2-9f11-c37e95ab3f25]
+description = "solution must have unique value for each letter"
+
+[4e3b81d2-be7b-4c5c-9a80-cd72bc6d465a]
+description = "leading zero solution is invalid"
+
+[8a3e3168-d1ee-4df7-94c7-b9c54845ac3a]
+description = "puzzle with two digits final carry"
+
+[a9630645-15bd-48b6-a61e-d85c4021cc09]
+description = "puzzle with four letters"
+
+[3d905a86-5a52-4e4e-bf80-8951535791bd]
+description = "puzzle with six letters"
+
+[4febca56-e7b7-4789-97b9-530d09ba95f0]
+description = "puzzle with seven letters"
+
+[12125a75-7284-4f9a-a5fa-191471e0d44f]
+description = "puzzle with eight letters"
+
+[fb05955f-38dc-477a-a0b6-5ef78969fffa]
+description = "puzzle with ten letters"
+
+[9a101e81-9216-472b-b458-b513a7adacf7]
+description = "puzzle with ten letters and 199 addends"

exercises/practice/alphametics/alphametics.pl

@@ -0,0 +1 @@
+solve(Equation, Solution).

exercises/practice/alphametics/alphametics_tests.plt

@@ -0,0 +1,55 @@
+pending :-
+    current_prolog_flag(argv, ['--all'|_]).
+pending :-
+    write('\nA TEST_IS PENDING!\n'),
+    fail.
+
+:- begin_tests(alphametics).
+
+    test(puzzle_with_three_letters, condition(true)) :-
+        solve("I + BB == ILL", Solution),
+        sort(Solution, SortedSolution),
+        SortedSolution == ['B'-9, 'I'-1, 'L'-0].
+
+    test(solution_must_have_unique_value_for_each_letter, [fail, condition(pending)]) :-
+        solve("A == B", _).
+
+    test(leading_zero_solution_is_invalid, [fail, condition(pending)]) :-
+        solve("ACA + DD == BD", _).
+
+    test(puzzle_with_two_digits_final_carry, condition(pending)) :-
+        solve("A + A + A + A + A + A + A + A + A + A + A + B == BCC", Solution),
+        sort(Solution, SortedSolution),
+        SortedSolution == ['A'-9, 'B'-1, 'C'-0].
+
+    test(puzzle_with_four_letters, condition(pending)) :-
+        solve("AS + A == MOM", Solution),
+        sort(Solution, SortedSolution),
+        SortedSolution == ['A'-9, 'M'-1, 'O'-0, 'S'-2].
+
+    test(puzzle_with_six_letters, condition(pending)) :-
+        solve("NO + NO + TOO == LATE", Solution),
+        sort(Solution, SortedSolution),
+        SortedSolution == ['A'-0, 'E'-2, 'L'-1, 'N'-7, 'O'-4, 'T'-9].
+
+    test(puzzle_with_seven_letters, condition(pending)) :-
+        solve("HE + SEES + THE == LIGHT", Solution),
+        sort(Solution, SortedSolution),
+        SortedSolution == ['E'-4, 'G'-2, 'H'-5, 'I'-0, 'L'-1, 'S'-9, 'T'-7].
+
+    test(puzzle_with_eight_letters, condition(pending)) :-
+        solve("SEND + MORE == MONEY", Solution),
+        sort(Solution, SortedSolution),
+        SortedSolution == ['D'-7, 'E'-5, 'M'-1, 'N'-6, 'O'-0, 'R'-8, 'S'-9, 'Y'-2].
+
+    test(puzzle_with_ten_letters, condition(pending)) :-
+        solve("AND + A + STRONG + OFFENSE + AS + A + GOOD == DEFENSE", Solution),
+        sort(Solution, SortedSolution),
+        SortedSolution == ['A'-5, 'D'-3, 'E'-4, 'F'-7, 'G'-8, 'N'-0, 'O'-2, 'R'-1, 'S'-6, 'T'-9].
+
+    test(puzzle_with_ten_letters_and_199_addends, condition(pending)) :-
+        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", Solution),
+        sort(Solution, SortedSolution),
+        SortedSolution == ['A'-1, 'E'-0, 'F'-5, 'H'-8, 'I'-7, 'L'-2, 'O'-6, 'R'-3, 'S'-4, 'T'-9].
+
+:- end_tests(alphametics).