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lp_practice.cpp

#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#include "bits/stdc++.h" // define macro "/D__MAI"

using namespace std;
typedef unsigned int uint;
typedef long long int ll;
typedef unsigned long long int ull;

#define debugv(v) printf("L%d %s => ",__LINE__,#v);for(auto e:v){cout<<e<<" ";}cout<<endl;
#define debugm(m) printf("L%d %s is..\n",__LINE__,#m);for(auto v:m){for(auto e:v){cout<<e<<" ";}cout<<endl;}
#define debuga(m,w) printf("L%d %s is => ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<<endl;
#define debugaa(m,w,h) printf("L%d %s is..\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[x][y]<<" ";}cout<<endl;}
#define debugaar(m,w,h) printf("L%d %s is..\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[y][x]<<" ";}cout<<endl;}
#define ALL(v) (v).begin(),(v).end()
#define repeat(l) for(auto cnt=0;cnt<(l);++cnt)
#define upto(l,r) for(auto cnt=l;cnt<=r;++cnt)
#define downto(r,l) for(auti cnt=r;cnt>=l;--cnt)
#define BIGINT 0x7FFFFFFF
#define MD 1000000007ll
#define PI 3.1415926535897932384626433832795
template<typename T1, typename T2>
ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << "(" << p.first << ":" << p.second << ")"; return o; }

#define TIME chrono::system_clock::now()
#define MILLISEC(t) (chrono::duration_cast<chrono::milliseconds>(t).count())
namespace {
    std::chrono::system_clock::time_point ttt;
    void tic() { ttt = TIME; }
    void toc() { fprintf(stderr, "TIME : %lldms\n", MILLISEC(TIME - ttt)); }
    std::chrono::system_clock::time_point tle = TIME;
#ifdef __MAI
    void safe_tle(int msec) { assert(MILLISEC(TIME - tle) < msec); }
#else
#define safe_tle(k) ;
#endif
}

#ifdef __MAI //_getchar_nolock
#define getchar_unlocked getchar
#endif
namespace {
    class MaiScanner {
    public:
        template<typename T>
        void input_integer(T& var) {
            var = 0;
            T sign = 1;
            int cc = getchar_unlocked();
            for (; cc<'0' || '9'<cc; cc = getchar_unlocked())
                if (cc == '-') sign = -1;
            for (; '0' <= cc&&cc <= '9'; cc = getchar_unlocked())
                var = (var << 3) + (var << 1) + cc - '0';
            var = var*sign;
        }
        inline int c() { return getchar_unlocked(); }
        inline MaiScanner& operator>>(int& var) {
            input_integer<int>(var);
            return *this;
        }
        inline MaiScanner& operator>>(long long& var) {
            input_integer<long long>(var);
            return *this;
        }
    };
}
MaiScanner scanner;



typedef int boolean;

class EasyLP {
public:
    const int dimension;
    vector<vector<double>> equation;
    vector<double> offset;
    vector<double> objective;
    double objective_c;

    EasyLP(int n) :dimension(n), objective(n) {
    }

    // void appendEquation() {}
    // void setObjective() {}

    double maximize() {

        while (true) {
            //printTableau();
            // 目的関数の値を増加させることができる変数を探す
            int idx = 0;
            {
                double val = objective[0];
                for (int i = 1; i < dimension; ++i) {
                    if (val > objective[i]) {
                        val = objective[i];
                        idx = i;
                    }
                }
                // 無いなら最適解が得られた
                if (val >= 0) break;
            }

            // どの程度まで増やせば良いだろうか
            int target = -1;
            {
                double val, lim = 0;
                for (int i = 0; i < equation.size(); ++i) {
                    if (equation[i][idx] == 0) continue; // 0除算防止
                    val = offset[i] / equation[i][idx];
                    if ((target == -1 || val < lim)) {
                        lim = val;
                        target = i;
                    }
                }
            };
            if (target == -1) break;

            // 参考 http://www.mk-mode.com/octopress/2014/02/21/cpp-linear-programming-by-simplex/
            // この実装だとうまく出来ないケースが存在するかもしれない
            {
                // ピボット係数
                double p = equation[target][idx];

                // ピボット係数を p で除算
                for (double& e : equation[target])
                    e /= p;
                offset[target] /= p;

                // ピボット列の掃き出し
                for (int i = 0; i < equation.size(); ++i) {
                    if (i == target) continue;

                    double d = equation[i][idx];
                    for (int j = 0; j < dimension; j++){
                        if (j!=idx)
                            equation[i][j] -= d * equation[target][j];
                        else
                            equation[i][j] = 0;
                    }
                        
                    offset[i] -= d * offset[target];
                }
                {
                    double d = objective[idx];
                    for (int j = 0; j < dimension; j++){
                        if (j!=idx)
                            objective[j] -= d * equation[target][j];
                        else
                            objective[j] = 0;
                        
                    }
                        
                    objective_c += d * offset[target];
                }
            }
        }
        return -objective_c;
    }

    void printTableau() {
        repeat(equation.size()) {
            for (double a : equation[cnt]) {
                printf(" %7.2f", a);
            }
            printf(" | %7.2f\n", offset[cnt]);
        }
        repeat(equation.size() + 1) { printf("---------"); }
        printf("\n");
        for (double a : objective) {
            printf(" %7.2f", a);
        }
        printf(" %7.2f\n#####\n",objective_c);
    }

};


int main() {

    EasyLP lp(5);

    lp.equation.push_back({ -1.0, 1.0, 1.0, 0.0, 0.0 }); lp.offset.push_back(1.0);
    lp.equation.push_back({ 1.0, 0.0, 0.0, 1.0, 0.0 }); lp.offset.push_back(3.0);
    lp.equation.push_back({ 0.0, 1.0, 0.0, 0.0, 1.0 }); lp.offset.push_back(2.0);
    lp.objective = { 1.0, 1.0, 0.0, 0.0, 0.0 };   lp.objective_c = 0.0;

    double result = lp.maximize();

    printf("result: %7.2f\n", result);

    return 0;
}