Merge pull request #236 from TCL606/TCL

chore: add score calculate algorithm

dependency/algorithm/final.cpp

@@ -0,0 +1,79 @@
+#include <iostream>
+#include <algorithm>
+#include <cmath>
+#include <cassert>
+using namespace std;
+
+template <typename T>
+using mypair = pair<T, T>;
+double maxScore = 100;
+
+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);
+    double deltaRate = 0.035;
+    double scoreRate = 2e-5;
+    // 赢者至少加 half of maxScore，平局只加 a quarter of maxScore
+    // 差值引入非线性，差值越大非线性贡献的分数越多；绝对分数只用线性
+    double score = maxScore / 2 + (deltaRate + log10(delta) / maxScore + winnerGameScore * scoreRate) * delta;
+
+    cout << "delta contribution: " << deltaRate + log10(delta) / maxScore << endl;
+    cout << "winnerGameScore contribution: " << scoreRate * winnerGameScore << endl;
+
+    return score < maxScore ? score : maxScore; 
+}
+
+// orgScore 是天梯中两队的分数；competitionScore 是这次游戏两队的得分
+mypair<double> cal(mypair<double> orgScore, mypair<double> 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;
+    }
+    else if (competitionScore.first == competitionScore.second)  // 平局，两边加quarter of maxScore
+    {
+        orgScore.first += maxScore / 4;
+        orgScore.second += maxScore / 4;
+        return orgScore;
+    }
+
+    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 = WinScore(delta, competitionScore.first);  
+    auto resScore = mypair<double>(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<double> score)
+{
+    std::cout << " team1: " << score.first << std::endl
+        << "team2: " << score.second << std::endl;
+}
+
+int main()
+{
+    int x, y;
+    std::cout << "origin score of team 1 and 2: " << std::endl;
+    std::cin >> x >> y;
+    auto ori = mypair<double>(x, y);
+    std::cout << "game score of team 1 and 2: " << std::endl;
+    std::cin >> x >> y;
+    auto sco = mypair<double>(x, y);
+    Print(cal(ori, sco));
+}

dependency/algorithm/high_ladder.cpp

@@ -0,0 +1,105 @@
+#include <iostream>
+#include <algorithm>
+#include <cmath>
+using namespace std;
+
+template <typename T>
+using mypair = pair<T, T>;
+
+double PHI(double x) // THUAI3: Sigmoid; THUAI4: Tanh; THUAI5: Normal Distribution CDF
+{
+    return erf(x / sqrt(2));
+}
+
+// orgScore 是天梯中两队的分数；competitionScore 是这次游戏两队的得分
+mypair<int> cal(mypair<int> orgScore, mypair<int> 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;
+    }
+    else if (competitionScore.first == competitionScore.second)
+    {
+        if (orgScore.first == orgScore.second)      // 完全平局，不改变天梯分数
+        {
+            return orgScore;
+        }
+
+        if (orgScore.first > orgScore.second)        // 本次游戏平局，但一方天梯分数高，另一方天梯分数低，需要将两者向中间略微靠拢，因此天梯分数低的定为获胜者
+        {
+            reverse = true;
+        }
+        else
+        {
+            reverse = false;
+        }
+    }
+
+    if (reverse)   // 如果需要换，换两者的顺序
+    {
+        swap(competitionScore.first, competitionScore.second);
+        swap(orgScore.first, orgScore.second);
+    }
+
+
+    // 转成浮点数
+    mypair<double> orgScoreLf;
+    mypair<double> competitionScoreLf;
+    orgScoreLf.first = orgScore.first;
+    orgScoreLf.second = orgScore.second;
+    competitionScoreLf.first = competitionScore.first;
+    competitionScoreLf.second = competitionScore.second;
+    mypair<int> resScore;
+
+    const double deltaWeight = 90.0;       // 差距悬殊判断参数，比赛分差超过此值就可以认定为非常悬殊了，天梯分数增量很小，防止大佬虐菜鸡的现象造成两极分化
+
+    double delta = (orgScoreLf.first - orgScoreLf.second) / deltaWeight;
+    cout << "Normal CDF delta: " << PHI(delta) << endl;
+    {
+
+        const double firstnerGet = 1e-4;           // 胜利者天梯得分权值
+        const double secondrGet = 7e-5;            // 失败者天梯得分权值
+        const double possibleMaxScore = 1500.0;         // 估计的最大得分数量
+
+        double deltaScore = 100.0;        // 两队竞争分差超过多少时就认为非常大
+        double correctRate = (orgScoreLf.first - orgScoreLf.second) / 100.0;       // 订正的幅度，该值越小，则在势均力敌时天梯分数改变越大
+        double correct = 0.5 * (PHI((competitionScoreLf.first - competitionScoreLf.second - deltaScore) / deltaScore - correctRate) + 1.0);      // 一场比赛中，在双方势均力敌时，减小天梯分数的改变量
+
+        resScore.first = orgScore.first + round(competitionScoreLf.first * competitionScoreLf.first * firstnerGet * (1 - PHI(delta)) * correct);  // 胜者所加天梯分
+        if (competitionScoreLf.second < possibleMaxScore)
+            resScore.second = orgScore.second - round((possibleMaxScore - competitionScoreLf.second) * (possibleMaxScore - competitionScoreLf.second) * secondrGet * (1 - PHI(delta)) * correct);  // 败者所扣天梯分
+        else
+            resScore.second = orgScore.second; // 败者拿maxScore分，已经很强了，不扣分
+    }
+
+    // 如果换过，再换回来
+    if (reverse)
+    {
+        swap(resScore.first, resScore.second);
+    }
+
+    return resScore;
+}
+
+void Print(mypair<int> score)
+{
+    std::cout << " team1: " << score.first << std::endl
+        << "team2: " << score.second << std::endl;
+}
+
+int main()
+{
+    int x, y;
+    std::cout << "origin score of team 1 and 2: " << std::endl;
+    std::cin >> x >> y;
+    auto ori = mypair<int>(x, y);
+    std::cout << "game score of team 1 and 2: " << std::endl;
+    std::cin >> x >> y;
+    auto sco = mypair<int>(x, y);
+    Print(cal(ori, sco));
+}