SWISH -- SWI-Prolog for SHaring

:- use_module(library(clpfd)).

% Main solver for a Sudoku puzzle
solver(Rows) :-
    initialize_grid(Rows),
    apply_constraints(Rows),
    maplist(labeling([ff]), Rows).

% Initializes a 9x9 grid with domain constraints
initialize_grid(Rows) :-
    length(Rows, 9),
    maplist(same_length(Rows), Rows),
    append(Rows, Cells),
    Cells ins 1..9.

% Applies row, column, and block constraints
apply_constraints(Rows) :-
    maplist(all_distinct, Rows),       % Ensure rows are unique
    transpose(Rows, Columns),
    maplist(all_distinct, Columns),   % Ensure columns are unique
    enforce_blocks(Rows).             % Ensure 3x3 blocks are unique

% Ensures all 3x3 blocks are distinct
enforce_blocks([A, B, C, D, E, F, G, H, I]) :-
    blocks(A, B, C),
    blocks(D, E, F),
    blocks(G, H, I).

blocks([], [], []).
blocks([A, B, C | Rest1], [D, E, F | Rest2], [G, H, I | Rest3]) :-
    all_distinct([A, B, C, D, E, F, G, H, I]),
    blocks(Rest1, Rest2, Rest3).

% Difficulty analysis
difficulty(Rows, Start, Weak, Constraint, Search) :-
    initialize_grid(Rows),
    count_filled_cells(Rows, Start),
    weak_propagation(Rows, Weak),
    constraint_propagation(Rows, Constraint),
    search_propagation(Rows, Search),
    print_analysis(Start, Weak, Constraint, Search).

% Calculates the number of pre-filled cells
count_filled_cells(Rows, Count) :-
    append(Rows, Cells),
    count_numbers(Cells, Count).

count_numbers([], 0).
count_numbers([H | T], Count) :-
    count_numbers(T, Rest),
    (number(H) -> Count is Rest + 1 ; Count = Rest).

% Weak propagation: Applies minimal constraints
weak_propagation(Rows, Filled) :-
    initialize_grid(Rows),
    apply_constraints(Rows),
    count_filled_cells(Rows, Filled).

% Constraint propagation: Uses domain reduction to propagate constraints
constraint_propagation(Rows, Filled) :-
    solver(Rows), % Solver automatically applies all constraints
    count_filled_cells(Rows, Filled).

% Search propagation: Solves with search and calculates filled cells
search_propagation(Rows, Filled) :-
    solver(Rows), % Reuse the solver for search-based filling
    count_filled_cells(Rows, Filled).

% Prints the percentage analysis
print_analysis(Start, Weak, Constraint, Search) :-
    write('\nPercent Solved from Start:\n'),
    percent_solved(Start, Weak, WeakPercent),
    format('Weak Propagation: ~2f%%\n', [WeakPercent]),
    percent_solved(Start, Constraint, ConstraintPercent),
    format('Constraint Propagation: ~2f%%\n', [ConstraintPercent]),
    percent_solved(Start, Search, SearchPercent),
    format('Search: ~2f%%\n', [SearchPercent]).

percent_solved(Start, End, Percent) :-
    Percent is ((End - Start) / (81 - Start)) * 100.

% Sample puzzles
puzzle(1, [[_,4,_,9,_,_,_,5,_],
           [2,_,_,_,_,_,_,4,_],
           [1,9,_,_,8,_,7,_,_],
           [5,_,_,_,_,_,1,_,_],
           [_,_,7,_,6,_,_,_,3],
           [_,_,_,_,3,_,8,9,_],
           [_,8,_,3,4,_,_,6,_],
           [3,_,_,2,_,8,_,_,_],
           [_,_,_,_,_,_,_,_,_]]).

puzzle(2, [[_,_,9,5,_,_,_,3,7],
           [1,3,7,9,_,_,_,5,2],
           [2,_,_,_,_,3,6,9,_],
           [3,5,2,_,1,_,_,_,6],
           [_,_,_,4,5,2,3,_,_],
           [_,8,1,_,3,_,2,_,_],
           [6,_,3,_,4,_,8,_,9],
           [5,2,_,_,_,1,_,6,_],
           [_,_,_,3,_,7,_,_,_]]).

puzzle(3, [[_,5,_,1,_,_,_,_,_],
           [2,_,_,5,_,_,6,_,_],
           [1,_,_,_,8,_,2,_,_],
           [_,8,_,4,3,_,_,_,_],
           [_,_,_,_,_,_,_,4,_],
           [_,_,_,_,_,7,9,3,2],
           [_,4,_,6,7,_,_,_,_],
           [_,7,_,_,_,_,_,1,9],
           [9,_,_,_,_,8,_,_,_]]).