wyrm/src/lib/game/board.ts

// The three boards and how every piece moves on them, on a bare array of
// cells so the engine, the bot and the board drawing share one source. The
// rules are docs/source.md, Gygax's text, read as its "Decisions" section
// says: board 3 is the air, 2 the land, 1 the underworld.

export type Side = 'gold' | 'scarlet';

/** One letter a piece: Gygax's initials, with R for the Dragon (he wrote Dr). */
export type Kind = 'S' | 'G' | 'R' | 'W' | 'O' | 'U' | 'H' | 'T' | 'C' | 'M' | 'K' | 'P' | 'D' | 'B' | 'E';

/** A cell holds '' or a side letter and a kind: 'gK' is Gold's King, 'sR' Scarlet's Dragon. */
export type Cell = string;

export type Setup = 'printed' | 'shifted';

export const FILES = 12;
export const RANKS = 8;
export const LEVELS = 3;
export const PER_LEVEL = FILES * RANKS;
export const CELLS = PER_LEVEL * LEVELS;

export const KINDS: Kind[] = ['S', 'G', 'R', 'W', 'O', 'U', 'H', 'T', 'C', 'M', 'K', 'P', 'D', 'B', 'E'];

export const NAMES: Record<Kind, string> = {
	S: 'Sylph', G: 'Griffon', R: 'Dragon', W: 'Warrior', O: 'Oliphant', U: 'Unicorn', H: 'Hero', T: 'Thief',
	C: 'Cleric', M: 'Mage', K: 'King', P: 'Paladin', D: 'Dwarf', B: 'Basilisk', E: 'Elemental'
};

/** The letters the pieces are written with: Gygax's initials, and Dr for the Dragon. */
export const LETTERS: Record<Kind, string> = {
	S: 'S', G: 'G', R: 'Dr', W: 'W', O: 'O', U: 'U', H: 'H', T: 'T', C: 'C', M: 'M', K: 'K', P: 'P', D: 'D', B: 'B', E: 'E'
};

/** Gygax's values. He gives the King none: 0 here, and the panel says "beyond price". */
export const VALUES: Record<Kind, number> = {
	K: 0, M: 11, P: 10, C: 9, R: 8, G: 5, O: 5, H: 4.5, T: 4, E: 4, B: 3, U: 2.5, D: 2, S: 1, W: 1
};

export const SIDES: Side[] = ['gold', 'scarlet'];
export const SIDE_NAMES: Record<Side, string> = { gold: 'Gold', scarlet: 'Scarlet' };
export const other = (side: Side): Side => (side === 'gold' ? 'scarlet' : 'gold');

/** A cell index from level 1 to 3, file 0 to 11 and rank 0 to 7. */
export const idx = (level: number, file: number, rank: number): number => (level - 1) * PER_LEVEL + rank * FILES + file;
export const levelOf = (i: number): number => Math.floor(i / PER_LEVEL) + 1;
export const fileOf = (i: number): number => i % FILES;
export const rankOf = (i: number): number => Math.floor((i % PER_LEVEL) / FILES);
const inBounds = (file: number, rank: number): boolean => file >= 0 && file < FILES && rank >= 0 && rank < RANKS;

/** The square written as Gygax writes it: 3c4 is the air, file c, rank 4. */
export function squareName(i: number): string {
	return `${levelOf(i)}${'abcdefghijkl'[fileOf(i)]}${rankOf(i) + 1}`;
}

/** The index of a square written as Gygax writes it. */
export function square(name: string): number {
	const level = Number(name[0]);
	const file = 'abcdefghijkl'.indexOf(name[1]);
	const rank = Number(name.slice(2)) - 1;
	if (!(level >= 1 && level <= 3) || file < 0 || !(rank >= 0 && rank < RANKS)) throw new Error(`no square ${name}`);
	return idx(level, file, rank);
}

/** Light squares: a light square sits in Gold's near right corner, l1. */
export const isLight = (i: number): boolean => (fileOf(i) + rankOf(i)) % 2 === 1;

export const sideOf = (cell: Cell): Side | null => (cell === '' ? null : cell[0] === 'g' ? 'gold' : 'scarlet');
export const kindOf = (cell: Cell): Kind => cell[1] as Kind;
export const cellOf = (side: Side, kind: Kind): Cell => (side === 'gold' ? 'g' : 's') + kind;

/** Which way is forward: Gold climbs the ranks, Scarlet descends them. */
export const forward = (side: Side): number => (side === 'gold' ? 1 : -1);

/** The home files of the Sylphs: as printed, or shifted onto the Dwarves' files. */
export const sylphFiles = (setup: Setup): number[] => (setup === 'shifted' ? [1, 3, 5, 7, 9, 11] : [0, 2, 4, 6, 8, 10]);

/** The opening position. */
export function opening(setup: Setup = 'printed'): Cell[] {
	const cells: Cell[] = new Array(CELLS).fill('');
	const backRank: Kind[] = ['O', 'U', 'H', 'T', 'C', 'M', 'K', 'P', 'T', 'H', 'U', 'O'];
	for (const side of SIDES) {
		const home = side === 'gold' ? 0 : RANKS - 1;
		const second = side === 'gold' ? 1 : RANKS - 2;
		for (let f = 0; f < FILES; f++) {
			cells[idx(2, f, home)] = cellOf(side, backRank[f]);
			cells[idx(2, f, second)] = cellOf(side, 'W');
		}
		for (const f of sylphFiles(setup)) cells[idx(3, f, second)] = cellOf(side, 'S');
		cells[idx(3, 2, home)] = cellOf(side, 'G');
		cells[idx(3, 10, home)] = cellOf(side, 'G');
		cells[idx(3, 6, home)] = cellOf(side, 'R');
		for (const f of [1, 3, 5, 7, 9, 11]) cells[idx(1, f, second)] = cellOf(side, 'D');
		cells[idx(1, 2, home)] = cellOf(side, 'B');
		cells[idx(1, 10, home)] = cellOf(side, 'B');
		cells[idx(1, 6, home)] = cellOf(side, 'E');
	}
	return cells;
}

/** A piece on the middle board with an enemy Basilisk beneath it cannot move, capture or give check. */
export function frozen(cells: Cell[], i: number): boolean {
	if (levelOf(i) !== 2) return false;
	const below = cells[i - PER_LEVEL];
	return below !== '' && kindOf(below) === 'B' && sideOf(below) !== sideOf(cells[i]);
}

const KNIGHT = [[1, 2], [2, 1], [-1, 2], [-2, 1], [1, -2], [2, -1], [-1, -2], [-2, -1]];
const GRIFFON = [[2, 3], [3, 2], [-2, 3], [-3, 2], [2, -3], [3, -2], [-2, -3], [-3, -2]];
const ORTHOGONAL = [[1, 0], [-1, 0], [0, 1], [0, -1]];
const DIAGONAL = [[1, 1], [1, -1], [-1, 1], [-1, -1]];
const AROUND = [...ORTHOGONAL, ...DIAGONAL];

/**
 * Every square the piece on `from` may move to or capture on, by the rules
 * alone: its own King may be left in check. The Dragon's capture from afar
 * is a move to the middle-board square it empties. A frozen piece has none.
 */
export function movesFrom(cells: Cell[], from: number, setup: Setup = 'printed'): number[] {
	const cell = cells[from];
	if (cell === '' || frozen(cells, from)) return [];
	const side = sideOf(cell)!;
	const kind = kindOf(cell);
	const level = levelOf(from);
	const f = fileOf(from);
	const r = rankOf(from);
	const fw = forward(side);
	const out: number[] = [];
	const empty = (i: number) => cells[i] === '';
	const enemy = (i: number) => cells[i] !== '' && sideOf(cells[i]) !== side;
	const open = (i: number) => cells[i] === '' || sideOf(cells[i]) !== side;
	/** Add the square if it is on the board and passes the test. */
	const add = (lv: number, file: number, rank: number, ok: (i: number) => boolean): void => {
		if (lv < 1 || lv > LEVELS || !inBounds(file, rank)) return;
		const i = idx(lv, file, rank);
		if (ok(i)) out.push(i);
	};
	/** Slide until something is in the way; a piece of the other side may be taken. */
	const slide = (dirs: number[][]) => {
		for (const [df, dr] of dirs) {
			let file = f + df;
			let rank = r + dr;
			while (inBounds(file, rank)) {
				const i = idx(level, file, rank);
				if (cells[i] === '') out.push(i);
				else {
					if (sideOf(cells[i]) !== side) out.push(i);
					break;
				}
				file += df;
				rank += dr;
			}
		}
	};
	const step = (dirs: number[][], lv = level, ok = open) => {
		for (const [df, dr] of dirs) add(lv, f + df, r + dr, ok);
	};
	const lastRank = side === 'gold' ? RANKS - 1 : 0;

	switch (kind) {
		case 'S':
			if (level === 3) {
				add(3, f - 1, r + fw, empty);
				add(3, f + 1, r + fw, empty);
				add(3, f, r + fw, enemy);
				add(2, f, r, enemy);
			} else if (level === 2) {
				add(3, f, r, empty);
				const homeRank = side === 'gold' ? 1 : RANKS - 2;
				for (const file of sylphFiles(setup)) add(3, file, homeRank, empty);
			}
			break;
		case 'G':
			if (level === 3) {
				step(GRIFFON);
				step(DIAGONAL, 2);
			} else if (level === 2) {
				step(DIAGONAL);
				step(DIAGONAL, 3);
			}
			break;
		case 'R':
			if (level === 3) {
				slide(DIAGONAL);
				step(ORTHOGONAL);
				add(2, f, r, enemy);
				step(ORTHOGONAL, 2, enemy);
			}
			break;
		case 'W':
			if (level === 2) {
				add(2, f, r + fw, empty);
				add(2, f - 1, r + fw, enemy);
				add(2, f + 1, r + fw, enemy);
			}
			break;
		case 'O':
			if (level === 2) slide(ORTHOGONAL);
			break;
		case 'U':
			if (level === 2) step(KNIGHT);
			break;
		case 'T':
			if (level === 2) slide(DIAGONAL);
			break;
		case 'H':
			if (level === 2) {
				step(DIAGONAL);
				step(DIAGONAL.map(([df, dr]) => [df * 2, dr * 2]));
				step(DIAGONAL, 1);
				step(DIAGONAL, 3);
			} else step(DIAGONAL, 2);
			break;
		case 'C':
			step(AROUND);
			add(level + 1, f, r, open);
			add(level - 1, f, r, open);
			break;
		case 'M':
			if (level === 2) {
				slide(ORTHOGONAL);
				slide(DIAGONAL);
				add(3, f, r, open);
				add(1, f, r, open);
			} else {
				step(ORTHOGONAL);
				add(2, f, r, open);
				if (cells[idx(2, f, r)] === '') add(level === 3 ? 1 : 3, f, r, open);
			}
			break;
		case 'K':
			if (level === 2) {
				step(AROUND);
				add(3, f, r, open);
				add(1, f, r, open);
			} else add(2, f, r, open);
			break;
		case 'P':
			step(AROUND);
			if (level === 2) {
				step(KNIGHT);
				for (const lv of [1, 3]) step(ORTHOGONAL.map(([df, dr]) => [df * 2, dr * 2]), lv);
			} else {
				step(ORTHOGONAL.map(([df, dr]) => [df * 2, dr * 2]), 2);
				step(ORTHOGONAL, level === 3 ? 1 : 3);
			}
			break;
		case 'D':
			if (level === 1 || level === 2) {
				if (r !== lastRank) {
					add(level, f, r + fw, empty);
					add(level, f - 1, r + fw, enemy);
					add(level, f + 1, r + fw, enemy);
				}
				add(level, f - 1, r, empty);
				add(level, f + 1, r, empty);
				if (level === 1) add(2, f, r, enemy);
				else add(1, f, r, empty);
			}
			break;
		case 'B':
			if (level === 1) {
				add(1, f, r + fw, open);
				add(1, f - 1, r + fw, open);
				add(1, f + 1, r + fw, open);
				add(1, f, r - fw, empty);
			}
			break;
		case 'E':
			if (level === 1) {
				for (const [df, dr] of ORTHOGONAL) {
					if (!inBounds(f + df, r + dr)) continue;
					const near = idx(1, f + df, r + dr);
					if (open(near)) out.push(near);
					if (cells[near] === '') {
						add(1, f + df * 2, r + dr * 2, open);
						add(2, f + df, r + dr, enemy);
					}
				}
				step(DIAGONAL, 1, empty);
			} else if (level === 2 && cells[idx(1, f, r)] === '') step(ORTHOGONAL, 1);
			break;
	}
	return out;
}

/** Whether `side` attacks square `i` in this position: one of its pieces could capture there now. */
export function attacked(cells: Cell[], i: number, by: Side): boolean {
	for (let from = 0; from < CELLS; from++) {
		const cell = cells[from];
		if (cell === '' || sideOf(cell) !== by) continue;
		if (movesFrom(cells, from).includes(i)) return true;
	}
	return false;
}

export function kingSquare(cells: Cell[], side: Side): number {
	const king = cellOf(side, 'K');
	for (let i = 0; i < CELLS; i++) if (cells[i] === king) return i;
	return -1;
}

export function inCheck(cells: Cell[], side: Side): boolean {
	const k = kingSquare(cells, side);
	return k >= 0 && attacked(cells, k, other(side));
}

export interface Played {
	cells: Cell[];
	captured: Kind | null;
	promoted: boolean;
	/** The Dragon's capture from afar: the Dragon stays and the square it struck is emptied. */
	afar: boolean;
}

/** The position after the move, on a copy. The move is taken to be one `movesFrom` offered. */
export function playOn(cells: Cell[], from: number, to: number): Played {
	const next = cells.slice();
	const piece = cells[from];
	const side = sideOf(piece)!;
	const kind = kindOf(piece);
	const captured = cells[to] === '' ? null : kindOf(cells[to]);
	if (kind === 'R' && levelOf(to) === 2) {
		next[to] = '';
		return { cells: next, captured, promoted: false, afar: true };
	}
	next[from] = '';
	const promoted = kind === 'W' && rankOf(to) === (side === 'gold' ? RANKS - 1 : 0);
	next[to] = promoted ? cellOf(side, 'H') : piece;
	return { cells: next, captured, promoted, afar: false };
}

/** The moves of the piece on `from` that leave its own King out of check. */
export function legalMovesFrom(cells: Cell[], from: number, setup: Setup = 'printed'): number[] {
	const side = sideOf(cells[from]);
	if (!side) return [];
	return movesFrom(cells, from, setup).filter((to) => !inCheck(playOn(cells, from, to).cells, side));
}

/** Every legal move for a side, as [from, to] pairs. */
export function legalMoves(cells: Cell[], side: Side, setup: Setup = 'printed'): [number, number][] {
	const out: [number, number][] = [];
	for (let from = 0; from < CELLS; from++) {
		if (cells[from] === '' || sideOf(cells[from]) !== side) continue;
		for (const to of legalMovesFrom(cells, from, setup)) out.push([from, to]);
	}
	return out;
}

/** Whether a side has any legal move at all, found without listing them. */
export function hasLegalMove(cells: Cell[], side: Side, setup: Setup = 'printed'): boolean {
	for (let from = 0; from < CELLS; from++) {
		if (cells[from] === '' || sideOf(cells[from]) !== side) continue;
		for (const to of movesFrom(cells, from, setup)) if (!inCheck(playOn(cells, from, to).cells, side)) return true;
	}
	return false;
}

/** The pieces a side has left, by kind. */
export function census(cells: Cell[], side: Side): Partial<Record<Kind, number>> {
	const count: Partial<Record<Kind, number>> = {};
	for (const cell of cells) if (cell !== '' && sideOf(cell) === side) count[kindOf(cell)] = (count[kindOf(cell)] ?? 0) + 1;
	return count;
}