cool
This commit is contained in:
Daniel Ledda
99
src/solver/SomaSolution.ts
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99
src/solver/SomaSolution.ts
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@@ -0,0 +1,99 @@
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import type VoxelSpace from "./VoxelSpace";
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export default class SomaSolution {
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private solutionSpaces: VoxelSpace[];
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private dim: number;
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constructor(dim: number) {
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if (dim < 0 || dim % 1 !== 0) {
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throw new Error("Dimension must be a whole positive integer!");
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}
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this.dim = dim;
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this.solutionSpaces = [];
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}
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static filterUnique(solutions: SomaSolution[]): SomaSolution[] {
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if (solutions.length === 0) {
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return [];
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}
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const uniqueSolns = [solutions[0]];
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for (const solution of solutions) {
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let foundMatch = false;
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for (const rotation of solution.getUniqueRotations()) {
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let end = uniqueSolns.length;
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for (let i = 0; i < end; i++) {
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if (rotation.matches(uniqueSolns[i])) {
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foundMatch = true;
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}
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}
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}
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if (!foundMatch) {
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uniqueSolns.push(solution);
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}
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}
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return uniqueSolns;
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}
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getUniqueRotations(): SomaSolution[] {
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if (this.solutionSpaces.length === 0) {
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return [];
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}
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const result: SomaSolution[] = [];
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const allRots = this.solutionSpaces.map(space => space.getAllRotations());
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for (let i = 0; i < allRots[0].length; i++) {
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const solnRot = new SomaSolution(this.dim);
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allRots.forEach(rotGroup => solnRot.addSpace(rotGroup[i]));
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result.push(solnRot);
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}
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return result;
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}
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matches(solution: SomaSolution) {
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for (let i = 0; i < this.solutionSpaces.length; i++) {
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if (!this.solutionSpaces[i].matches(solution.solutionSpaces[i])) {
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return false;
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}
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}
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return true;
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}
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addSpace(space: VoxelSpace) {
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this.solutionSpaces.push(space);
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}
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print() {
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let accum = "";
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console.log("---");
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for (let x = 0; x < this.dim; x++) {
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for (let y = 0; y < this.dim; y++) {
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for (let z = 0; z < this.dim; z++) {
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for (const space of this.solutionSpaces) {
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if (space.at(x, y, z)) {
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accum += space.getId();
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}
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}
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}
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console.log(accum);
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accum = "";
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}
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if (x !== this.dim - 1) {
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console.log("-");
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}
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}
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console.log("---");
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}
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at(x: number, y: number, z: number) {
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for (const space of this.solutionSpaces) {
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if (space.at(x, y, z)) {
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return space.getId();
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}
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}
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return 0;
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}
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clone() {
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const clone = new SomaSolution(this.dim);
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clone.solutionSpaces = this.solutionSpaces.slice();
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return clone;
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}
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}
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49
src/solver/SomaSolver.ts
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49
src/solver/SomaSolver.ts
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@@ -0,0 +1,49 @@
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import VoxelSpace from "./VoxelSpace";
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import SomaSolution from "./SomaSolution";
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export default class SomaSolver {
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private solutionCube: VoxelSpace;
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private dim: number;
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private solutions: SomaSolution[] = [];
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private iterations: number = 0;
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constructor(dimension: number) {
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if (dimension % 1 !== 0 || dimension < 0) {
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throw new Error("The argument 'dimension' must be a positive whole number");
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}
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this.dim = dimension;
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this.solutionCube = new VoxelSpace(0, [dimension, dimension, dimension], Array(dimension**3).fill(0));
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}
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solve(polycubes: VoxelSpace[]) {
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if (polycubes.length === 0) {
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throw new Error("You must pass at least one polycube to solve the puzzle.");
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}
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let cumulativeSize = polycubes.reduce((prev, curr) => prev + curr.size(), 0);
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if (cumulativeSize !== this.dim**3) {
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throw new Error(`The polycubes passed do not add up to exactly enough units to form a cube of dimension ${this.dim}! Got: ${cumulativeSize}, need: ${this.dim**3}`);
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}
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const combosWithRots = polycubes.slice(1).map(polycube => polycube.getUniqueRotations().map(rot => rot.getAllPositionsInCube(this.dim)).flat());
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const combos = [polycubes[0].getAllPositionsInCube(this.dim), ...combosWithRots];
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this.backtrackSolve(this.solutionCube, combos, new SomaSolution(this.dim));
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this.solutions = SomaSolution.filterUnique(this.solutions);
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this.solutions.forEach(sol => sol.print());
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}
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private backtrackSolve(workingSolution: VoxelSpace, polycubes: VoxelSpace[][], currentSoln: SomaSolution, depth = 0) {
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const nextCubeGroup = polycubes[0];
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for (let i = 0; i < nextCubeGroup.length; i++) {
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const fusionAttempt = workingSolution.plus(nextCubeGroup[i]);
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if (fusionAttempt) {
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const nextSoln = currentSoln.clone();
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nextSoln.addSpace(nextCubeGroup[i]);
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if (polycubes.length === 1) {
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this.solutions.push(nextSoln);
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currentSoln = new SomaSolution(this.dim);
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return;
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} else {
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this.backtrackSolve(fusionAttempt, polycubes.slice(1), nextSoln, depth + 1);
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}
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}
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}
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}
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}
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297
src/solver/VoxelSpace.ts
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297
src/solver/VoxelSpace.ts
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@@ -0,0 +1,297 @@
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export type DimensionDef = [number, number, number];
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export default class VoxelSpace {
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private dims: DimensionDef;
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private length: number;
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private space: bigint;
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private id: number;
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constructor(id: number, dims: DimensionDef, space?: boolean[] | bigint, cullEmpty?: boolean) {
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if (!space) {
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space = 0n;
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} else if (Array.isArray(space)) {
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if (space.length !== dims[0] * dims[1] * dims[2]) {
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throw new Error("Vals don't fit in given dimensions.");
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}
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space = VoxelSpace.boolArrayToBigInt(space)
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}
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this.id = id;
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this.length = dims[0] * dims[1] * dims[2];
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this.dims = dims;
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this.space = space;
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if (cullEmpty) {
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this.cullEmptySpace();
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}
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}
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private static boolArrayToBigInt(boolArray: boolean[]): bigint {
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let result = 0n;
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for (let i = 0; i < boolArray.length; i++) {
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if (boolArray[i]) {
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result |= BigInt(1 << i);
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}
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}
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return result;
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}
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binaryRep() {
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return this.space.toString(2);
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}
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private cullEmptySpace() {
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const extrema = {
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xMax: -Infinity,
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xMin: Infinity,
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yMax: -Infinity,
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yMin: Infinity,
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zMax: -Infinity,
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zMin: Infinity,
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};
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let newSpace = 0n;
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this.forEachCell((val, x, y, z) => {
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if (val) {
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extrema.xMax = Math.max(extrema.xMax, x);
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extrema.xMin = Math.min(extrema.xMin, x);
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extrema.yMax = Math.max(extrema.yMax, y);
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extrema.yMin = Math.min(extrema.yMin, y);
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extrema.zMax = Math.max(extrema.zMax, z);
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extrema.zMin = Math.min(extrema.zMin, z);
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}
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});
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let index = 0n;
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for (let x = extrema.xMin; x <= extrema.xMax; x++) {
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for (let y = extrema.yMin; y <= extrema.yMax; y++) {
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for (let z = extrema.zMin; z <= extrema.zMax; z++) {
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if (this.at(x, y, z)) {
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newSpace |= 1n << index;
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}
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index++;
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}
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}
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}
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this.dims[0] = extrema.xMax - extrema.xMin + 1;
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this.dims[1] = extrema.yMax - extrema.yMin + 1;
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this.dims[2] = extrema.zMax - extrema.zMin + 1;
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this.space = newSpace;
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}
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forEachCell(cb: (val: boolean, x: number, y: number, z: number) => any) {
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loopStart: for (let x = 0; x < this.dims[0]; x++) {
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for (let y = 0; y < this.dims[1]; y++) {
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for (let z = 0; z < this.dims[2]; z++) {
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if (cb(this.at(x, y, z), x, y, z) === 0) {
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break loopStart;
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}
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}
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}
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}
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}
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getId() {
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return this.id;
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}
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print() {
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let accum = "";
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console.log("---");
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for (let i = 0; i < this.dims[0]; i++) {
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for (let j = 0; j < this.dims[1]; j++) {
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for (let k = 0; k < this.dims[2]; k++) {
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accum += this.at(i, j, k) ? '#' : 'O';
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}
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console.log(accum);
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accum = "";
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}
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if (i !== this.dims[0] - 1) {
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console.log("-");
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}
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}
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console.log("---");
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}
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getUniqueRotations() {
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const rotations: VoxelSpace[] = [];
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const refSpace = this.clone();
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VoxelSpace.pushNewUniqueSpaces(rotations, refSpace.getAxisSpins('x'));
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refSpace.rot90('y');
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VoxelSpace.pushNewUniqueSpaces(rotations, refSpace.getAxisSpins('x'));
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refSpace.rot90('y');
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VoxelSpace.pushNewUniqueSpaces(rotations, refSpace.getAxisSpins('x'));
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refSpace.rot90('y');
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VoxelSpace.pushNewUniqueSpaces(rotations, refSpace.getAxisSpins('x'));
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refSpace.rot90('z');
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VoxelSpace.pushNewUniqueSpaces(rotations, refSpace.getAxisSpins('x'));
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refSpace.rot90('z');
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refSpace.rot90('z');
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VoxelSpace.pushNewUniqueSpaces(rotations, refSpace.getAxisSpins('x'));
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return rotations;
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}
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getAllRotations() {
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const rotations: VoxelSpace[] = [];
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const refSpace = this.clone();
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rotations.push(...refSpace.getAxisSpins('x'));
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refSpace.rot90('y');
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rotations.push(...refSpace.getAxisSpins('x'));
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refSpace.rot90('y');
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rotations.push(...refSpace.getAxisSpins('x'));
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refSpace.rot90('y');
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rotations.push(...refSpace.getAxisSpins('x'));
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refSpace.rot90('z');
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rotations.push(...refSpace.getAxisSpins('x'));
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refSpace.rot90('z');
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refSpace.rot90('z');
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rotations.push(...refSpace.getAxisSpins('x'));
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return rotations;
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}
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protected static pushNewUniqueSpaces(existingSpaces: VoxelSpace[], newSpaces: VoxelSpace[]) {
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for (const newSpace of newSpaces) {
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let matchFound = false;
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for (const existingSpace of existingSpaces) {
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if (newSpace.matches(existingSpace)) {
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matchFound = true;
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break;
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}
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}
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if (!matchFound) {
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existingSpaces.push(newSpace);
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}
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}
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}
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getAllPositionsInCube(cubeDim: number): VoxelSpace[] {
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if ((cubeDim > 0) && (cubeDim % 1 === 0)) {
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const cubePositions: VoxelSpace[] = [];
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for (let x = 0; x < cubeDim - this.dims[0] + 1; x++) {
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for (let y = 0; y < cubeDim - this.dims[1] + 1; y++) {
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for (let z = 0; z < cubeDim - this.dims[2] + 1; z++) {
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const cubePos = new VoxelSpace(this.id, [cubeDim, cubeDim, cubeDim]);
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this.forEachCell((val, rotX, rotY, rotZ) => {
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cubePos.set(x + rotX, y + rotY, z + rotZ, val);
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});
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cubePositions.push(cubePos);
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}
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}
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}
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return cubePositions;
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} else {
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throw new Error("cubeDim must be a positive integer.");
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}
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}
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matches(space: VoxelSpace) {
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const otherDims = space.getDims();
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for (let i = 0; i < this.dims.length; i++) {
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if (otherDims[i] !== this.dims[i]) {
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return false;
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}
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}
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return this.space === space.getRaw();
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}
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clone() {
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return new VoxelSpace(this.id, this.getDims(), this.getRaw());
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}
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private getAxisSpins(axis: 'x' | 'y' | 'z'): VoxelSpace[] {
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const rotations = [this.clone()];
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for (let i = 0; i < 3; i++) {
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rotations.push(rotations[i].rotated90(axis));
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}
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return rotations;
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}
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getDims(): DimensionDef {
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return this.dims.slice() as DimensionDef;
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}
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getRaw() {
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return this.space;
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}
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// [1, 0, 0] [x] [ x]
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// [0, 0, -1] * [y] = [-z]
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// [0, 1, 0] [z] [ y]
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private newIndexRotX(x: number, y: number, z: number) {
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return this.dims[2] * this.dims[1] * x + this.dims[1] * (this.dims[2] - 1 - z) + y;
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}
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// [ 0, 0, 1] [x] [ z]
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// [ 0, 1, 0] * [y] = [ y]
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// [-1, 0, 0] [z] [-x]
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private newIndexRotY(x: number, y: number, z: number) {
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return this.dims[1] * this.dims[0] * z + this.dims[0] * y + (this.dims[0] - 1 - x);
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}
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// [0, -1, 0] [x] [-y]
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// [1, 0, 0] * [y] = [ x]
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// [0, 0, 1] [z] [ z]
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private newIndexRotZ(x: number, y: number, z: number) {
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return this.dims[0] * this.dims[2] * (this.dims[1] - 1 - y) + this.dims[2] * x + z;
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}
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at(x: number, y: number, z: number) {
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const mask = 1n << BigInt(this.dims[1] * this.dims[2] * x + this.dims[2] * y + z);
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return (this.space & mask) !== 0n;
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}
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toggle(x: number, y: number, z: number) {
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const mask = BigInt(1 << this.dims[1] * this.dims[2] * x + this.dims[2] * y + z);
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this.space ^= mask;
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}
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set(x: number, y: number, z: number, val: boolean) {
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const mask = BigInt(1 << this.dims[1] * this.dims[2] * x + this.dims[2] * y + z);
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if (val) {
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this.space |= mask;
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} else {
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this.space &= ~mask;
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}
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}
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rotated90(dim: 'x' | 'y' | 'z') {
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let newSpace = 0n;
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let newDims: DimensionDef;
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let rotIndex: (i: number, j: number, k: number) => number;
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if (dim === 'x') {
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newDims = [this.dims[0], this.dims[2], this.dims[1]];
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rotIndex = this.newIndexRotX.bind(this);
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} else if (dim === 'y') {
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newDims = [this.dims[2], this.dims[1], this.dims[0]];
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rotIndex = this.newIndexRotY.bind(this);
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} else {
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newDims = [this.dims[1], this.dims[0], this.dims[2]];
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rotIndex = this.newIndexRotZ.bind(this);
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}
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this.forEachCell((val, i, j, k) => {
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if (val) {
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newSpace |= BigInt(1 << rotIndex(i, j, k));
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}
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})
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return new VoxelSpace(this.id, newDims, newSpace);
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}
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rot90(dim: 'x' | 'y' | 'z') {
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const rot = this.rotated90(dim);
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this.space = rot.getRaw();
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this.dims = rot.getDims();
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}
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plus(space: VoxelSpace): VoxelSpace | null {
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const otherSpace = space.getRaw();
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if ((this.space | otherSpace) === (this.space ^ otherSpace)) {
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return new VoxelSpace(this.id, this.dims, otherSpace | this.space);
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}
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return null;
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}
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size() {
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let size = 0;
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this.forEachCell((val) => {
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if (val) {
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size++;
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}
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});
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return size;
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||||
}
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||||
}
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10
src/solver/main.js
Normal file
10
src/solver/main.js
Normal file
@@ -0,0 +1,10 @@
|
||||
import App from './App.svelte';
|
||||
|
||||
const app = new App({
|
||||
target: document.body,
|
||||
props: {
|
||||
name: 'world'
|
||||
}
|
||||
});
|
||||
|
||||
export default app;
|
||||
109
src/solver/main.ts
Normal file
109
src/solver/main.ts
Normal file
@@ -0,0 +1,109 @@
|
||||
import SomaSolver from "./SomaSolver";
|
||||
import VoxelSpace from "./VoxelSpace";
|
||||
|
||||
const tetromino1 = new VoxelSpace(1, [3, 3, 3], [
|
||||
true, true, true,
|
||||
false, true, false,
|
||||
false, false, false,
|
||||
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
], true);
|
||||
|
||||
const tetromino2 = new VoxelSpace(2, [3, 3, 3], [
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, true, false,
|
||||
|
||||
false, true, false,
|
||||
false, true, false,
|
||||
false, true, false,
|
||||
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
], true);
|
||||
|
||||
const tetromino3 = new VoxelSpace(3, [3, 3, 3], [
|
||||
true, false, false,
|
||||
true, true, false,
|
||||
false, true, false,
|
||||
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
], true);
|
||||
|
||||
const tetromino4 = new VoxelSpace(4, [3, 3, 3], [
|
||||
true, true, false,
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
|
||||
true, false, false,
|
||||
true, false, false,
|
||||
false, false, false,
|
||||
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
], true);
|
||||
|
||||
const tetromino5 = new VoxelSpace(5, [3, 3, 3], [
|
||||
true, true, false,
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
|
||||
false, true, false,
|
||||
false, true, false,
|
||||
false, false, false,
|
||||
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
], true);
|
||||
|
||||
const tetromino6 = new VoxelSpace(6, [3, 3, 3], [
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, true, false,
|
||||
|
||||
false, false, false,
|
||||
false, true, false,
|
||||
false, true, true,
|
||||
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
], true);
|
||||
|
||||
const triomino1 = new VoxelSpace(7, [3, 3, 3], [
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, true, false,
|
||||
|
||||
false, false, false,
|
||||
false, true, false,
|
||||
false, true, false,
|
||||
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
false, false, false,
|
||||
], true);
|
||||
|
||||
|
||||
|
||||
// const cube = new VoxelSpace([3, 3, 3], Array(3**3).fill(0));
|
||||
// cube.plus(triomino1)?.plus(tetromino2, {x: 1, y: 0, z: 1})?.print();
|
||||
|
||||
const solver = new SomaSolver(3);
|
||||
console.log("solving");
|
||||
solver.solve([triomino1, tetromino2, tetromino3, tetromino1, tetromino4, tetromino5, tetromino6]);
|
||||
Reference in New Issue
Block a user