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/* -*- tab-width: 2; indent-tabs-mode: nil; js-indent-level: 2 -*- */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
function copy(obj) {
var o = {};
for (var i in obj)
o[i] = obj[i];
return o;
}
Array.prototype.repeat = function (n) {
var s = this.constructor();
for (var i = 0; i < n; i++)
s = s.concat(this);
return s;
}
String.prototype.center = function (w) {
var n = this.length;
if (w <= n)
return this;
var m = Math.floor((w - n) / 2);
return ' '.repeat(m) + this + ' '.repeat(w - n - m);
}
Array.prototype.toString = Array.prototype.toSource
Object.prototype.toString = Object.prototype.toSource
function all(seq) {
for (var e of seq)
if (!e)
return false;
return true;
}
function some(seq) {
for (var e of seq)
if (e)
return e;
return false;
}
function cross(A, B) {
return [for (a of A) for (b of B) a+b];
}
function dict(A) {
var d = {};
for (var e of A)
d[e[0]] = e[1];
return d;
}
function set(A) {
var s = [];
for (var e of A)
if (!s.includes(e))
s.push(e);
return s;
}
function zip(A, B) {
var z = [];
var n = Math.min(A.length, B.length);
for (var i = 0; i < n; i++)
z.push([A[i], B[i]]);
return z;
}
rows = 'ABCDEFGHI';
cols = '123456789';
digits = '123456789';
squares = cross(rows, cols);
unitlist = [for (c of cols) cross(rows, c)]
.concat([for (r of rows) cross(r, cols)])
.concat([for (rs of ['ABC','DEF','GHI']) for (cs of ['123','456','789']) cross(rs, cs)]);
units = dict((for (s of squares)
[s, [for (u of unitlist) if (u.includes(s)) u]]));
peers = dict((for (s of squares)
[s, set([for (u of units[s]) for (s2 of u) if (s2 != s) s2])]));
// Given a string of 81 digits (or . or 0 or -), return a dict of {cell:values}.
function parse_grid(grid) {
grid = [for (c of grid) if ('0.-123456789'.includes(c)) c];
var values = dict((for (s of squares) [s, digits]));
for (var pair of zip(squares, grid)) {
var s = pair[0], d = pair[1];
if (digits.includes(d) && !assign(values, s, d))
return false;
}
return values;
}
// Eliminate all the other values (except d) from values[s] and propagate.
function assign(values, s, d) {
if (all((for (d2 of values[s]) if (d2 != d) eliminate(values, s, d2))))
return values;
return false;
}
// Eliminate d from values[s]; propagate when values or places <= 2.
function eliminate(values, s, d) {
if (!values[s].includes(d))
return values; // Already eliminated
values[s] = values[s].replace(d, '');
if (values[s].length == 0)
return false; // Contradiction: removed last value
if (values[s].length == 1) {
// If there is only one value (d2) left in square, remove it from peers
var d2 = values[s][0];
if (!all((for (s2 of peers[s]) eliminate(values, s2, d2))))
return false;
}
// Now check the places where d appears in the units of s
for (var u of units[s]) {
var dplaces = [for (s of u) if (values[s].includes(d)) s];
if (dplaces.length == 0)
return false;
if (dplaces.length == 1)
// d can only be in one place in unit; assign it there
if (!assign(values, dplaces[0], d))
return false;
}
return values;
}
// Used for debugging.
function print_board(values) {
var width = 1 + Math.max.apply(Math, [for (s of squares) values[s].length]);
var line = '\n' + ['-'.repeat(width*3)].repeat(3).join('+');
for (var r of rows)
print([for (c of cols)
values[r+c].center(width) + ('36'.includes(c) && '|' || '')]
.join('') + ('CF'.includes(r) && line || ''));
print('\n');
}
easy = "..3.2.6..9..3.5..1..18.64....81.29..7.......8..67.82....26.95..8..2.3..9..5.1.3..";
print_board(parse_grid(easy));
// Using depth-first search and constraint propagation, try all possible values.
function search(values) {
if (!values)
return false; // Failed earlier
if (all((for (s of squares) values[s].length == 1)))
return values; // Solved!
// Choose the unfilled square s with the fewest possibilities
// XXX Math.min etc. should work with generator expressions and other iterators
// XXX Math.min etc. should work on arrays (lists or tuples in Python) as well as numbers
var a = [for (s of squares) if (values[s].length > 1) values[s].length + s].sort();
var s = a[0].slice(-2);
return some((for (d of values[s]) search(assign(copy(values), s, d))));
}
hard = '4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......';
print_board(search(parse_grid(hard)))
if (typeof reportCompare === "function")
reportCompare(true, true);
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