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const std = @import("std");
const Input = []Machine;
const Machine = struct {
a: @Vector(2, u32),
b: @Vector(2, u32),
prize: @Vector(2, u32),
};
const test_input =
\\Button A: X+94, Y+34
\\Button B: X+22, Y+67
\\Prize: X=8400, Y=5400
\\
\\Button A: X+26, Y+66
\\Button B: X+67, Y+21
\\Prize: X=12748, Y=12176
\\
\\Button A: X+17, Y+86
\\Button B: X+84, Y+37
\\Prize: X=7870, Y=6450
\\
\\Button A: X+69, Y+23
\\Button B: X+27, Y+71
\\Prize: X=18641, Y=10279
\\
;
pub fn parse(allocator: std.mem.Allocator, data: []const u8) !Input {
var it = std.mem.splitSequence(u8, data, "\n\n");
var machines = std.ArrayList(Machine).init(allocator);
while (it.next()) |m| {
var itt = std.mem.splitSequence(u8, m, ": ");
_ = itt.next() orelse return error.InvalidInput;
const a = itt.next() orelse return error.InvalidInput;
const b = itt.next() orelse return error.InvalidInput;
const prize = itt.next() orelse return error.InvalidInput;
if (itt.next() != null) return error.InvalidInput;
var machine: Machine = undefined;
inline for (.{ a, b, prize }, .{ "a", "b", "prize" }) |str, name| {
const comma = std.mem.indexOf(u8, str, ", ") orelse return error.InvalidInput;
const end = std.mem.indexOfScalar(u8, str, '\n') orelse str.len;
const x = try std.fmt.parseInt(u32, str[2..comma], 10);
const y = try std.fmt.parseInt(u32, str[comma + 4 .. end], 10);
@field(machine, name) = .{ x, y };
}
try machines.append(machine);
}
return machines.items;
}
test "part1" {
var arena = std.heap.ArenaAllocator.init(std.testing.allocator);
defer arena.deinit();
const output = try part1(arena.allocator(), try parse(arena.allocator(), test_input));
try std.testing.expectEqual(480, output);
}
pub fn part1(_: std.mem.Allocator, input: Input) !u32 {
var total_tokens: u32 = 0;
for (input) |machine| {
var fewest: u32 = std.math.maxInt(u32);
for (0..101) |a_presses| for (0..101) |b_presses| {
const tokens: u32 = @intCast(a_presses * 3 + b_presses);
if (tokens >= fewest) continue;
const a_presses_vec: @Vector(2, u32) = @splat(@intCast(a_presses));
const b_presses_vec: @Vector(2, u32) = @splat(@intCast(b_presses));
if (@reduce(
.And,
machine.a * a_presses_vec + machine.b * b_presses_vec == machine.prize,
)) {
// std.debug.print("can win {} with A={}, B={}, tokens={}\n", .{ machine, a_presses, b_presses, tokens });
fewest = tokens;
}
};
if (fewest != std.math.maxInt(@TypeOf(fewest)))
total_tokens += fewest;
}
return total_tokens;
}
test "part2" {
var arena = std.heap.ArenaAllocator.init(std.testing.allocator);
defer arena.deinit();
const output = try part2(arena.allocator(), try parse(arena.allocator(), test_input));
std.debug.print("got {}\n", .{output});
try std.testing.expectEqual(875318608908, output);
}
test "solveDiophantine" {
inline for (.{
.{ .a = 69, .b = 42, .c = 100071, .solutions = 104 },
.{ .a = 2, .b = 4, .c = 7, .solutions = 0 },
.{ .a = 2, .b = 4, .c = 6, .solutions = 2 },
}) |t| {
var it = solveDiophantine(t.a, t.b, t.c);
var solutions: usize = 0;
while (it.next()) |sol| {
std.debug.print("{} * {} + {} * {} = {}\n", .{ t.a, sol[0], t.b, sol[1], t.c });
try std.testing.expectEqual(t.c, t.a * sol[0] + t.b * sol[1]);
try std.testing.expect(sol[0] >= 0);
try std.testing.expect(sol[1] >= 0);
solutions += 1;
}
try std.testing.expectEqual(t.solutions, solutions);
}
}
const DiophantineIterator = struct {
curr: @Vector(2, i64),
diff: @Vector(2, i64),
pub fn next(self: *@This()) ?@Vector(2, i64) {
if (self.curr[1] < 0) return null;
defer self.curr += self.diff;
return self.curr;
}
};
fn solveDiophantine(a: u64, b: u64, c: u64) DiophantineIterator {
const Vec = @Vector(2, i64);
const cast = struct {
fn f(x: u64) i64 {
return @intCast(x);
}
}.f;
const d = std.math.gcd(a, b);
if (c % d != 0) return .{ .curr = .{ undefined, -1 }, .diff = undefined };
const u = @divExact(a, d);
const v = @divExact(b, d);
var x = u;
var y = v;
var sub_x: Vec = .{ 1, 0 };
var sub_y: Vec = .{ 0, 1 };
if (x < y) {
std.mem.swap(u64, &x, &y);
std.mem.swap(Vec, &sub_x, &sub_y);
}
while (y > 1) {
const rem = x % y;
const quot = x / y;
const sub: Vec = sub_x - @as(Vec, @splat(cast(quot))) * sub_y;
// std.debug.print("{} = {} * {} + {}. {} = {} * {} + {} * {}\n", .{ x, y, quot, rem, rem, @divExact(a, d), sub[0], @divExact(b, d), sub[1] });
x = y;
y = rem;
sub_x = sub_y;
sub_y = sub;
}
std.debug.assert(y == 1);
const one = sub_y;
var solution = one * @as(Vec, @splat(cast(@divExact(c, d))));
const k: i64 = -@divFloor(solution[0], cast(v));
solution += .{ k * cast(v), -k * cast(u) };
return .{ .curr = solution, .diff = .{ cast(v), -cast(u) } };
}
pub fn part2(_: std.mem.Allocator, input: Input) !u64 {
var total_tokens: u64 = 0;
for (input) |machine| {
std.debug.print("machine = {}\n", .{machine});
var fewest: u64 = std.math.maxInt(u64);
var x_sols = solveDiophantine(machine.a[0], machine.b[0], @as(u64, @intCast(machine.prize[0])) + 10000000000000);
const y_sols = solveDiophantine(machine.a[1], machine.b[1], @as(u64, @intCast(machine.prize[1])) + 10000000000000);
while (x_sols.next()) |sol_x| {
const ks = (sol_x - y_sols.curr) / y_sols.diff;
if (@reduce(.And, @rem(sol_x - y_sols.curr, y_sols.diff) == @Vector(2, i64){ 0, 0 }) and ks[0] == ks[1]) {
const tokens = @reduce(.Add, sol_x * @Vector(2, i64){ 3, 1 });
fewest = @min(fewest, @as(u64, @intCast(tokens)));
std.debug.print(" possible solution {} for {} tokens\n", .{ sol_x, tokens });
}
}
if (fewest != std.math.maxInt(@TypeOf(fewest)))
total_tokens += fewest;
}
return total_tokens;
}
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