diff --git a/dependency/algorithm/README.md b/dependency/algorithm/README.md index fe9624e..1ea7788 100644 --- a/dependency/algorithm/README.md +++ b/dependency/algorithm/README.md @@ -247,6 +247,8 @@ int main() ## THUAI6 +### high-ladder + 因为今年的对局得分是两局得分之和,所以会出现一定程度的“数值膨胀”,在这里调低了胜者得分权值,同时提高了比赛分差距悬殊阈值和天梯分差距悬殊阈值。同时由于今年得分的上限不好确定,所以负者失分的基础值变为与胜者的得分之差。 ```c++ @@ -330,3 +332,126 @@ mypair cal(mypair orgScore, mypair competitionScore) } ``` +### competition + +与天梯得分算法要满足的“枫氏七条”类似,比赛得分算法也要满足“唐氏四律”,分别如下: + +1. 两队经过某场比赛的得分变化,应只与该场比赛有关,而与历史积分无关。 +2. 须赋予比赛获胜一方基础得分,哪怕获胜一方的优势非常小。也就是说,哪怕胜利一方仅以微弱优势获胜,也需要拉开胜者与败者的分差。 +3. 胜利一方优势越大,得分理应越高。 +4. 对于一场比赛,胜利一方的得分不能无限大,须控制在一个合理的数值以下。 + +- 在非平局的情况下,(胜者)天梯得分与双方比赛分差值成正相关,得分函数如下(以x表示得分差值,y表示(胜者)天梯得分,a、b为固定参数) + +​ $$y=ax^2(1-0.375\cdot(\tanh(\frac{x}{b}-1)+1))$$ + +- 在平局情况下,(双方)天梯得分与比赛分成正相关,得分函数如下(以x表示比赛分,y表示(双方)天梯得分,c为固定参数) + +​ $$y=cx^2$$ + +- 不管是哪种情况,都有得分下界,非平局为100,平局为25 + +```c++ +#include +#include +#include +#include +using namespace std; + +template +using mypair = pair; +double minScore = 100; + +double TieScore(double gameScore) +{ + const double get = 9e-5; // 天梯得分权值 + double deltaScore = 2000.0; // 订正的幅度,该值越小,则在双方分差较大时,天梯分数改变量越小,整个函数的变化范围大约为0~2*deltaScore + double highScore = 6000.0; // 将highScore设定为较大值,使得correct较小 + double correct = 1 - 0.375 * (tanh((highScore - deltaScore) / deltaScore) + 1.0); // 一场比赛中,在双方分差较大时,减小天梯分数的改变量 + cout << "correct: " << correct << endl; + int score = round(gameScore * gameScore * get * correct / 4); + return score > minScore / 4 ? score : minScore / 4; +} + +double WinScore(double delta, double winnerGameScore) // 根据游戏得分差值,与绝对分数,决定最后的加分 +{ + assert(delta > 0); + const double firstnerGet = 9e-5; // 胜利者天梯得分权值 + double deltaScore = 2000.0; // 订正的幅度,该值越小,则在双方分差较大时,天梯分数改变量越小,整个函数的变化范围大约为0~2*deltaScore + double correct = 1 - 0.375 * (tanh((delta - deltaScore) / deltaScore) + 1.0); // 一场比赛中,在双方分差较大时,减小天梯分数的改变量 + cout << "correct: " << correct << endl; + int score = round(delta * delta * firstnerGet * correct); + return score > minScore ? score : minScore; +} + +// orgScore 是天梯中两队的分数;competitionScore 是这次游戏两队的得分 +mypair cal(mypair orgScore, mypair competitionScore) +{ + // 调整顺序,让第一个元素成为获胜者,便于计算 + + bool reverse = false; // 记录是否需要调整 + + if (competitionScore.first < competitionScore.second) + { + reverse = true; + } + + if (reverse) // 如果需要换,换两者的顺序 + { + swap(competitionScore.first, competitionScore.second); + swap(orgScore.first, orgScore.second); + } + + double delta = competitionScore.first - competitionScore.second; + double addScore; + mypair resScore; + + // 先处理平局的情况 + if (delta == 0) + { + addScore = TieScore(competitionScore.first); + resScore = mypair(orgScore.first + addScore, orgScore.second + addScore); + } + + // 再处理有胜负的情况 + else + { + addScore = WinScore(delta, competitionScore.first); + resScore = mypair(orgScore.first + addScore, orgScore.second); + } + + // 如果换过,再换回来 + if (reverse) + { + swap(resScore.first, resScore.second); + } + + return resScore; +} + +void Print(mypair score) +{ + std::cout << "team1: " << score.first << std::endl + << "team2: " << score.second << std::endl; +} + +int main() +{ + double x, y, t, i = 0; + cin >> t; + while (i < t) + { + cout << "----------------------------------------\n"; + std::cout << "origin score of team 1 and 2: " << std::endl; + std::cin >> x >> y; + auto ori = mypair(x, y); + std::cout << "game score of team 1 and 2: " << std::endl; + std::cin >> x >> y; + auto sco = mypair(x, y); + Print(cal(ori, sco)); + ++i; + } + return 0; +} +``` +