Как найти минимальный элемент среди некоторых объектов класса?

Прошу, пожалуйста, помочь с нахождением минимального элемента по полю cost. Нужно найти минимальную цену на выбранном маршруте (например: 1981(outstation) - 1902(instation)) (уточнение: их может быть несколько, но поле numoftrain будет отличаться (например: 920(numoftrain), 921(numoftrain))

#include <iostream>

using namespace std;



class TIMETABLE
{
public:

    double outtime;
    double intime;
    int numoftrain;
    int outstation;
    int instation;
    double cost;
    double timeinroad;
  
    void print()
    {
        cout << numoftrain << "\n" << outstation << "\n" << instation << "\n" << cost <<
            "\n" << outtime << "\n" << intime << endl;
    }

    void search(TIMETABLE* a, int size)
    {
        TIMETABLE b;

        b.outstation;
        b.instation;
        
        cout << "Введите станцию отправления" << endl;
        cin >> outstation;
        b.outstation = outstation;
        cout << "Введите станцию прибытия" << endl;
        cin >> instation;
        b.instation = instation;

        TIMETABLE *min = new TIMETABLE[NULL];

        min[0].cost = 0;
       
        for (int i = 0; i < size; i++)
        {
            if (a[i].outstation == b.outstation && a[i].instation == b.instation)
            {   
                
                cout << "Номер поезда : " << a[i].numoftrain << "\n" << "Цена переезда : " << a[i].cost << endl;

                if (a[i].cost < min[i].cost)
                {
                    min[i].cost = a[i].cost;

                    cout << "Номер поезда : " << a[i].numoftrain << "Минимальная цена : " << min[i].cost << endl;
                }
                else
                {
                    cout << "Erorr" << endl;
                }
            }

        }



        
    }

};


int main()
{
    setlocale(LC_ALL, "Rus");

    TIMETABLE a[250];

        a[0].numoftrain = 907;
        a[0].outstation = 1909;
        a[0].instation = 1929;
        a[0].cost = 1790.87;
        a[0].outtime = 00.50;
        a[0].intime = 20.00;
        a[0].timeinroad = (((a[0].intime) * 60) - ((a[0].outtime) * 60))/60;

        a[1].numoftrain = 908;
        a[1].outstation = 1909;
        a[1].instation = 1929;
        a[1].cost = 1790.87;
        a[1].outtime = 00.50;
        a[1].intime = 20.00;
        a[1].timeinroad = (((a[1].intime) * 60) - ((a[1].outtime) * 60)) / 60;
        
        a[2].numoftrain = 909;
        a[2].outstation = 1929;
        a[2].instation = 1909;
        a[2].cost = 1790.87;
        a[2].outtime = 10.01;
        a[2].intime = 00.01;
        a[2].timeinroad = ((24 * 60) - ((((a[2].outtime * 60)) - (a[2].intime * 60)))) / 60;

        a[3].numoftrain = 909;
        a[3].outstation = 1929;
        a[3].instation = 1921;
        a[3].cost = 199.15;
        a[3].outtime = 11.10;
        a[3].intime = 01.00;
        a[3].timeinroad = 13.50;

        a[4].numoftrain = 910;
        a[4].outstation = 1929;
        a[4].instation = 1909;
        a[4].cost = 1790.87;
        a[4].outtime = 10.01;
        a[4].intime = 00.01;
        a[4].timeinroad = ((24 * 60) - ((((a[4].outtime * 60)) - (a[4].intime * 60)))) / 60;

        a[5].numoftrain = 910;
        a[5].outstation = 1929;
        a[5].instation = 1921;
        a[5].cost = 199.15;
        a[5].outtime = 11.10;
        a[5].intime = 01.00;
        a[5].timeinroad = 13.50;

        a[6].numoftrain = 911;
        a[6].outstation = 1902;
        a[6].instation = 1937;
        a[6].cost = 191.87;
        a[6].outtime = 23.00;
        a[6].intime = 14.40;
        a[6].timeinroad = 15.40;

        a[7].numoftrain = 914;
        a[7].outstation = 1937;
        a[7].instation = 1902;
        a[7].cost = 191.89;
        a[7].outtime = 09.24;
        a[7].intime = 00.52;
        a[7].timeinroad = ((24 * 60) - ((((a[7].outtime * 60)) - (a[7].intime * 60)))) / 60;

        a[8].numoftrain = 917;
        a[8].outstation = 1902;
        a[8].instation = 1929;
        a[8].cost = 300.18;
        a[8].outtime = 09.25;
        a[8].intime = 20.01;
        a[8].timeinroad = 10.36;

        a[9].numoftrain = 918;
        a[9].outstation = 1929;
        a[9].instation = 1902;
        a[9].cost = 300.20;
        a[9].outtime = 06.55;
        a[9].intime = 17.10;
        a[9].timeinroad = 10.15;

        a[10].numoftrain = 919;
        a[10].outstation = 1902;
        a[10].instation = 1981;
        a[10].cost = 130.60;
        a[10].outtime = 04.59;
        a[10].intime = 20.06;
        a[10].timeinroad = 15.07;

        a[11].numoftrain = 920;
        a[11].outstation = 1981;
        a[11].instation = 1902;
        a[11].cost = 120.55;
        a[11].outtime = 10.00;
        a[11].intime = 01.05;
        a[11].timeinroad = 15.05;

        a[12].numoftrain = 921;
        a[12].outstation = 1981;
        a[12].instation = 1902;
        a[12].cost = 120.55;
        a[12].outtime = 10.00;
        a[12].intime = 01.05;
        a[12].timeinroad = 15.05;

        a[13].numoftrain = 935;
        a[13].outstation = 1981;
        a[13].instation = 1902;
        a[13].cost = 191.48;
        a[13].outtime = 20.03;
        a[13].intime = 10.56;
        a[13].timeinroad = 14.53;

        a[14].numoftrain = 936;
        a[14].outstation = 1981;
        a[14].instation = 1902;
        a[14].cost = 191.48;
        a[14].outtime = 20.03;
        a[14].intime = 10.56;
        a[14].timeinroad = 14.53;

        a[15].numoftrain = 957;
        a[15].outstation = 1937;
        a[15].instation = 1902;
        a[15].cost = 131.36;
        a[15].outtime = 00.55;
        a[15].intime = 15.02;
        a[15].timeinroad = 14.07;

        a[16].numoftrain = 965;
        a[16].outstation = 1902;
        a[16].instation = 1929;
        a[16].cost = 180.27;
        a[16].outtime = 09.33;
        a[16].intime = 17.57;
        a[16].timeinroad = 08.24;

        for (int i = 0; i < 1; i++)
        {
            a[i].search(a, 13);
        }

        return 0;
}