hnefatafl/src/lib/game/index.ts

// Hnefatafl: the Viking board game of a king's escape. Two sides: the
// attackers, who move first and must capture the king; the defenders, whose
// king must reach a corner (Copenhagen) or the edge (Tablut). Every piece
// moves like a rook, and a piece is taken by being sandwiched between two
// enemies. Nothing is hidden, so a view is the whole state.

import type { GameSpec, Outcome, SeatId, TableOptions } from './spec';
import { RULESETS, type Cell, type Ruleset } from './rules';
import { chooseMove } from './bot';

export const CURRENT_RULES = 1;

export type Side = 'attackers' | 'defenders';
/** One square: empty, an attacker, a defender, or the king. */
export type Piece = '.' | 'a' | 'd' | 'k';

export interface Player {
	id: SeatId;
	name: string;
	side: Side;
}

export interface Move {
	from: number;
	to: number;
	/** Squares emptied by this move's captures. */
	captured: number[];
}

export interface State {
	rules: number;
	set: Ruleset['id'];
	size: number;
	/** Row-major, y * size + x. */
	cells: Piece[];
	seats: SeatId[];
	players: Record<SeatId, Player>;
	toMove: Side;
	moves: Move[];
	/** How often each position (cells and side to move) has stood, for the repetition rule. */
	seen: Record<string, number>;
	over: Outcome | null;
}

export type Input = { from: number; to: number };

export const SIDES: { value: Side; label: string; note: string }[] = [
	{ value: 'defenders', label: 'the defenders, with the king', note: 'Fewer pieces, and the king must reach safety before the ring closes.' },
	{ value: 'attackers', label: 'the attackers', note: 'Twice the pieces, and the first move; close every road and take the king.' }
];

// --- The board ---------------------------------------------------------------

export function at(size: number, c: Cell): number {
	return c.y * size + c.x;
}

export function cellOf(size: number, i: number): Cell {
	return { x: i % size, y: Math.floor(i / size) };
}

export function throneOf(size: number): number {
	const mid = (size - 1) / 2;
	return mid * size + mid;
}

export function cornersOf(size: number): number[] {
	return [0, size - 1, size * (size - 1), size * size - 1];
}

export function isEdge(size: number, i: number): boolean {
	const { x, y } = cellOf(size, i);
	return x === 0 || y === 0 || x === size - 1 || y === size - 1;
}

const DIRECTIONS = [
	[1, 0],
	[-1, 0],
	[0, 1],
	[0, -1]
] as const;

function neighbors(size: number, i: number): number[] {
	const { x, y } = cellOf(size, i);
	const out: number[] = [];
	if (y > 0) out.push(i - size);
	if (y < size - 1) out.push(i + size);
	if (x > 0) out.push(i - 1);
	if (x < size - 1) out.push(i + 1);
	return out;
}

/** The square on the far side of `mid` from `from`, or -1 off the board. */
export function beyond(size: number, from: number, mid: number): number {
	const a = cellOf(size, from);
	const b = cellOf(size, mid);
	const c = { x: b.x + (b.x - a.x), y: b.y + (b.y - a.y) };
	if (c.x < 0 || c.y < 0 || c.x >= size || c.y >= size) return -1;
	return at(size, c);
}

export function sideOf(p: Piece | undefined): Side | null {
	return p === 'a' ? 'attackers' : p === 'd' || p === 'k' ? 'defenders' : null;
}

export function rulesetOf(state: State): Ruleset {
	return RULESETS[state.set];
}

// --- Setting up ---------------------------------------------------------------

export function createGame(names: Record<SeatId, string>, _seed = 0, rules = CURRENT_RULES, options?: TableOptions): State {
	const set = options?.set === 'tablut' ? RULESETS.tablut : RULESETS.copenhagen;
	const size = set.size;
	const cells: Piece[] = Array(size * size).fill('.');
	for (const c of set.attackers) cells[at(size, c)] = 'a';
	for (const c of set.defenders) cells[at(size, c)] = 'd';
	cells[throneOf(size)] = 'k';
	const seats = Object.keys(names);
	const hostSide: Side = options?.side === 'attackers' ? 'attackers' : 'defenders';
	const players: Record<SeatId, Player> = {};
	seats.forEach((id, i) => {
		players[id] = { id, name: names[id], side: i === 0 ? hostSide : hostSide === 'attackers' ? 'defenders' : 'attackers' };
	});
	const state: State = { rules, set: set.id, size, cells, seats, players, toMove: 'attackers', moves: [], seen: {}, over: null };
	state.seen[positionKey(state)] = 1;
	return state;
}

function positionKey(state: State): string {
	return state.cells.join('') + (state.toMove === 'attackers' ? 'a' : 'd');
}

export function seatOfSide(state: State, side: Side): SeatId | null {
	return state.seats.find((id) => state.players[id].side === side) ?? null;
}

// --- Moving -----------------------------------------------------------------------

/** Where the piece on `from` may go: along its row and column, through empty squares. */
export function movesFrom(state: State, from: number): number[] {
	return movesOn(rulesetOf(state), state.cells, from);
}

export function movesOn(set: Ruleset, cells: Piece[], from: number): number[] {
	const size = set.size;
	const piece = cells[from];
	if (piece === '.' || piece === undefined) return [];
	const king = piece === 'k';
	const throne = throneOf(size);
	const corners = set.markedCorners ? cornersOf(size) : [];
	const { x, y } = cellOf(size, from);
	const out: number[] = [];
	for (const [dx, dy] of DIRECTIONS) {
		for (let step = 1; ; step++) {
			const nx = x + dx * step;
			const ny = y + dy * step;
			if (nx < 0 || ny < 0 || nx >= size || ny >= size) break;
			const i = at(size, { x: nx, y: ny });
			if (cells[i] !== '.') break;
			if (corners.includes(i)) {
				if (king) out.push(i);
				break;
			}
			if (i === throne) {
				if (king) out.push(i);
				else if (!set.passThrone) break;
				continue;
			}
			out.push(i);
		}
	}
	return out;
}

export function legalMoves(state: State, side: Side = state.toMove): Move[] {
	const out: Move[] = [];
	if (state.over) return out;
	state.cells.forEach((p, i) => {
		if (sideOf(p) !== side) return;
		for (const to of movesFrom(state, i)) out.push({ from: i, to, captured: [] });
	});
	return out;
}

/** Whether `i` closes a capture on a piece of `side`: an enemy (an armed king counts), a marked corner, or the empty throne. */
function hostile(set: Ruleset, cells: Piece[], i: number, side: Side): boolean {
	const p = cells[i];
	if (p !== '.') {
		const s = sideOf(p);
		if (s === null || s === side) return false;
		return p !== 'k' || set.kingArmed;
	}
	if (set.markedCorners && cornersOf(set.size).includes(i)) return true;
	return i === throneOf(set.size);
}

/** Whether the attackers have the king where he stands. */
function kingTaken(set: Ruleset, cells: Piece[], kingAt: number): boolean {
	const size = set.size;
	const throne = throneOf(size);
	const around = neighbors(size, kingAt);
	const attackersAround = around.filter((n) => cells[n] === 'a').length;
	if (kingAt === throne) return attackersAround === 4;
	if (around.includes(throne) && cells[throne] === '.') return attackersAround === 3;
	if (set.kingCapturedByFour) return around.length === 4 && attackersAround === 4;
	// Like any piece: two attackers on opposite sides.
	const { x, y } = cellOf(size, kingAt);
	if (x > 0 && x < size - 1 && cells[kingAt - 1] === 'a' && cells[kingAt + 1] === 'a') return true;
	return y > 0 && y < size - 1 && cells[kingAt - size] === 'a' && cells[kingAt + size] === 'a';
}

/** The squares a piece just landed on `to` takes: custodial captures, the king by his own rule, a shieldwall along the edge. */
export function capturesOn(set: Ruleset, cells: Piece[], to: number): number[] {
	const size = set.size;
	const piece = cells[to];
	const side = sideOf(piece)!;
	const captured: number[] = [];
	for (const n of neighbors(size, to)) {
		const target = cells[n];
		if (target === '.' || target === 'k' || sideOf(target) === side) continue;
		const far = beyond(size, to, n);
		if (far !== -1 && hostile(set, cells, far, sideOf(target)!)) captured.push(n);
	}
	if (side === 'attackers') {
		const kingAt = cells.indexOf('k');
		if (kingAt !== -1 && neighbors(size, kingAt).includes(to) && kingTaken(set, cells, kingAt)) captured.push(kingAt);
	}
	if (set.shieldwall && isEdge(size, to)) {
		for (const run of shieldwallRuns(set, cells, to, side)) captured.push(...run);
	}
	return captured;
}

/** Slide a piece and take what it takes, on a copy of the board. */
export function playOn(set: Ruleset, cells: Piece[], from: number, to: number): { cells: Piece[]; captured: number[] } {
	const next = cells.slice();
	next[to] = next[from];
	next[from] = '.';
	const captured = capturesOn(set, next, to);
	for (const i of captured) next[i] = '.';
	return { cells: next, captured };
}

/** Apply a move to a copy of the state: the piece slides, captures fall, and the game may end. */
export function applyMove(previous: State, from: number, to: number): State {
	const set = rulesetOf(previous);
	const piece = previous.cells[from];
	const side = sideOf(piece)!;
	const played = playOn(set, previous.cells, from, to);
	const state: State = { ...previous, cells: played.cells, moves: [...previous.moves, { from, to, captured: played.captured }], seen: { ...previous.seen } };
	const { size, cells } = state;

	const kingAt = cells.indexOf('k');
	const win = (winner: Side, reason: string) => {
		state.over = { winner: seatOfSide(state, winner), reason };
	};
	if (kingAt === -1) win('attackers', 'The king is taken.');
	else if (side === 'defenders' && piece === 'k' && escaped(state, kingAt)) win('defenders', set.escape === 'corner' ? 'The king reaches a corner.' : 'The king reaches the edge.');
	else if (set.edgeFort && side === 'defenders' && edgeFort(state, kingAt)) win('defenders', 'The king holds an edge fort the attackers cannot break.');
	else if (set.encirclement && side === 'attackers' && encircled(state)) win('attackers', 'The defenders are sealed away from every edge.');

	state.toMove = side === 'attackers' ? 'defenders' : 'attackers';
	if (!state.over) {
		const key = positionKey(state);
		state.seen[key] = (state.seen[key] ?? 0) + 1;
		const next = state.players[seatOfSide(state, state.toMove)!]?.name ?? state.toMove;
		// Perpetual repetition is forbidden, and the Copenhagen rule lays the loss on the defenders.
		if (state.seen[key] >= 3) win('attackers', 'The position stands a third time: perpetual repetition loses for the defenders.');
		else if (legalMoves(state, state.toMove).length === 0) win(side, `${next} has no move.`);
	}
	return state;
}

function escaped(state: State, kingAt: number): boolean {
	return rulesetOf(state).escape === 'corner' ? cornersOf(state.size).includes(kingAt) : isEdge(state.size, kingAt);
}

/** Runs of enemy pieces along the edge beside `to`, bracketed at both ends and each faced from inland. */
function shieldwallRuns(set: Ruleset, cells: Piece[], to: number, side: Side): number[][] {
	const size = set.size;
	const { x, y } = cellOf(size, to);
	const along: [number, number][] = x === 0 || x === size - 1 ? [[0, 1], [0, -1]] : [[1, 0], [-1, 0]];
	const inland = x === 0 ? { x: 1, y: 0 } : x === size - 1 ? { x: -1, y: 0 } : y === 0 ? { x: 0, y: 1 } : { x: 0, y: -1 };
	const runs: number[][] = [];
	for (const [dx, dy] of along) {
		const run: number[] = [];
		let cx = x + dx;
		let cy = y + dy;
		let closed = false;
		while (cx >= 0 && cy >= 0 && cx < size && cy < size) {
			const i = at(size, { x: cx, y: cy });
			const p = cells[i];
			if (p === '.') {
				closed = cornersOf(size).includes(i);
				break;
			}
			if (sideOf(p) === side) {
				closed = true;
				break;
			}
			const facing = cells[at(size, { x: cx + inland.x, y: cy + inland.y })];
			if (sideOf(facing) !== side) break;
			run.push(i);
			cx += dx;
			cy += dy;
		}
		if (closed && run.length >= 2) runs.push(run.filter((i) => cells[i] !== 'k'));
	}
	return runs;
}

/** The pieces that bound the empty squares reachable from `start`. */
function bounds(state: State, start: number): Set<number> {
	const squares = new Set<number>([start]);
	const out = new Set<number>();
	const queue = [start];
	while (queue.length) {
		const i = queue.pop()!;
		for (const n of neighbors(state.size, i)) {
			if (state.cells[n] === '.') {
				if (!squares.has(n)) {
					squares.add(n);
					queue.push(n);
				}
			} else out.add(n);
		}
	}
	return out;
}

/** The king on the edge, walled in by defenders alone, with a move to make. */
function edgeFort(state: State, kingAt: number): boolean {
	if (!isEdge(state.size, kingAt) || movesFrom(state, kingAt).length === 0) return false;
	for (const b of bounds(state, kingAt)) if (state.cells[b] === 'a') return false;
	return true;
}

/** No defender, king included, can ever reach an edge square. */
function encircled(state: State): boolean {
	const { size, cells } = state;
	const seen = new Set<number>();
	const queue: number[] = [];
	cells.forEach((p, i) => {
		if (sideOf(p) === 'defenders') {
			seen.add(i);
			queue.push(i);
		}
	});
	if (queue.length === 0) return false;
	while (queue.length) {
		const i = queue.pop()!;
		if (isEdge(size, i)) return false;
		for (const n of neighbors(size, i)) {
			if (cells[n] === 'a' || seen.has(n)) continue;
			seen.add(n);
			queue.push(n);
		}
	}
	return true;
}

// --- The contract ---------------------------------------------------------------

export function resolveRound(previous: State, inputs: Record<SeatId, Input>): State {
	if (previous.over) return previous;
	const seat = seatOfSide(previous, previous.toMove);
	const input = seat ? inputs[seat] : undefined;
	if (!seat || !input || validateMove(previous, seat, input)) return previous;
	return applyMove(previous, input.from, input.to);
}

export function validateMove(state: State, seat: SeatId, input: Input): string | null {
	if (state.over) return 'The game is over.';
	const player = state.players[seat];
	if (!player) return 'You hold no seat.';
	if (player.side !== state.toMove) return 'It is not your side to move.';
	if (sideOf(state.cells[input.from]) !== player.side) return 'That is not one of your pieces.';
	if (!movesFrom(state, input.from).includes(input.to)) return 'That piece cannot move there.';
	return null;
}

export const game: GameSpec<State, Input> = {
	seatIds: ['A', 'B'],
	minSeats: 2,
	botNames: ['Hrothgar', 'Ingrid', 'Sigrid', 'Torvald', 'Astrid', 'Leif'],
	currentRules: CURRENT_RULES,
	options: [
		{
			key: 'set',
			label: 'Rules',
			choices: [
				{ value: 'copenhagen', label: 'Copenhagen, 11 by 11', note: 'The modern tournament game. The king escapes to a corner and falls only to four attackers, three beside the throne.' },
				{ value: 'tablut', label: 'Tablut, 9 by 9, after Linnaeus', note: 'The older game. The king escapes to any edge square, and away from the throne two attackers take him like any piece.' }
			],
			default: 'copenhagen'
		},
		{ key: 'side', label: 'You play', choices: SIDES, default: 'defenders' }
	],
	create: createGame,
	resolve: resolveRound,
	needsInput: (state, seat) => !state.over && state.players[seat]?.side === state.toMove,
	over: (state) => state.over,
	turn: (state) => state.moves.length + 1,
	view: (state) => state,
	botInput: (state, seat) => chooseMove(state, seat),
	cleanInput: (raw) => {
		const r = (typeof raw === 'object' && raw !== null ? raw : {}) as Record<string, unknown>;
		return { from: Number.isInteger(r.from) ? (r.from as number) : -1, to: Number.isInteger(r.to) ? (r.to as number) : -1 };
	},
	validate: validateMove,
	nameOf: (state, seat) => state.players[seat]?.name ?? seat,
	tally: (state) => {
		const lines: Record<string, number> = {};
		lines[state.set === 'tablut' ? 'played as Tablut' : 'played by Copenhagen rules'] = 1;
		const reason = state.over?.reason ?? '';
		if (/reaches/.test(reason)) lines["won by the king's escape"] = 1;
		else if (/taken/.test(reason)) lines["won by taking the king"] = 1;
		else if (/edge fort/.test(reason)) lines['won by an edge fort'] = 1;
		else if (/sealed/.test(reason)) lines['won by encirclement'] = 1;
		else if (/repetition|no move/.test(reason)) lines['decided by repetition or a stalemate'] = 1;
		return lines;
	}
};