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calculate_movable.ts
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calculate_movable.ts
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import {
Side,
NonTam2PieceUpward,
Board,
Piece,
Coord,
coordEq,
} from "./type__piece";
import { Profession } from "cerke_online_api";
function applyDeltas(coord: Coord, deltas: Array<[number, number]>): Coord[] {
const [i, j] = coord;
const assertCoord: (k: number[]) => Coord = ([l, m]) => [l, m] as Coord;
return deltas
.map(([delta_x, delta_y]) => [i + delta_x, j + delta_y])
.filter(([l, m]) => 0 <= l && l <= 8 && 0 <= m && m <= 8)
.map(assertCoord);
}
console.assert(JSON.stringify(getBlockerDeltas([-6, 3])) === "[[-4,2],[-2,1]]");
console.assert(JSON.stringify(getBlockerDeltas([-3, 0])) === "[[-2,0],[-1,0]]");
console.assert(JSON.stringify(getBlockerDeltas([0, 3])) === "[[0,1],[0,2]]");
function getBlockerDeltas(delta: [number, number]): Array<[number, number]> {
/* blocking occurs only when there exists [dx_block, dy_block] such that
- the dot product with [dx, dy] is positive
- the cross product with [dx, dy] is zero
- abs(dx_block, dy_block) < abs(dx, dy)
*/
const [dx, dy] = delta;
const ans: Array<[number, number]> = [];
for (let dx_block = -8; dx_block <= 8; dx_block++) {
for (let dy_block = -8; dy_block <= 8; dy_block++) {
if (dx * dy_block - dy * dx_block !== 0) {
continue;
} // cross product must be zero
if (dx * dx_block + dy * dy_block <= 0) {
continue;
} // cross product must be positive
if (dx_block * dx_block + dy_block * dy_block >= dx * dx + dy * dy) {
continue;
}
// must be strictly small in absolute value
ans[ans.length] = [dx_block, dy_block];
}
}
return ans;
}
function applyDeltasIfNoIntervention(
coord: Coord,
deltas: Array<[number, number]>,
board: Board
): Coord[] {
return ([] as Coord[]).concat(
...deltas.map((delta) =>
applySingleDeltaIfNoIntervention(coord, delta, board)
)
);
}
function applySingleDeltaIfNoIntervention(
coord: Coord,
delta: [number, number],
board: Board
): Coord[] {
const blocker: Coord[] = applyDeltas(coord, getBlockerDeltas(delta));
// if nothing is blocking the way
if (blocker.every(([i, j]) => board[i][j] == null)) {
return applyDeltas(coord, [delta]);
} else {
return [];
}
}
function applySingleDeltaIfZeroOrOneIntervention(
coord: Coord,
delta: [number, number],
board: Board
): Coord[] {
const blocker: Coord[] = applyDeltas(coord, getBlockerDeltas(delta));
// if no piece or a single piece is blocking the way
if (blocker.filter(([i, j]) => board[i][j] != null).length <= 1) {
return applyDeltas(coord, [delta]);
} else {
return [];
}
}
function applyDeltasIfZeroOrOneIntervention(
coord: Coord,
deltas: Array<[number, number]>,
board: Board
): Coord[] {
return ([] as Coord[]).concat(
...deltas.map((delta) =>
applySingleDeltaIfZeroOrOneIntervention(coord, delta, board)
)
);
}
export function eightNeighborhood(coord: Coord): Coord[] {
return applyDeltas(coord, [
[-1, -1],
[-1, 0],
[-1, 1],
[0, -1],
[0, 1],
[1, -1],
[1, 0],
[1, 1],
]);
}
export function isTamHue(
coord: Coord,
board: Readonly<Board>,
tam_itself_is_tam_hue: boolean
): boolean {
// unconditionally TamHue
if (
coordEq(coord, [2, 2]) ||
coordEq(coord, [2, 6]) ||
coordEq(coord, [3, 3]) ||
coordEq(coord, [3, 5]) ||
coordEq(coord, [4, 4]) ||
coordEq(coord, [5, 3]) ||
coordEq(coord, [5, 5]) ||
coordEq(coord, [6, 2]) ||
coordEq(coord, [6, 6])
) {
return true;
}
if (tam_itself_is_tam_hue && board[coord[0]][coord[1]] === "Tam2") {
return true;
}
// is Tam2 available at any neighborhood?
return eightNeighborhood(coord).some(([i, j]) => board[i][j] === "Tam2");
}
/** Checks whether it is possible for the moving piece to occupy the destination, either by moving to an empty square or taking the opponent's piece.
* @param {Side} side the side who is moving the piece
* @param {Coord} dest destination
* @param {Piece} piece_to_move piece that is moving
* @param {Readonly<Board>} board the board
* @param {boolean} tam_itself_is_tam_hue whether tam2 itself is tam2 hue
*/
export function canGetOccupiedBy(
side: Side,
dest: Coord,
piece_to_move: Piece,
board: Readonly<Board>,
tam_itself_is_tam_hue: boolean
) {
if (piece_to_move === "Tam2") {
const [i, j] = dest;
const destPiece = board[i][j];
/* It is allowed to enter an empty square */
return destPiece === null;
} else {
return canGetOccupiedByNonTam(side, dest, board, tam_itself_is_tam_hue);
}
}
export function canGetOccupiedByNonTam(
side: Side,
dest: Coord,
board: Readonly<Board>,
tam_itself_is_tam_hue: boolean
) {
/* Intentionally does not verify whether the piece itself is of opponent */
const isProtectedByOpponentTamHueAUai = (side: Side, coord: Coord) =>
eightNeighborhood(coord).filter(([a, b]) => {
const piece = board[a][b];
if (piece == null) {
return false;
}
if (piece === "Tam2") {
return false;
}
return (
piece.prof === Profession.Uai1 &&
piece.side !== side &&
isTamHue([a, b], board, tam_itself_is_tam_hue)
);
}).length > 0;
const [i, j] = dest;
const destPiece = board[i][j];
/* Tam2 can never be taken */
if (destPiece === "Tam2") {
return false;
}
/* It is always allowed to enter an empty square */
if (destPiece === null) {
return true;
} else {
return (
destPiece.side !== side /* cannot take your own piece */ &&
!isProtectedByOpponentTamHueAUai(
side,
dest
) /* must not be protected by tam2 hue a uai1 */
);
}
}
/**
* Calculates the possible squares to which the piece can MOVE to. THIS INCLUDES SQUARES OCCUPIED BY TAM2, ALLIES, OR OPPONENTS PROTECTED BY TAM2HUEAUAI1
* @param coord the square from which the piece moves
* @param piece the piece to be moved
* @param board the board
* @param tam_itself_is_tam_hue rule variation: does Tam2 itself count as a tam2 hue?
*/
export function calculateMovablePositions(
coord: Coord,
piece: "Tam2" | NonTam2PieceUpward,
board: Board,
tam_itself_is_tam_hue: boolean
): { finite: Coord[]; infinite: Coord[] } {
if (piece === "Tam2") {
return { finite: eightNeighborhood(coord), infinite: [] };
}
if (piece.prof === Profession.Io) {
return { finite: eightNeighborhood(coord), infinite: [] };
}
const UPLEFT: Array<[number, number]> = [
[-8, -8],
[-7, -7],
[-6, -6],
[-5, -5],
[-4, -4],
[-3, -3],
[-2, -2],
[-1, -1],
];
const UPRIGHT: Array<[number, number]> = [
[-8, 8],
[-7, 7],
[-6, 6],
[-5, 5],
[-4, 4],
[-3, 3],
[-2, 2],
[-1, 1],
];
const DOWNLEFT: Array<[number, number]> = [
[8, -8],
[7, -7],
[6, -6],
[5, -5],
[4, -4],
[3, -3],
[2, -2],
[1, -1],
];
const DOWNRIGHT: Array<[number, number]> = [
[8, 8],
[7, 7],
[6, 6],
[5, 5],
[4, 4],
[3, 3],
[2, 2],
[1, 1],
];
const UP: Array<[number, number]> = [
[-1, 0],
[-2, 0],
[-3, 0],
[-4, 0],
[-5, 0],
[-6, 0],
[-7, 0],
[-8, 0],
];
const DOWN: Array<[number, number]> = [
[1, 0],
[2, 0],
[3, 0],
[4, 0],
[5, 0],
[6, 0],
[7, 0],
[8, 0],
];
const LEFT: Array<[number, number]> = [
[0, -1],
[0, -2],
[0, -3],
[0, -4],
[0, -5],
[0, -6],
[0, -7],
[0, -8],
];
const RIGHT: Array<[number, number]> = [
[0, 1],
[0, 2],
[0, 3],
[0, 4],
[0, 5],
[0, 6],
[0, 7],
[0, 8],
];
if (isTamHue(coord, board, tam_itself_is_tam_hue)) {
switch (piece.prof) {
case Profession.Uai1: // General, 将, varxle
return { finite: eightNeighborhood(coord), infinite: [] };
case Profession.Kaun1:
return {
finite: applyDeltas(coord, [
[-2, -2],
[-2, 2],
[2, 2],
[2, -2],
]),
infinite: [],
}; // 車, vadyrd
case Profession.Kauk2: // Pawn, 兵, elmer
return {
finite: [
...applyDeltas(coord, [
[-1, 0],
[0, -1],
[0, 1],
[1, 0],
]),
...applySingleDeltaIfNoIntervention(coord, [-2, 0], board),
],
infinite: [],
};
case Profession.Nuak1: // Vessel, 船, felkana
return {
finite: [
...applyDeltas(coord, [
[0, -1],
[0, 1],
]),
...applyDeltasIfNoIntervention(
coord,
[
[0, -2],
[0, 2],
],
board
),
],
infinite: applyDeltasIfNoIntervention(coord, [...UP, ...DOWN], board),
};
case Profession.Gua2: // Rook, 弓, gustuer
case Profession.Dau2: // Tiger, 虎, stistyst
return {
finite: [],
infinite: applyDeltasIfNoIntervention(
coord,
[...UPLEFT, ...UPRIGHT, ...DOWNLEFT, ...DOWNRIGHT],
board
),
};
case Profession.Maun1: {
// Horse, 馬, dodor
const deltas: Array<[number, number]> = [
[-8, -8],
[-7, -7],
[-6, -6],
[-5, -5],
[-4, -4],
[-3, -3],
[-2, -2],
[-8, 8],
[-7, 7],
[-6, 6],
[-5, 5],
[-4, 4],
[-3, 3],
[-2, 2],
[8, -8],
[7, -7],
[6, -6],
[5, -5],
[4, -4],
[3, -3],
[2, -2],
[8, 8],
[7, 7],
[6, 6],
[5, 5],
[4, 4],
[3, 3],
[2, 2],
];
let inf: Coord[] = [];
for (let i = 0; i < deltas.length; i++) {
const delta = deltas[i];
const blocker_deltas = getBlockerDeltas(delta).filter(
(d) =>
/*
* remove [-1, 1], [-1, -1], [1, -1] and [1, 1], because
* pieces here will not prevent Tam2HueAMaun1 from moving.
*/
!([-1, 1].includes(d[0]) && [-1, 1].includes(d[1]))
);
const blocker: Coord[] = applyDeltas(coord, blocker_deltas);
// if nothing is blocking the way
if (blocker.every(([i, j]) => board[i][j] == null)) {
inf = [...inf, ...applyDeltas(coord, [delta])];
}
}
return {
finite: [],
infinite: inf,
};
}
case Profession.Kua2: // Clerk, 筆, kua
return {
finite: [],
infinite: applyDeltasIfNoIntervention(
coord,
[...UP, ...DOWN, ...LEFT, ...RIGHT],
board
),
};
case Profession.Tuk2: // Shaman, 巫, terlsk
return {
finite: [],
infinite: applyDeltasIfZeroOrOneIntervention(
coord,
[
...UP,
...DOWN,
...LEFT,
...RIGHT,
...UPLEFT,
...UPRIGHT,
...DOWNLEFT,
...DOWNRIGHT,
],
board
),
};
}
} else {
switch (piece.prof) {
case Profession.Kauk2:
return { finite: applyDeltas(coord, [[-1, 0]]), infinite: [] }; // Pawn, 兵, elmer
case Profession.Kaun1:
return {
finite: applyDeltas(coord, [
[-2, 0],
[2, 0],
[0, -2],
[0, 2],
]),
infinite: [],
}; // 車, vadyrd
case Profession.Dau2: // Tiger, 虎, stistyst
return {
finite: applyDeltas(coord, [
[-1, -1],
[-1, 1],
[1, -1],
[1, 1],
]),
infinite: [],
};
case Profession.Maun1: // Horse, 馬, dodor
return {
finite: applyDeltas(coord, [
[-2, -2],
[-2, 2],
[2, 2],
[2, -2],
]),
infinite: [],
};
case Profession.Nuak1: // Vessel, 船, felkana
return {
finite: [],
infinite: applyDeltasIfNoIntervention(coord, UP, board),
};
case Profession.Gua2: // Rook, 弓, gustuer
return {
finite: [],
infinite: applyDeltasIfNoIntervention(
coord,
[...UP, ...DOWN, ...LEFT, ...RIGHT],
board
),
};
case Profession.Kua2: // Clerk, 筆, kua
return {
finite: applyDeltas(coord, [
[0, -1],
[0, 1],
]),
infinite: applyDeltasIfNoIntervention(coord, [...UP, ...DOWN], board),
};
case Profession.Tuk2: // Shaman, 巫, terlsk
return {
finite: applyDeltas(coord, [
[-1, 0],
[1, 0],
]),
infinite: applyDeltasIfNoIntervention(
coord,
[...LEFT, ...RIGHT],
board
),
};
case Profession.Uai1: // General, 将, varxle
return {
finite: applyDeltas(coord, [
[-1, -1],
[-1, 0],
[-1, 1],
[0, -1],
[0, 1],
[1, -1],
[1, 1],
]),
infinite: [],
};
}
}
}