EvbCFfp1XB

problem and my answer.



Approach simulated annealing を使いました。1億から4億イテレーション。

スコア

  • knight の数 - 2 * 無効な knightの数


近傍
  • ランダムな pawn でない点を選んで、フリップする。
    • 攻撃されている数が2より多い点も含む。
      • 含めたほうがいいかどうかは確認していない。
  • 無効な knight が有れば、
    • この knight を取り除く。確率10%。
    • この knight  を攻撃している数が2より多いとき、攻撃している knight を1つ取り除く。2より少ないとき、攻撃している数が増えるように knight を置く。確率90%。
高速化

  • 次の状態にするときのスコアの差を事前に計算しておく。
  • 1次元の配列を使う。

SAの受理判定

  • KnightsAttacks の wleite さんの受理判定を使ったら、ローカルでは5%くらいスコアが上がったけど、提出したら変わらなかった。(謎)


atsさんのマネ

  • 無効な knight の保持は例の挿入、削除、ランダム取得がO(1)のsetを使った。

初期解

  • knight を置いていない状態から始めました。
  • initialSolution
    こういう状態から始めたほうが、スコアが上がる場合が多かったが、最終的に無効な knight が残って0点になるのを避けられなくて、使えなかった。


source code

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class KnightsAndPawns {
    private static final int EMPTY = 0;
    private static final int PAWN = 1;
    private static final int KNIGHT = 2;
    private static final int[] dr = { -2, -2, -1, 1, 2, 2, 1, -1, };
    private static final int[] dc = { -1, 1, 2, 2, 1, -1, -2, -2, };
    private static final int[] dz = { -2, -2, -1, 1, 2, 2, 1, -1, };
    private static final int[] dr2 = { 2, 0, -2, -1, -3, 3, 1, -4, 0, 4, -1, -3, 3, 1, -4, 0, -2, 2, 4, -3, -1, 1, 3, -4, 0, 4, -3, -1, 1, 3, -2, 0, 2, };
    private static final int[] dc2 = { -4, -4, -4, -3, -3, -3, -3, -2, -2, -2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, };
    static final XorShift rng = new XorShift(System.nanoTime());
    static final Watch watch = new Watch();
    private SAState sa = new SAState();

    private int R;
    private int C;

    private int[] board;

    private int[] attacks;
    private int numKnights;

    private IntSet invalidSet;

    private double score;
    private boolean[] solution;

    private double bestScore;
    private boolean[] bestSolution;

    private int[] deltaScores;

    private IntSet[] directionSet;
    private int RC;

    public String[] placeKnights(String[] board) {
        init(board);
        solve();
        return makeSolution();
    }

    private void init(String[] board) {
        this.R = board.length;
        this.C = board[0].length();
        RC = R * C;
        for (int i = 0; i < dz.length; i++) {
            dz[i] = z(dr[i], dc[i]);
        }
        this.board = new int[RC];
        for (int r = 0; r < R; r++) {
            for (int c = 0; c < C; c++) {
                char charAt = board[r].charAt(c);
                if (charAt == '.') {
                    this.board[z(r, c)] = EMPTY;
                } else if (charAt == 'P') {
                    this.board[z(r, c)] = PAWN;
                }
            }
        }

        attacks = new int[RC];
        for (int z = 0; z < RC; z++) {
            attacks[z] = calculateAttacks(z);
        }

        this.solution = new boolean[RC];
        this.bestSolution = new boolean[RC];
        score = 0;
        bestScore = 0;

        invalidSet = new IntSet(RC);

        directionSet = new IntSet[RC];
        for (int z = 0; z < RC; z++) {
            directionSet[z] = new IntSet(8);
        }

        int numPawns = 0;
        for (int z = 0; z < RC; z++) {
            if (this.board[z] == PAWN) {
                numPawns++;
            }
        }

        Utils.debug("R", R, "C", C, "numPawns", numPawns, String.format("%.1f%%", numPawns * 100.0 / (R * C)));
    }

    private int calculateAttacks(int z) {
        int count = 0;
        for (int d = 0; d < dr.length; d++) {
            int r2 = r(z) + dr[d];
            int c2 = c(z) + dc[d];
            if (!isValid(r2, 0, R) || !isValid(c2, 0, C)) {
                continue;
            }
            int z2 = z(r2, c2);
            if (board[z2] != EMPTY) {
                count++;
            }
        }
        return count;
    }

    private int z(int r, int c) {
        return r * C + c;
    }

    private int r(int z) {
        return z / C;
    }

    private int c(int z) {
        return z % C;
    }

    private boolean isValid(int v, int min, int minUpper) {
        return v >= min && v < minUpper;
    }

    private void solve() {
        initDeltaScores();
        SA();
    }

    private void initDeltaScores() {
        if (deltaScores == null) {
            deltaScores = new int[RC];
        }
        for (int z = 0; z < RC; z++) {
            if (board[z] == PAWN) {
                continue;
            }
            updateDeltaScore(z);
        }
    }

    private void SA() {
        double second = Math.ceil(watch.getSecond());

        sa.init();
        for (;; sa.numIterations++) {
            if ((sa.numIterations & ((1 << 10) - 1)) == 0) {
                sa.update();

                if (sa.isTLE()) {
                    loadBest();
                    Utils.debug(sa.numIterations, String.format("%.2f%%", 100.0 * sa.validIterations / sa.numIterations), String.format("%.2f%%", 100.0 * sa.acceptIterations / sa.validIterations), String.format("%7.2f", score), String.format("%7.2f", bestScore), String.format("%.6f", 1.0 / sa.inverseTemperature), String.format("%.6f", 1.0 / sa.lastAcceptTemperature));
                    break;
                }
                if (watch.getSecond() > second) {
                    second++;
                    Utils.debug(sa.numIterations, String.format("%.2f%%", 100.0 * sa.validIterations / sa.numIterations), String.format("%.2f%%", 100.0 * sa.acceptIterations / sa.validIterations), String.format("%7.2f", score), String.format("%7.2f", bestScore), String.format("%.6f", 1.0 / sa.inverseTemperature), String.format("%.6f", 1.0 / sa.lastAcceptTemperature));
                }
            }

            mutate();
        }
        Utils.debug("SA", "time", watch.getSecondString());
    }

    private void mutate() {
        if (invalidSet.size() > 0) {
            reduceInvalidKnight();
            return;
        }
        flip();
    }

    private void flip() {
        int z = (int) (RC * rng.nextDouble());
        while (board[z] == PAWN) {
            z = (int) (RC * rng.nextDouble());
        }
        if (sa.accept(deltaScores[z])) {
            score += deltaScores[z];
            if (solution[z]) {
                removeKnight(z);
            } else {
                putKnight(z);
            }
            updateDeltaScores(z);
            saveBest();
            assert score == calculateScore() : Utils.toString(sa.numIterations, sa.acceptIterations, score, calculateScore(), numKnights, invalidSet.size());
        }

    }

    private boolean check() {
        assert invalidSet.size() == 0;
        for (int r = 0; r < R; r++) {
            for (int c = 0; c < C; c++) {
                int z = z(r, c);
                assert calculateAttacks(z) == attacks[z];
                if (solution[z]) {
                    assert attacks[z] == 2;
                }
            }
        }
        return true;
    }

    private void reduceInvalidKnight() {
        int z = invalidSet.get((int) (invalidSet.size() * rng.nextDouble()));
        boolean removeMe = rng.nextDouble() < 0.1;
        if (removeMe) {
            if (sa.accept(deltaScores[z])) {
                score += deltaScores[z];
                removeKnight(z);
                updateDeltaScores(z);
                saveBest();
            }
        } else {
            if (attacks[z] > 2) {
                int d = (int) (dr.length * rng.nextDouble());
                int r2 = r(z) + dr[d];
                int c2 = c(z) + dc[d];
                int z2 = z(r2, c2);
                if (!isValid(r2, 0, R) || !isValid(c2, 0, C) || board[z2] != KNIGHT) {
                    d = (int) (dr.length * rng.nextDouble());
                    r2 = r(z) + dr[d];
                    c2 = c(z) + dc[d];
                    z2 = z(r2, c2);
                    if (!isValid(r2, 0, R) || !isValid(c2, 0, C) || board[z2] != KNIGHT) {
                        d = (int) (dr.length * rng.nextDouble());
                        r2 = r(z) + dr[d];
                        c2 = c(z) + dc[d];
                        z2 = z(r2, c2);
                        if (!isValid(r2, 0, R) || !isValid(c2, 0, C) || board[z2] != KNIGHT) {
                            d = (int) (dr.length * rng.nextDouble());
                            r2 = r(z) + dr[d];
                            c2 = c(z) + dc[d];
                            z2 = z(r2, c2);
                            if (!isValid(r2, 0, R) || !isValid(c2, 0, C) || board[z2] != KNIGHT) {
                                return;
                            }
                        }
                    }
                }
                if (sa.accept(deltaScores[z2])) {
                    score += deltaScores[z2];
                    removeKnight(z2);
                    updateDeltaScores(z2);
                    saveBest();
                }
            } else {
                int d = (int) (dr.length * rng.nextDouble());
                int r2 = r(z) + dr[d];
                int c2 = c(z) + dc[d];
                int z2 = z(r2, c2);
                if (!isValid(r2, 0, R) || !isValid(c2, 0, C) || board[z2] != EMPTY) {
                    d = (int) (dr.length * rng.nextDouble());
                    r2 = r(z) + dr[d];
                    c2 = c(z) + dc[d];
                    z2 = z(r2, c2);
                    if (!isValid(r2, 0, R) || !isValid(c2, 0, C) || board[z2] != EMPTY) {
                        d = (int) (dr.length * rng.nextDouble());
                        r2 = r(z) + dr[d];
                        c2 = c(z) + dc[d];
                        z2 = z(r2, c2);
                        if (!isValid(r2, 0, R) || !isValid(c2, 0, C) || board[z2] != EMPTY) {
                            d = (int) (dr.length * rng.nextDouble());
                            r2 = r(z) + dr[d];
                            c2 = c(z) + dc[d];
                            z2 = z(r2, c2);
                            if (!isValid(r2, 0, R) || !isValid(c2, 0, C) || board[z2] != EMPTY) {
                                return;
                            }
                        }
                    }
                }
                if (sa.accept(deltaScores[z2])) {
                    score += deltaScores[z2];
                    putKnight(z2);
                    updateDeltaScores(z2);
                    saveBest();
                }
            }
        }
    }

    private void updateDeltaScores(int z) {
        for (int d = 0; d < dr.length; d++) {
            int r2 = r(z) + dr[d];
            int c2 = c(z) + dc[d];
            int z2 = z(r2, c2);
            if (!isValid(r2, 0, R) || !isValid(c2, 0, C) || board[z2] == PAWN) {
                continue;
            }
            updateDeltaScore(z2);
        }

        for (int d = 0; d < dr2.length; d++) {
            int r2 = r(z) + dr2[d];
            int c2 = c(z) + dc2[d];
            int z2 = z(r2, c2);
            if (!isValid(r2, 0, R) || !isValid(c2, 0, C) || board[z2] == PAWN) {
                continue;
            }
            updateDeltaScore(z2);
        }
    }

    private void updateDeltaScore(int z) {
        if (solution[z]) {
            deltaScores[z] = (int) (calculateScoreRemove(z) - score);
        } else {
            deltaScores[z] = (int) (calculateScorePut(z) - score);
        }
    }

    private void putKnight(int z) {
        solution[z] = true;
        board[z] = KNIGHT;
        numKnights++;
        for (int d = 0; d < dr.length; d++) {
            int r2 = r(z) + dr[d];
            int c2 = c(z) + dc[d];
            if (!isValid(r2, 0, R) || !isValid(c2, 0, C)) {
                continue;
            }
            int z2 = z(r2, c2);
            attacks[z2]++;

            if (solution[z2]) {
                if (attacks[z2] == 2) {
                    invalidSet.removeValue(z2);
                } else {
                    invalidSet.add(z2);
                }
            }

            directionSet[z2].add((d + 4) % dr.length);

        }

        if (attacks[z] == 2) {
            invalidSet.removeValue(z);
        } else {
            invalidSet.add(z);
        }
    }

    private void removeKnight(int z) {
        solution[z] = false;
        board[z] = EMPTY;
        numKnights--;
        for (int d = 0; d < dr.length; d++) {
            int r2 = r(z) + dr[d];
            int c2 = c(z) + dc[d];
            if (!isValid(r2, 0, R) || !isValid(c2, 0, C)) {
                continue;
            }
            int z2 = z(r2, c2);
            attacks[z2]--;

            if (solution[z2]) {
                if (attacks[z2] == 2) {
                    invalidSet.removeValue(z2);
                } else {
                    invalidSet.add(z2);
                }
            }

            directionSet[z2].removeValue((d + 4) % dr.length);

        }
        invalidSet.removeValue(z);
    }

    private double calculateScore() {
        return numKnights - 2 * invalidSet.size();
    }

    private double calculateScorePut(int z) {
        int numInvalids = invalidSet.size();
        for (int i = 0; i < directionSet[z].size(); i++) {
            int d = directionSet[z].get(i);
            int z2 = z + dz[d];
            if (attacks[z2] == 1) {
                numInvalids--;
            } else if (attacks[z2] == 2) {
                numInvalids++;
            }
        }
        if (attacks[z] != 2) {
            numInvalids++;
        }
        return (numKnights + 1) - 2 * numInvalids;
    }

    private double calculateScoreRemove(int z) {
        int numInvalids = invalidSet.size();
        for (int i = 0; i < directionSet[z].size(); i++) {
            int d = directionSet[z].get(i);
            int z2 = z + dz[d];
            if (attacks[z2] == 3) {
                numInvalids--;
            } else if (attacks[z2] == 2) {
                numInvalids++;

            }
        }
        if (attacks[z] != 2) {
            numInvalids--;
        }
        return (numKnights - 1) - 2 * numInvalids;
    }

    private String[] makeSolution() {
        String[] res = new String[R];
        for (int r = 0; r < R; r++) {
            StringBuilder line = new StringBuilder();
            for (int c = 0; c < C; c++) {
                line.append(solution[z(r, c)] ? 'K' : '.');
            }
            res[r] = line.toString();
        }
        return res;
    }

    private void saveBest() {
        if (invalidSet.size() > 0) {
            return;
        }
        if (score > bestScore) {
            bestScore = score;
            for (int i = 0; i < RC; i++) {
                bestSolution[i] = solution[i];
            }
        }
    }

    private void loadBest() {
        score = bestScore;
        for (int i = 0; i < RC; i++) {
            solution[i] = bestSolution[i];
        }
    }

    public static void main(String[] args) {
        try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {

            int H = Integer.parseInt(br.readLine());
            String[] board = new String[H];
            for (int i = 0; i < H; ++i) {
                board[i] = br.readLine();
            }

            KnightsAndPawns kap = new KnightsAndPawns();
            String[] ret = kap.placeKnights(board);

            System.out.println(ret.length);
            for (int i = 0; i < ret.length; ++i) {
                System.out.println(ret[i]);
            }
            System.out.flush();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
}

class SAState {

    public static final boolean useTime = true;

    public double startTime = 0;
    public double endTime = 9.5;
    public double time = startTime;

    public double startTemperature = 0.4;
    public double endTemperature = 0.1;
    public double inverseTemperature = 1.0 / startTemperature;
    public double lastAcceptTemperature = startTemperature;

    public double startRange = 0;
    public double endRange = 1e1;
    public double range = startRange;

    public int numIterations;
    public int validIterations;
    public int acceptIterations;

    private int lastAcceptIterations;

    final int[] log = new int[32768];
    int remain;

    public void init() {
        numIterations = 0;
        validIterations = 0;
        acceptIterations = 0;

        startTime = useTime ? KnightsAndPawns.watch.getSecond() : numIterations;

        update();
        lastAcceptTemperature = inverseTemperature;

        double start = KnightsAndPawns.watch.getSecond();
        double m = -0.6 / (endTime - start) * (1 << 28);
        for (int i = 0; i < log.length; i++) {
            log[i] = (int) (m * Math.log((i + 0.5) / log.length));
        }
        remain = (int) (endTime - start);
    }

    public void update() {
        updateTime();
        updateTemperature();
        updateRange();
    }

    public void updateTemperature() {
        inverseTemperature = 1.0 / (endTemperature + (startTemperature - endTemperature) * Math.pow((endTime - time) / (endTime - startTime), 0.5));
    }

    public void updateRange() {
        range = endRange + (startRange - endRange) * Math.pow((endTime - time) / (endTime - startTime), 1.0);
    }

    public void updateTime() {
        time = useTime ? KnightsAndPawns.watch.getSecond() : numIterations;
        remain = (int) (endTime - time);
    }

    public boolean isTLE() {
        return time >= endTime;
    }

    public boolean accept(int deltaScore) {
        return acceptB(deltaScore);
    }

    public boolean acceptB(int deltaScore) {
        validIterations++;

        if (deltaScore > -1e-9) {
            acceptIterations++;
            lastAcceptIterations = numIterations;
            return true;
        }
        if ((deltaScore > -6 && (-deltaScore << 28) <= log[KnightsAndPawns.rng.nextInt(log.length)] * remain)) {
            acceptIterations++;
            lastAcceptTemperature = inverseTemperature;
            lastAcceptIterations = numIterations;
            return true;
        }
        return false;
    }

    public boolean acceptS(double deltaScore) {
        validIterations++;

        if (deltaScore < 1e-9) {
            acceptIterations++;
            return true;
        }
        if (-deltaScore * inverseTemperature < -10) {
            return false;
        }

        if (KnightsAndPawns.rng.nextDouble() < Math.exp(-deltaScore * inverseTemperature)) {
            acceptIterations++;
            lastAcceptTemperature = inverseTemperature;
            return true;
        }
        return false;
    }

}

final class Utils {
    private Utils() {
    }

    public static final void debug(Object... o) {
        System.err.println(toString(o));
    }

    public static final String toString(Object... o) {
        return Arrays.deepToString(o);
    }

}

class Watch {
    private long start;

    public Watch() {
        init();
    }

    public double getSecond() {
        return (System.nanoTime() - start) * 1e-9;
    }

    public void init() {
        init(System.nanoTime());
    }

    private void init(long start) {
        this.start = start;
    }

    public String getSecondString() {
        return toString(getSecond());
    }

    public static final String toString(double second) {
        if (second < 60) {
            return String.format("%5.2fs", second);
        } else if (second < 60 * 60) {
            int minute = (int) (second / 60);
            return String.format("%2dm%2ds", minute, (int) (second % 60));
        } else {
            int hour = (int) (second / (60 * 60));
            int minute = (int) (second / 60);
            return String.format("%2dh%2dm%2ds", hour, minute % (60), (int) (second % 60));
        }
    }

}

class XorShift {
    private int w = 88675123;
    private int x = 123456789;
    private int y = 362436069;
    private int z = 521288629;

    public XorShift(long l) {
        x = (int) l;
    }

    public int nextInt() {
        final int t = x ^ (x << 11);
        x = y;
        y = z;
        z = w;
        w = w ^ (w >>> 19) ^ (t ^ (t >>> 8));
        return w;
    }

    public long nextLong() {
        return ((long) nextInt() << 32) ^ (long) nextInt();
    }

    public double nextDouble() {
        return (nextInt() >>> 1) * 4.6566128730773926E-10;
    }

    public int nextInt(int n) {
        return (int) (n * nextDouble());
    }

}

class IntSet {
    private static final int EMPTY = -1;
    private int size;
    private int[] indexToValue;
    private int[] valueToIndex;

    public IntSet(int capacity) {
        this.size = 0;
        indexToValue = new int[capacity];
        valueToIndex = new int[capacity];
        Arrays.fill(valueToIndex, EMPTY);
    }

    public boolean add(int value) {
        if (valueToIndex[value] != EMPTY) {
            return false;
        }
        indexToValue[size] = value;
        valueToIndex[indexToValue[size]] = size;
        size++;
        return true;
    }

    public boolean remove(int index) {
        if (size == 0) {
            return false;
        }
        int swap = indexToValue[index];
        indexToValue[index] = indexToValue[size - 1];
        indexToValue[size - 1] = swap;

        valueToIndex[indexToValue[index]] = index;
        valueToIndex[indexToValue[size - 1]] = EMPTY;

        size--;
        return true;
    }

    public boolean removeValue(int value) {
        int index = indexOf(value);
        if (index == EMPTY) {
            return false;
        }
        remove(index);
        return true;
    }

    public int get(int index) {
        return indexToValue[index];
    }

    public int indexOf(int value) {
        return valueToIndex[value];
    }

    public int size() {
        return size;
    }

    public boolean isEmpty() {
        return size() <= 0;
    }

    public void clear() {
        for (; size() > 0;) {
            remove(0);
        }
    }

    public boolean contains(int value) {
        return indexOf(value) != EMPTY;
    }

}




Approach
  • 各Expert のこれまで Round の予想と結果のデータから、Random Forest で、各Expert の今の Round の結果を予想する。
  • Random Forest は事前に学習したもの。
  • 予想の値が正で大きい方から、賭けれるだけお金をかける。
  • データを取るために毎 Round、すべての Expert に少なくとも 100 は賭ける。


Random Forest

  • 1 ケースごとに平均約1500のデータが集まる。300ケース分約45万のデータで学習した。
  • 学習に使った特徴は、今の Round数, 予想,  予想と結果の差の絶対値の最小値、平均、最大値、標準偏差、歪度、尖度、和、sum of squared error, 25パーセンタイル, 50パーセンタイル, 75パーセンタイル。
  • 重要な方から、予想, 予想と結果の差の絶対値の平均、予想と結果の差の絶対値の最大値, ... 。
  • 決定木の数 : 32
  • 決定木の深さ : 10


Source code

埋め込んだ Random Forest のせいで、文字数制限を超過したため省略。


Score 201225


Approach SAを使いました。L字型の経路を最大9個使いました。

L字型の経路は次のような感じで、
class L {
int r;
int c;
boolean rFirst;
}
目的地の"行"と"列"と"先にどちらの方向に進むか"を持つ。


近傍

  • L字型の経路の追加(画面端のランダムな点まで)
  • L字型の経路の追加(ランダムな点まで)
  • L字型の経路の追加(次のL字型の経路が作る長方形内のランダムな点まで)
  • L字型の経路の削除
  • L字型の経路の変更(ランダムな点まで)
  • L字型の経路の変更(現在の点の隣の点まで)
  • L字型の経路の交換

source code



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