minesweeper/src/main/js/Solver.ts

import {range} from "./Common";
import {Field, Square} from "./Field";


/**
 * A solver for a game of Minesweeper.
 */
export class Solver {
    /**
     * Solves the given field as far as the algorithm is able to.
     *
     * The `#startSequence` function on the field must NOT be called before invoking this function.
     *
     * @param field the field to solve
     */
    static solve(field: Field): void {
        if (field.hasWon || field.hasLost) return;
        if (field.hasStarted && !this.step(field.copy())) return;

        if (!field.hasStarted) {
            field.isAutoSolving = true;
            field.runUndoably(() => {
                const target = {x: Math.floor(field.width / 2), y: Math.floor(field.height / 2)};
                const targetSquare = field.getSquareOrElse(target, undefined)!;
                if (targetSquare.hasFlag) field.toggleFlag(target);
                if (targetSquare.hasMark) field.toggleMark(target);
                field.uncover(target);
            });
            field.isAutoSolving = false;
        }

        field.isAutoSolving = true;
        field.runUndoably(() => {
            field.squareList.filter(it => it.hasFlag).forEach(it => field.toggleFlag(it.coords));
            field.squareList.filter(it => it.hasMark).forEach(it => field.toggleMark(it.coords));

            while (this.step(field)) {
                // Repeat until `step` returns false
            }
        });
        field.isAutoSolving = false;
    }

    /**
     * Returns `true` if and only if this solver can solve the given field.
     *
     * This function does not change anything in the given field; solvability is checked on a copy of the field.
     *
     * If the given field has not started and no initial square is given, the solver will start solving at an arbitrary
     * position.
     *
     * @param field the field to check for solvability
     * @param initialSquare the initial coordinates to click at
     */
    static canSolve(field: Field, initialSquare: { x: number, y: number } | undefined = undefined): boolean {
        const copy = field.copy();
        if (initialSquare !== undefined) copy.runUndoably(() => copy.uncover(initialSquare));
        this.solve(copy);
        return copy.hasWon;
    }

    /**
     * Returns a suggestion for a next move based on the current state of the field.
     *
     * @param field the field to suggest a move for
     * @returns a suggestion for a next move based on the current state of the field
     */
    static getHint(field: Field): Square | null {
        if (!field.hasStarted || field.hasWon || field.hasLost) return null;
        const knowns = Solver.getKnowns(field);

        const candidate = knowns.find(square =>
            // Can chord
            square.getNeighborCount(it => it.hasFlag) === square.getNeighborCount(it => it.hasMine) ||
            // Can flag
            square.getNeighborCount(it => it.isCovered && !it.hasFlag) ===
            (square.getNeighborCount(it => it.hasMine) - square.getNeighborCount(it => it.hasFlag))
        );
        if (candidate !== undefined) return candidate;

        for (let i = 0; i < knowns.length; i++) {
            const square = knowns[i];
            const solution = this.matrixSolve(field, square.neighbors.filter(it => !it.isCovered).concat(square), true);
            const candidate = solution.find(it => it !== undefined);
            if (candidate !== undefined)
                return candidate[1];
        }

        const solution = this.matrixSolve(field, knowns, false);
        const candidate2 = solution.find(it => it !== undefined);
        if (candidate2 !== undefined)
            return candidate2[1];

        return null;
    }


    /**
     * Solves in one step through the field.
     *
     * @param field the field to solve one step in
     * @returns `true` if a step could be solved
     * @private
     */
    private static step(field: Field): boolean {
        let flagCount = field.flagCount;
        let coveredCount = field.coveredNonMineCount;

        if (field.hasWon || field.hasLost)
            return false;

        this.stepSingleSquares(field);
        if (field.hasWon || field.flagCount !== flagCount || field.coveredNonMineCount !== coveredCount)
            return true;

        this.stepNeighboringSquares(field);
        if (field.hasWon || field.flagCount !== flagCount || field.coveredNonMineCount !== coveredCount)
            return true;

        this.stepAllSquares(field);
        // noinspection RedundantIfStatementJS // Makes it easier to add more steps
        if (field.hasWon || field.flagCount !== flagCount || field.coveredNonMineCount !== coveredCount)
            return true;

        return false;
    }

    /**
     * Solves the field as much as by considering just one square at a time and looking for trivial solutions.
     *
     * This function is very fast but only finds trivial moves such as a square that can be chorded or a square of which
     * all neighbors can be flagged.
     *
     * @param field the field to solve
     * @private
     */
    private static stepSingleSquares(field: Field): void {
        Solver.getKnowns(field)
            .forEach(square => {
                field.chord(square);
                if (square.getNeighborCount(it => it.isCovered) === square.getNeighborCount(it => it.hasMine))
                    square.neighbors.filter(it => !it.hasFlag).forEach(it => field.toggleFlag(it));
            });
    }

    /**
     * Solves the field as much as possible by considering only one uncovered square and its uncovered neighbors at a
     * time.
     *
     * This function is slower than `#stepSingleSquares` but finds some more advanced moves by effectively considering
     * two squares at time. Meanwhile, this function does not look at the bigger picture so it cannot infer some more
     * complicated moves. On the other hand, for some reason this function finds some edge cases that `#stepAllSquares`
     * overlooks.
     *
     * @param field the field to solve
     * @private
     */
    private static stepNeighboringSquares(field: Field): void {
        const knowns = Solver.getKnowns(field);
        knowns.forEach(known => {
            Solver.applySolution(
                field,
                this.matrixSolve(field, known.neighbors.filter(it => !it.isCovered).concat(known), true)
            );
        });
    }

    /**
     * Solves the field as much as possible by looking at all uncovered squares and the remaining number of mines.
     *
     * Because this function considers all squares in the field, it is very slow. Then again, it finds a lot of steps
     * as well.
     *
     * @param field the field to solve
     * @private
     */
    private static stepAllSquares(field: Field): void {
        if (!field.hasStarted || field.hasWon || field.hasLost) return;

        const knowns = Solver.getKnowns(field);
        Solver.applySolution(
            field,
            this.matrixSolve(field, knowns, false)
        );
    }

    /**
     * Solves as much as possible from the field assuming knowledge of the uncovered squares in `known`.
     *
     * @param field the field to solve in
     * @param knowns the uncovered squares that the solver should consider
     * @param adjacentSquaresOnly `true` if the solver should only look at the squares adjacent to `known` and not at
     * all squares in the field. Enabling this option increases complexity, but may uncover some edge cases
     * @returns the solution that has been found
     * @private
     */
    private static matrixSolve(field: Field, knowns: Square[], adjacentSquaresOnly: boolean): Solution {
        if (knowns.length === 0) return [];

        let unknowns: Square[];
        if (adjacentSquaresOnly)
            unknowns = Array
                .from(new Set(knowns.reduce((acc, it) => acc.concat(it.neighbors), <Square[]> [])))
                .filter(it => it.isCovered && !it.hasFlag && knowns.indexOf(it) < 0);
        else
            unknowns = field.squareList
                .filter(it => it.isCovered && !it.hasFlag && knowns.indexOf(it) < 0);
        if (unknowns.length === 0) return [];

        const matrix: number[][] = [];
        knowns.forEach(square => {
            const row = Array(unknowns.length).fill(0);
            square.neighbors
                .filter(it => it.isCovered && !it.hasFlag)
                .forEach(it => row[unknowns.indexOf(it)] = 1);

            row.push(square.getNeighborCount(it => it.hasMine) - square.getNeighborCount(it => it.hasFlag));
            matrix.push(row);
        });
        if (!adjacentSquaresOnly)
            matrix.push(Array(unknowns.length).fill(1).concat(field.mineCount - field.flagCount));

        return (new Matrix(matrix))
            .solveBinary()
            .map((it, i) => it === undefined ? undefined : [it, unknowns[i]]);
    }


    /**
     * Returns all uncovered squares that have at least one covered unflagged neighbor.
     *
     * @param field the field to find the known squares in
     * @returns all uncovered squares that have at least one covered unflagged neighbor
     * @private
     */
    private static getKnowns(field: Field): Square[] {
        return field.squareList
            .filter(it => !it.isCovered)
            .filter(it => it.getNeighborCount(it => it.isCovered && !it.hasFlag) > 0);
    }

    /**
     * Applies the given solution to the field.
     *
     * @param field the field to apply the solution to
     * @param solution the solution to apply
     * @private
     */
    private static applySolution(field: Field, solution: Solution): void {
        solution.forEach(target => {
            if (target === undefined) return;

            const [solution, square] = target;
            if (solution === 0) field.uncover(square.coords);
            else if (solution === 1) field.toggleFlag(square.coords);
        });
    }
}


/**
 * A matrix of numbers.
 */
export class Matrix {
    private readonly cells: number[][];
    private readonly rowCount: number;
    private readonly colCount: number;


    /**
     * Constructs a new matrix from the given numbers.
     *
     * @param cells an array of rows of numbers
     */
    constructor(cells: number[][]) {
        if (cells.length === 0) throw new Error("Matrix must have at least 1 row.");
        if (cells[0].length === 0) throw new Error("Matrix must have at least 1 column.");

        this.cells = cells;
        this.rowCount = this.cells.length;
        this.colCount = this.cells[0].length;
    }


    /**
     * Returns the `row`th row of numbers.
     *
     * @param row the index of the row to return
     * @returns the `row`th row of numbers
     */
    getRow(row: number): number[] {
        if (row < 0 || row >= this.rowCount)
            throw new Error(`Row must be in range [0, ${this.rowCount}) but was ${row}.`);

        return this.cells[row];
    }

    /**
     * Returns the `col`th column of numbers.
     *
     * @param col the index of the column to return
     * @returns the `col`th column of numbers
     */
    getCol(col: number): number[] {
        if (col < 0 || col >= this.colCount)
            throw new Error(`Col must be in range [0, ${this.colCount}) but was ${col}.`);

        return this.cells.map(row => row[col]);
    }

    /**
     * Returns the `col`th number in the `row`th row.
     *
     * @param row the index of the row to find the number in
     * @param col the index of the column to find the number in
     * @returns the `col`th number in the `row`th row
     */
    getCell(row: number, col: number): number {
        if (row < 0 || row >= this.rowCount)
            throw new Error(`Row must be in range [0, ${this.rowCount}) but was ${row}.`);
        if (col < 0 || col >= this.colCount)
            throw new Error(`Row must be in range [0, ${this.colCount}) but was ${col}.`);

        return this.cells[row][col];
    }


    /**
     * Transforms this matrix into its row-reduced echelon form using Gauss-Jordan elimination.
     */
    rref(): void {
        let pivot = 0;
        for (let row = 0; row < this.rowCount; row++) {
            // Find pivot
            while (pivot < this.colCount && this.getCol(pivot).slice(row).every(it => it === 0)) pivot++;
            if (pivot >= this.colCount) return;

            // Set pivot to non-zero
            if (this.getCell(row, pivot) === 0)
                this.swap(row, this.getCol(pivot).slice(row + 1).findIndex(it => it !== 0) + row + 1);
            // Set pivot to 1
            this.multiply(row, 1 / this.getCell(row, pivot));

            // Set all other cells in this column to 0
            for (let row2 = 0; row2 < this.rowCount; row2++) {
                if (row2 === row) continue;
                this.add(row2, row, -this.getCell(row2, pivot));
            }
        }
    }

    /**
     * Interprets this matrix as an augmented matrix and returns for each variable the value or `undefined` if its value
     * could not be determined.
     *
     * This function invokes `#rref`, so this matrix will change as a result.
     *
     * @returns the value of each variable, and `undefined` for each variable that could not be determined uniquely
     */
    solve(): (number | undefined)[] {
        this.rref();

        return range(this.colCount - 1)
            .map(it => {
                const rowPivotIndex = this.getCol(it).findIndex(it => it === 1);
                if (rowPivotIndex < 0) return undefined;

                const row = this.getRow(rowPivotIndex);
                if (row.slice(0, it).every(it => it === 0) && row.slice(it + 1, -1).every(it => it === 0))
                    return row.slice(-1)[0];

                return undefined;
            });
    }

    /**
     * Same as `#solve`, except that it assumes that every variable is an integer in the range [0, 1].
     *
     * @returns the value of each variable, and `undefined` for each variable that could not be determined uniquely
     */
    solveBinary(): (number | undefined)[] {
        const resultsA = this.solve();
        const resultsB = this.solveBinarySub();
        return resultsA.map((it, i) => it ?? resultsB[i]);
    }

    /**
     * Helper function for `#solveBinary` that tries to solve for variables in the range [0, 1] in the current matrix
     * without applying transformations.
     *
     * @returns the value of each variable, and `undefined` for each variable that could not be determined uniquely
     * @private
     */
    private solveBinarySub(): (number | undefined)[] {
        const results = Array(this.colCount - 1).fill(undefined);
        this.cells.forEach(row => {
            // ax = b
            const a = row.slice(0, -1);
            const b = row.slice(-1)[0];

            const negSum = a.filter(it => it < 0).reduce((sum, cell) => sum + cell, 0);
            const posSum = a.filter(it => it > 0).reduce((sum, cell) => sum + cell, 0);

            if (b === negSum) {
                a.forEach((it, i) => {
                    if (it < 0) results[i] = 1;
                    if (it > 0) results[i] = 0;
                });
            } else if (b === posSum) {
                a.forEach((it, i) => {
                    if (it < 0) results[i] = 0;
                    if (it > 0) results[i] = 1;
                });
            }
        });
        return results;
    }


    /**
     * Swaps the rows at the given indices.
     *
     * @param rowA the index of the row to swap
     * @param rowB the index of the other row to swap
     */
    swap(rowA: number, rowB: number) {
        [this.cells[rowA], this.cells[rowB]] = [this.cells[rowB], this.cells[rowA]];
    }

    /**
     * Multiplies all numbers in the `row`th number by `factor`.
     *
     * @param row the index of the row to multiply
     * @param factor the factory to multiply each number with
     */
    multiply(row: number, factor: number) {
        this.cells[row] = this.cells[row].map(it => it * factor);
    }

    /**
     * Adds `factor` multiples of the `rowB`th row to the `rowA`th row.
     *
     * Effectively, sets `A = A + B * factor`.
     *
     * @param rowA the index of the row to add to
     * @param rowB the index of the row to add a multiple of
     * @param factor the factor to multiply each added number with
     */
    add(rowA: number, rowB: number, factor: number) {
        this.cells[rowA] =
            this.cells[rowA].map((it, i) => this.cells[rowA][i] + this.cells[rowB][i] * factor);
    }
}


/**
 * A partial solution to a field.
 *
 * Each element of the array describes an instruction to apply to the field. If the instruction is `undefined`, then
 * nothing should be done. Otherwise, the tuple describes the instruction: If the number is 0, the associated square
 * should be uncovered because it definitely does not contain a mine. Otherwise, the number is 1 and the associated
 * square should be flagged because it definitely contains a mine.
 */
type Solution = ([number, Square] | undefined)[]