将来，当“时光旅行”（Time Travel，简称TT）盛行时，抛硬币将成为一种严肃的思想运动。为了为未来做准备，我们为参赛作品创建了竞赛，从参赛作品的角度出发，时空旅行将真正发生。

比赛是循环式的山丘之王，由Java类之间的抛硬币比赛组成。

投币比赛规则

• 有两个玩家和100个回合。
• 在每一轮中，掷出一枚硬币，并且根据结果一名玩家得到1分。每个玩家都有50％的机会得分。
• 投掷后，两个玩家都有机会通过拉杆来控制时间。
• 如果您拉动蓝色手柄（回位限位器），则无法对使用该手柄的那一轮或之前的任何一轮进行TT操作。TT尝试进行这些回合不会产生任何效果。
• 如果您拉动红色手柄（还原器），则尝试将时间还原为前一轮。如果成功，则在选择的回合之前，对手的记忆将恢复到其记忆，并且从选择的回合开始的抛硬币结果也将被删除。对于您的对手来说，唯一可能的关于TT的信号是其未使用的操纵杆数量，这些数量不会恢复原状。
• 比赛开始时，每位球员有5个蓝色和20个红色未使用的操纵杆。这些杠杆不受TT的影响。
• 如果在第100局结束时没有TT，则游戏结束，得分较高的玩家获胜。

细节

• 轮次具有从1开始的索引（形式1至100）。
• 回合之前x，向您提供了可用的蓝色和红色杠杆数量，抛硬币的结果一直到x（包括）回合为止，并且记忆了您的（最后一个）x-1回合。
• 一圈拉动蓝色操纵杆将x停止在目的地x或之前有目的地的所有TT （如果它也发生在同一确切的回合中，则会阻止TT）。
• 恢复到一轮x意味着下一轮将是一轮x。
• 如果两个玩家都选择在回合结束时还原，则时间将还原到未被阻止的较早目的地。尝试还原到此时间的播放器将保留其记忆。

技术细节

• 您应该编写实现提供的Bot接口的Java类。
• 将您的机器人添加到项目中。
• 将Bot的实例添加到Bot文件中的Controller.java。
• 您的班级不应在通话之间保留信息。（在大多数情况下，只有final函数外部的变量才能满足此要求。）
• 您可以在memory返回Action对象的字段中向控制器提供信息。如果未发生任何TT，这将在下一轮退还给您。如果发生TT，您将收到相应的较早记忆。
• 您可以使用该类的totalScore()方法Game来获取历史记录字符串的分数。

协议

• 在任何时候都takeTurn(...)使用5个参数调用您的方法：

  • 未使用的蓝色杠杆数
  • 未使用的红色杠杆数量
  • 抛硬币的历史记录，一个由1和0组成的字符串，表示您在前几轮中的得失。第一个字符对应于第一次掷硬币。（在第一轮中，字符串的长度为1。）
  • 字符串，您上一轮存储的内存
  • 本轮基于1的索引

• 在任何时候，您的方法都会返回一个Action包含

  • move描述您的操作的字段中的整数：

    • 0 不采取行动
    • -1 拉一个蓝色的杆并阻止TT通过本轮
    • 一个正整数x，不大于当前的回合，以拉动红色杠杆并尝试恢复为回合x
    • 无效的整数被视为0。

  • 一个字符串，其中包含您要保留的这一轮记忆。请注意，存储内存并不是挑战的关键部分。您可以进行良好的输入，而无需在字符串中存储任何有用的数据。在第一轮中，该字符串将为空字符串。

• 在一场比赛中，您的方法平均每轮不超过10毫秒。

• 定期超过时限会导致失格。

计分

• 赢得一场比赛均获得2分，而两人平局则获得1分。损失不赚分。
• 机器人的分数将是其收集的总分。
• 每对参赛者之间进行比赛的次数将取决于参赛作品的数量及其速度。

发布了两个简单的示例机器人作为答案。

控制器和前几个机器人在这里可用。

在11月3日之前提交的机器人测试结果：

总成绩：

Oldschool: 3163
Random: 5871
RegretBot: 5269
Nostalgia: 8601
Little Ten: 8772
Analyzer: 17746
NoRegretsBot: 5833
Oracle: 15539
Deja Vu: 5491
Bad Loser: 13715

^{（该控制器基于Cat catcher Challenge的控制器。感谢@flawr为它提供了基础。）}

奖励：一部基于类似概念的精彩6分钟电影。

分析仪

这将分析过去，以对未来做出最佳预测。

编辑：避免蓝色杠杆时间。有效地使用蓝色手柄。更有效地使用红色手柄。在万圣节季节增加了恐惧感。

编辑：修正了1错误。

编辑：改进的computeWinningProbability功能。现在更积极地使用红色杠杆和蓝色杠杆。

//Boo!
package bots;

import main.Action;
import main.Game;

import java.util.*;
import java.util.stream.Collectors;

/**
 * Created 10/24/15
 *
 * @author TheNumberOne
 */
public class Analyzer implements Bot{

    @Override
    public String getName(){
        return "Analyzer";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history,
                           String memory, int roundNumber) {
        /*System.out.println(Game.totalScore(history) + " : " + history);
        try {
            Thread.sleep(100);
        } catch (InterruptedException e) {
        }*/
        int roundsLeft = 100 - roundNumber;
        int myScore = (Game.totalScore(history) + roundNumber) / 2; //My number of wins.
        int enemyScore = roundNumber - myScore;                     //Enemy's number of wins.
        Map<Integer, Double> bestRounds = new HashMap<>();
        int timeLimit = 0;

        Scanner scanner = new Scanner(memory);
        if (scanner.hasNext()){     //No memory, first turn.
            boolean triedTimeTravel = scanner.nextBoolean();
            if (triedTimeTravel){
                int time = scanner.nextInt();
                if (roundNumber > time) {     //Failed.
                    timeLimit = time;
                }
            }
            timeLimit = Math.max(timeLimit, scanner.nextInt());
            int size = scanner.nextInt();
            for (int i = 0; i < size; i++) {
                bestRounds.put(scanner.nextInt(), scanner.nextDouble());
            }
        } else {
            bestRounds.put(1, 0.5);
        }

        clean(bestRounds, roundNumber, timeLimit);
        double winningProb = computeWinningProbability(myScore, enemyScore, roundsLeft);
        String newMemory = computeMemory(bestRounds, roundNumber, winningProb);

        if (winningProb >= new double[]{1.5, .75, .7, .65, .6, .55}[blue_levers]){ //Ensure success ... slowly.
            return getAction(-1, newMemory, timeLimit, roundNumber);
        }

        int bestRound = bestRound(bestRounds);
        double bestRoundProb = bestRounds.get(bestRound);

        if ((winningProb <= bestRoundProb - .05 || winningProb < .5 && bestRoundProb > winningProb) && red_levers > 0){
            return getAction(bestRound, newMemory, timeLimit, roundNumber);  //Let's find the best past.
        } else {
            return getAction(0, newMemory, timeLimit, roundNumber); //Let's wait it out :)
        }
    }

    //Should be combined with computeMemory.
    private static Action getAction(int actionNum, String newMemory, int timeLimit, int roundNumber){
        if (actionNum == -1){
            timeLimit = Math.max(timeLimit, roundNumber);
            newMemory = "false " + timeLimit + " " + newMemory;
            return new Action(actionNum, newMemory);
        }
        if (actionNum == 0){
            return new Action(actionNum, "false " + timeLimit + " " + newMemory);
        }
        if (actionNum > 0){
            return new Action(actionNum, "true " + actionNum + " " + timeLimit + " " + newMemory);
        }
        return null;
    }

    private static int bestRound(Map<Integer, Double> bestRounds) {
        int best = 0;           //If no previous rounds ... just go forward a round.
        double bestScore = -1;
        for (Map.Entry<Integer, Double> entry : bestRounds.entrySet()){
            if (entry.getValue() > bestScore){
                best = entry.getKey();
                bestScore = entry.getValue();
            }
        }
        return best;
    }

    private static String computeMemory(Map<Integer, Double> map, int roundNumber, double winningProb) {
        StringBuilder builder = new StringBuilder();
        builder.append(map.size() + 1).append(" ");
        for (Map.Entry<Integer, Double> entry : map.entrySet()){
            builder.append(entry.getKey()).append(" ").append(entry.getValue()).append(" ");
        }
        builder.append(roundNumber + 1).append(" ").append(winningProb);
        return builder.toString();
    }

    private static void clean(Map<Integer, Double> data, int round, int timeLimit) {
        data
                .entrySet()
                .stream()
                .filter(entry -> entry.getKey() > round || entry.getKey() <= timeLimit)
                .map(Map.Entry::getKey)
                .collect(Collectors.toList()).forEach(data::remove);
    }

    private static double computeWinningProbability(int myScore, int enemyScore, int roundsLeft){ //Too complex for IntelliJ
        int height = myScore - enemyScore;
        double total = 0.0;
        for (int i = Math.max(height - roundsLeft, 2); i <= height + roundsLeft; i += 2){
            total += prob(roundsLeft, height, i);
        }
        total += prob(roundsLeft, height, 0) / 2;
        return total;
    }

    private static double prob(int roundsLeft, int height, int i){
        double prob = 1;
        int up = i - height + (roundsLeft - Math.abs(i - height))/2;
        int down = roundsLeft - up;
        int r = roundsLeft;
        int p = roundsLeft;
        while (up > 1 || down > 1 || r > 1 || p > 0){  //Weird algorithm to avoid loss of precision.
            //Computes roundsLeft!/(2**roundsLeft*up!*down!)

            if ((prob >= 1.0 || r <= 1) && (up > 1 || down > 1 || p > 1)){
                if (p > 0){
                    p--;
                    prob /= 2;
                    continue;
                } else if (up > 1){
                    prob /= up--;
                    continue;
                } else if (down > 1){
                    prob /= down--;
                    continue;
                } else {
                    break;
                }
            }
            if (r > 1) {
                prob *= r--;
                continue;
            }
            break;
        }
        return prob;
    }

}

得分（自11月2日起）：

Total Scores:
Oldschool: 3096
Random: 5756
RegretBot: 5362
Nostalgia: 8843
Little Ten: 8929
Analyzer: 17764
NoRegretsBot: 5621
Oracle: 15528
Deja Vu: 5281
Bad Loser: 13820

怀旧

package bots;

import main.Action;
import main.Game;

public class Nostalgia implements Bot {

    @Override
    public String getName() {
        return "Nostalgia";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history,
            String memory, int roundNumber) {

        int current_score = Game.totalScore(history);

        // wait until the end to use blue levers
        if (current_score > 0 && blue_levers >= (100 - roundNumber)) {
            return new Action(-1, memory);
        }

        // become increasingly likely to go back as the gap between the good old days
        // and the horrible present increases
        if (current_score < 0 && red_levers > 0) {
            //identify the best time to travel back to
            int best_score = -100;
            int good_old_days = 1;
            int past_score = 0;

            int unreachable_past = 0;
            if(memory != "") {
              unreachable_past = Integer.parseInt(memory, 10);
            }

            for(int i = unreachable_past; i<roundNumber ; i++) {
              if(history.charAt(i) == '1') {
                past_score += 1;
                if(past_score > best_score) {
                  best_score = past_score;
                  good_old_days = i + 1;
                }
              }
              else {
                past_score -= 1;
              }
            }
            if(roundNumber >= 95 || Math.random() < (best_score - current_score) / 100.0) {
              return new Action(good_old_days, Integer.toString(good_old_days));
            }
        }

        // if neither action was needed do nothing
        return new Action(0, memory);
    }
}

未经测试，只是试图制造一个很难被阻止的机器人（因为它决定何时随机拉动红色手柄）只是一个快速的尝试，但是它做出了不错的决定。

编辑：我错过了这条规则：

如果您拉动蓝色手柄（回位限位器），则该回合中不再有TT

这似乎是使用内存的一个很好的理由-如果您记得尝试将TT转到给定的回合，则可能已失败，因此您不应尝试再次将TT插入该回合。编辑了我的漫游器以尝试避免这种情况。

甲骨文

我无耻地从Analyzer中复制了一些代码（用于解析内存）。此提交尝试尽早拉动蓝色杠杆，然后慢慢建立起领先优势。我认为该机器人的性能弥补了难看的代码:)

package bots;

import java.util.*;
import java.util.Map.Entry;
import main.*;

public class Oracle implements Bot {

    @Override
    public String getName() {
        return "Oracle";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history, String memory, int roundNumber) {
        int roundsLeft = 100 - roundNumber;
        Map<Integer, Integer> rounds = new HashMap<>();
        int myScore = (Game.totalScore(history) + roundNumber) / 2;
        int difference = myScore*2 - roundNumber;
        int highestBlockedRound = -1;
        int bestScore = 0;
        boolean hasUsedBlueLever = false;

        Scanner scanner = new Scanner(memory);
        if (scanner.hasNext()) {
            //timeTravel toRound highestBlockedRound hasUsedBlueLever bestScore rounds round1 percent1 round2 percent2 round3 percent3...
            boolean triedTravel = scanner.nextBoolean();
            int time = scanner.nextInt();
            if (triedTravel){
                if (roundNumber > time) {
                    highestBlockedRound = time;
                }
            }
            highestBlockedRound = Math.max(highestBlockedRound, scanner.nextInt());

            hasUsedBlueLever = scanner.nextBoolean();
            bestScore = scanner.nextInt();

            int size = scanner.nextInt();
            for (int i = 0; i < size && i < roundNumber; i++) {
                int number = scanner.nextInt();
                int diff = scanner.nextInt();
                if (number < roundNumber) {
                    rounds.put(number, diff);
                }
            }
        }
        rounds.put(roundNumber, difference);
        final int blockedRound = highestBlockedRound;

        int roundToRevert = 0;
        if (rounds.size() > 2) {
            Optional<Entry<Integer, Integer>> bestRound = rounds.entrySet()
                    .stream()
                    .filter(x -> x.getKey() >= blockedRound && x.getKey() <= roundNumber)
                    .sorted(Comparator
                        .comparingInt((Entry<Integer, Integer> x) -> x.getValue()*-1)
                        .thenComparingInt(x -> x.getKey()))
                    .findFirst();
            if (bestRound.isPresent()) {
                roundToRevert = bestRound.get().getKey();
            }
        }

        if (roundsLeft + Game.totalScore(history) <= 0 && red_levers > 0) {
            roundToRevert = highestBlockedRound+1;
        } else if (blue_levers > 0 && roundToRevert == roundNumber && ((hasUsedBlueLever && difference >= bestScore*1.5) || (!hasUsedBlueLever && difference > 1))) {
            roundToRevert = -1;
            hasUsedBlueLever = true;
            bestScore = difference;
            highestBlockedRound = roundNumber;
        } else if (red_levers > 0 && roundToRevert > 0 && rounds.get(roundToRevert) > difference+2) {
            roundToRevert += 1;
        } else {
            roundToRevert = 0;
        }

        StringBuilder sb = new StringBuilder();
        sb.append(roundToRevert > 0).append(' ');
        sb.append(roundToRevert).append(' ');
        sb.append(highestBlockedRound).append(' ');
        sb.append(hasUsedBlueLever).append(' ');
        sb.append(bestScore).append(' ');
        sb.append(rounds.size()).append(' ');
        rounds.entrySet().stream().forEach((entry) -> {
            sb.append(entry.getKey()).append(' ').append(entry.getValue()).append(' ');
        });
        String mem = sb.toString().trim();
        scanner.close();
        return new Action(roundToRevert, mem);
    }
}

遗憾的是

在比赛的生命尽头，我们对过去的失败感到遗憾，并试图回过头来修复它们。

package bots;

import main.Action;
import main.Game;

public final class RegretBot implements Bot {

    @Override
    public String getName() {
        return "RegretBot";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history, String memory, int roundNumber) {
        int actionNum = 0;
        if(roundNumber == 100) {
            // if it's the end of the game and we're losing, go back
            //  in time to the first loss, in hopes of doing better
            if(Game.totalScore(history)<=0 && red_levers > 0) {
                actionNum = history.indexOf("0")+1;
            }
            // if we're winning at the end, pull a blue lever if we can,
            //  to prevent our opponent from undoing our victory
            else if(blue_levers > 0) {
                actionNum = -1;
            }
        }
        // we don't need no stinkin' memory!
        return new Action(actionNum, null);
    }

}

小十

小十号使用10的倍数进行多次乘除除运算，然后返回10的倍数回合。

package bots;

import main.Action;
import main.Game;

public class LittleTen implements Bot {

    @Override
    public String getName() {
        return "Little Ten";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history, String memory, int roundNumber) {
        int score = Game.totalScore(history);
        char c = history.charAt(history.length() - 1);
        if (memory.isEmpty())
            memory = "1";

        if (roundNumber == 100) {
            if (score >= 0)
                // We're tied or ahead by the end of the match. Prevent time
                // travel if we can; otherwise whatever happens happens.
                return new Action(blue_levers > 0 ? -1 : 0, memory);
            else {
                // Travel to earlier rounds the farther behind we are if we can
                // (of course using 10 as a reference)
                if (red_levers > 0) {
                    int i = Integer.parseInt(memory);
                    int round = score <= -10 ? i : 100 - ((100 - i) / (11 + (score <= -10 ? -10 : score)));
                    return new Action(round, memory);
                }
            }
        }
        else if (score >= 7 + roundNumber / 20 && blue_levers > 0) {
            // We're ahead; we don't want to lose our lead, especially if the
            // match is close to ending. But we don't want to use up our blue
            // levers too quickly.
            int choice = (int) (Math.random() * 100),
                bound = (roundNumber / 10 + 1) * 5 - ((6 - blue_levers) * 5 - 2);
            if (choice < bound) {
                memory = String.valueOf(roundNumber);
                return new Action(-1, memory);
            }
        }
        else if (score <= -3) {
            // Possibly use a red lever if we're falling too far behind
            if (red_levers > 0) {
                int choice = (int) (Math.random() * 100),
                    bound = score <= -11 ? 90 : 10 * (-3 - score + 1);
                if (choice < bound) {
                    // Check the first round that is the lower multiple of ten
                    // and decide if we've been successful up to that point; if
                    // so, travel back to that round, otherwise go back 10 more
                    int round = roundNumber / 10 * 10;
                    if (round < 10)
                        return new Action(1, memory);
                    String seq = history.substring(0, round-1);
                    int minRound = Integer.parseInt(memory);
                    while (Game.totalScore(seq) <= 0 && round > 10 && round > minRound) {
                        round -= 10;
                        seq = history.substring(0, round-1);
                    }
                    if (round == 0)
                        round = 1;
                    return new Action(round, memory);
                }
            }
        }
        return new Action(0, memory);
    }
}

编辑：现在，对机制进行了一些更改，更清楚了当拉动蓝色手柄时会发生什么的解释。也做了一些重新平衡。

随机

Random的策略如下：

• 如果领先，则有10％的机会被挡住，并且还剩蓝色杆
• 旅游回来一圈（重播最后一轮）有10％的机会如果比分落后，有左冲杆

package bots;

import main.Action;
import main.Game;

public class RandomBot implements Bot {

    @Override
    public String getName() {
        return "Random";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history,
            String memory, int roundNumber) {

        // if in the lead and has blocks left, blocks with a 10% chance
        if (Game.totalScore(history) > 0 && blue_levers > 0
                && Math.random() > 0.9) {
            return new Action(-1, null);
        }

        // if behind and has travels left, travel back the current step to
        // replay it with a 10% chance
        if (Game.totalScore(history) < 0 && red_levers > 0
                && Math.random() > 0.9) {
            return new Action(roundNumber, null);
        }

        // if neither action were needed do nothing
        return new Action(0, null);
    }
}

没有遗憾

package bots;

import main.Action;
import main.Game;

public final class NoRegretsBot implements Bot {

    @Override
    public String getName() {
        return "NoRegretsBot";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history, String memory, int roundNumber) {
        // every 20 turns, pull a blue lever to lock in the past
        // hopefully this will thwart some of those pesky time-travelers
        return new Action(roundNumber%20==0?-1:0, null);
    }

}

失败者

该机器人不占用内存，而且出奇的出色（但它没有击败Analyzer或Oracle）。

package main;

import bots.Bot;

/**
 * Created 11/2/15
 *
 * @author TheNumberOne
 */
public class BadLoser implements Bot{
    @Override
    public String getName() {
        return "Bad Loser";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history, String memory, int roundNumber) {
        if (history.contains("00") && red_levers > 0){       //Subtract a zero for better performance against
            return new Action(history.indexOf("00") + 1, "");// Analyzer and Nostalgia, and worse performance 
                                                             // against everything else.
        }
        int wins = 0;
        for (char c : history.toCharArray()){
            wins += c - '0';
        }
        if (wins >= new int[]{101, 51, 40, 30, 20, 10}[blue_levers]){
            return new Action(-1, "");
        }
        return new Action(0, "");
    }
}

老套

这个机器人从不做任何动作，因为Oldschool不相信时间旅行。

package bots;

import main.Action;

public class OldschoolBot implements Bot {

    @Override
    public String getName() {
        return "Oldschool";
    }

    @Override
    public Action takeTurn(int blue_levers, int red_levers, String history,
            String memory, int roundNumber) {       
        // never tries to block or travel at all
        return new Action(0, null);
    }
}

黛娅·沃·波特

该机器人试图跟踪何时将其拉到蓝色，以避免红色将其拖入该区域。仅在比分显着落后时才拉红色杆。

package bots;

import main.*;

public class Dejavu implements Bot
{
    @Override
    public String getName()
    {
        return "Deja Vu";
    }

@Override
public Action takeTurn(int blue_levers, int red_levers, String history,
                       String memory, int roundNumber) {

    if(roundNumber == 1)
    {
        memory = "-1";
    }
    int[] blevers = getBlueLevers(memory);
    char[] hist = history.toCharArray();
    int ms = 0;
    int ts = 0;
    int rl = -1;
    boolean bl = false;
    boolean url = false;

    for(int i = 0; i < hist.length; i++)
    {
        switch(hist[i])
        {
            case '1':
            ms++;
            break;
            case '0':
            ts++;
            break;
        }
    }

    if(ts - ms >= 10)
    {   
        for(rl = hist.length - 1; ts - ms <= 5 && rl >= 0; rl--)
        {
            switch(hist[rl])
            {
                case '1':
                ms--;
                break;
                case '0':
                ts--;
                break;
            }
        }
        url = true;
    }

    if(ms - ts >= 7)
    {
        bl = true;
        url = false;
        memory += "," + roundNumber;
    }

    for(int i = 0; i < blevers.length; i++)
    {
        if(rl <= blevers[i])
        {
            rl = blevers[i] + 1;
        }
    }

    if(url)
    {
        return new Action(rl, memory);
    }
    else if(bl)
    {
        return new Action(-1, memory);
    }
    else
    {
        return new Action(0, memory);
    }              
}

private int[] getBlueLevers(String s)
{
    String[] b = s.split(",");

    int[] bl = new int[b.length];
    for(int i = 0; i < b.length; i++)
    {
        bl[i] = Integer.parseInt(b[i]);
    }

    return bl;
}

}