#include <iostream>
#include <math.h>
#include <cmath>
#include <vector>
#include <Windows.h>
#include <stdlib.h>
#include <fstream>
#include <string.h>
#include <time.h>
#include <iomanip>
using namespace std;

/* Рандом даёт ток целое число, поэтому отказались от этого
    int flag = 0;
    double r,h;

    h = (Array[CountSegments + 1].x - Array[0].x) / CountSegments;
    if (CountSegments % 2 == 0)
        flag = 1;

    if (flag == 1) {
        for (int i = 1; i < CountSegments + 1; i=i+2) {
            r = (rand() % h + 1);
            Array[i].x = h + r;
            Array[i].y = (*f)(Array[i].x);
            Array[i + 1].x = h - r;
            Array[i + 1].y = (*f)(Array[i + 1].x);
        }
    }
    else {
        Array[1].x = Array[0].x+h;
        Array[1].y = (*f)(Array[1].x);
        for (int i = 2; i < CountSegments; i=i+2) {
            r = (rand() % 3 + 1);
            Array[i].x = h+r;
            Array[i].y = (*f)(Array[i].x);
            Array[i+1].x = h-r;
            Array[i+1].y = (*f)(Array[i+1].x);
        }

    }

*/

typedef double(*functiontype)(double x);
typedef struct Node
{
    double x, y;
} Node;
typedef double(*method)(double x, Node* Array, int Count, double* DD_massiv);
typedef struct Interval
{
    double InitialNode, EndNode;
} Interval;
const double PI = 3.141592653589793238463;
double Myfunc(double x)
{
    return x;
}
functiontype Func = &Myfunc;

//Равномерная сетка
void ValueUniformTable(functiontype* f, Node* Array, double Initial, double End, int CountSegments)
{
    int i;
    double alpha, h;

    Array[0].x = Initial;
    Array[CountSegments].x = End;
    Array[0].y = (*f)(Array[0].x);
    Array[CountSegments].y = (*f)(Array[CountSegments].x);

    h = (Array[CountSegments].x - Array[0].x) / CountSegments;

    cout << "(" << Array[0].x << ":" << Array[0].y << ")" << endl;
    for (int i = 1; i < CountSegments; i++)
    {
        Array[i].x = Array[i - 1].x + h;
        Array[i].y = (*f)(Array[i].x);
        cout << "(" << Array[i].x << ":" << Array[i].y << ")" << endl;
    }
    cout << "(" << Array[CountSegments].x << ":" << Array[CountSegments].y << ")" << endl;
}

//Неравномерная сетка
void ValueIrregularTable(functiontype* f, Node* Array, double Initial, double End, int CountSegments, double *Array_steps) //Инитиал и Енд запихать в Array
{
    int i;
    double alpha,h;

    Array[0].x = Initial;
    Array[CountSegments].x = End;
    Array[0].y = (*f)(Array[0].x);
    Array[CountSegments].y = (*f)(Array[CountSegments].x);
    h = (Array[CountSegments].x - Array[0].x) / CountSegments;
    Array_steps[0] = 0;
    alpha = 2 * PI / CountSegments;

    cout << "(" << Array[0].x << ":" << Array[0].y << ")" << endl;
    for (i = 1; i < CountSegments; i++) {
        Array_steps[i] = h + cos(alpha*i);
        Array[i].x = Array[i-1].x+ Array_steps[i];
        Array[i].y = (*f)(Array[i].x);
        cout << "(" << Array[i].x << ":" << Array[i].y << ")" << endl;
    }
    Array_steps[CountSegments] = Array[CountSegments].x - Array[CountSegments - 1].x;
    cout << "(" << Array[CountSegments].x << ":" << Array[CountSegments ].y << ")" << endl;

}


/* Принимает на вход коэффициенты матриц в виде массива. Заполняет массив прогоночных коэффициентов
 matrix_coeffs - двумерный массив вида [[a1,b1,c1,d1],[a2,b2,c2,d2],...,[an,bn,cn,dn]
надо сделать чтобы а1=с1=0, переделать под ашки
*/
void tridiagonal_matrix_algorithm(double** matrix_coeffs, int matrix_size) {
    int i;
    double denominator;
    double K, E, K_prev = 0, E_prev = 0; //Прогоночные коэффициенты
    double* x_massiv = new double[matrix_size];

    double** coeffs_massiv; //Двумерный массив, хранящий прогоночные коэффициенты, 0 - Кси, 1 - Эта
    coeffs_massiv = new double*[matrix_size+1];
    for (i = 0; i < matrix_size; i++)
        coeffs_massiv[i] = new double[2];

    coeffs_massiv[0][0] = 0; coeffs_massiv[0][1] = 0;
    matrix_coeffs[0][0] = 0; matrix_coeffs[matrix_size - 1][2] = 0; //а1=с1=0

    //Прямой ход
    for (i = 1; i <= matrix_size; i++) { //Ищем K_i+1 и E_i+1 на iом шаге
        denominator = (matrix_coeffs[i - 1][0] * K_prev + matrix_coeffs[i - 1][1]);
        K = -(matrix_coeffs[i - 1][2]) / denominator;
        E = (matrix_coeffs[i - 1][3] - matrix_coeffs[i - 1][0] * E_prev) / denominator;
        K_prev = K;
        E_prev = E;
        coeffs_massiv[i][0] = K; coeffs_massiv[i][1] = E;
    }

    //Обратный ход
    x_massiv[matrix_size - 1] = coeffs_massiv[matrix_size][1];
    for (i = matrix_size - 2; i >= 0; i--) {
        x_massiv[i] = coeffs_massiv[i + 1][0] * x_massiv[i + 1] + coeffs_massiv[i + 1][1];
    }

}

void get_matrix_coeffs(double Initial, double End, int matrix_size, functiontype* f, double** matrix_coeffs, Node* Array, double *Array_steps) {
    int i;
    double h1,h2,h_prev;
    //double* gamma_massiv = new double[matrix_size]; //Гаммы яв решением ур, т.е. ответом.


    for (i = 1; i <= matrix_size; i++) {
        h1 = Array_steps[i]; //i
        h2 = Array_steps[i+1];; //i+1
        h_prev = h2;
        matrix_coeffs[i - 1][0] = h1;
        matrix_coeffs[i - 1][1] = 2*(h1+h2);
        matrix_coeffs[i - 1][2] = h2;
        matrix_coeffs[i - 1][3] = 6*(  (Array[i+1].y- Array[i].y) / h2 - (Array[i].y - Array[i-1].y)/h1  );
        //cout << matrix_coeffs[i - 1][0] << " " << matrix_coeffs[i - 1][1] << " " << matrix_coeffs[i - 1][2] << " " << endl;
    }
    //matrix_coeffs[matrix_size][3] = 6 * ((Array[i + 1].y - Array[i].y) / h2 - (Array[i].y - Array[i - 1].y) / h1);
    h1 = Array_steps[matrix_size];
    h2 = Array_steps[matrix_size+1];
    y1 = Array[matrix_size].y;
    y2 = Array[matrix_size + 1].y;
    x1 = Array[matrix_size].x;
    x2 = Array[matrix_size + 1].x;
    matrix_coeffs[matrix_size-1][0] = h1;
    matrix_coeffs[matrix_size-1][1] = 2 * (h1 + h2);
    matrix_coeffs[matrix_size - 1][2] = 0;
    matrix_coeffs[matrix_size-1][3] = 6 * ((Array[i + 1].y - Array[i].y) / h2 - (Array[i].y - Array[i - 1].y) / h1);
    matrix_coeffs[0][0] = 0;
    d2 = h2/6 * 6*(B*h2- y2+ y1) / (  (x2- x1)*(x2 - x1)*((x2 - x1)-h2*h2)   )
    g2 = h2/6 * h2*h2 / ( (x2-x1)*(   (x2-x1)*(x2-x1)-h2*h2   ))

}

int main()
{
    setlocale(LC_ALL, "RUS");
    functiontype Func = &Myfunc;
    double Initial = 0, End = 5;
    int CountSegments,i;
    cout << "Введите N: ";
    cin >> CountSegments;
    cout << "Точек: " << CountSegments + 1 << endl << endl;
    double *Array_steps = new double[CountSegments + 1];

    //Построение сетки
    cout << "Равномерная Сетка: " << endl;
    Node* ArrayUniformNodes = new Node[CountSegments+1];
    ValueUniformTable(&Func, ArrayUniformNodes, Initial, End, CountSegments);

    cout << endl << "Неравномерная Сетка: " << endl;
    Node* ArrayIrregulaNodes = new Node[CountSegments + 1];
    ValueIrregularTable(&Func, ArrayIrregulaNodes, Initial, End, CountSegments, Array_steps);
    cout << endl;

    //Заполнение массива коэффициентами матрицы
    double** matrix_coeffs;
    matrix_coeffs = new double*[CountSegments-1];
    for (i = 0; i < CountSegments-1; i++)
        matrix_coeffs[i] = new double[3];

    cout << "Полученная матрица: " << endl;
    get_matrix_coeffs(Initial,End, CountSegments-1, &Func, matrix_coeffs, ArrayIrregulaNodes, Array_steps);

    /*
    //Получение ответа в x_massiv
    double* x_massiv = new double[CountSegments+1];
    tridiagonal_matrix_algorithm(matrix_coeffs, CountSegments+1);
    */

    cout << endl;
    system("pause");
    return 0;
}