Numerki_Newton_04.cpp

#include <iostream>

using namespace std;




double newton(int ** &resultsTable, int * tabX, int* tabY, int k , int i) {
	
	if (resultsTable[i][k] == NULL) {
		if (k == 0) {
			cout << "Dla rzedu=" << k << "[X" << i  << ", X" << i+k << "]="<<1<<endl;
			resultsTable[i][k]=1;
			return 1;
		}	
		if (k == 1) {
		cout << "Dla rzedu=" << k << "[X" << i << ", X" << i+k << "]="<< (tabY[i + 1] - tabY[i]) / (tabX[i + k] - tabX[i]) << endl;
		
			resultsTable[i][k] = (tabY[i + 1] - tabY[i]) / (tabX[i + k] - tabX[i]);
			return (tabY[i + 1] - tabY[i]) / (tabX[i + k] - tabX[i]);
		}
	
		cout << "Dla rzedu=" << k << "[X" << i  << ", X" << i+k << "]="<<(newton(resultsTable, tabX, tabY, k - 1, i + 1) - newton(resultsTable, tabX, tabY, k - 1, i)) / (tabX[i + k] - tabX[i]) << endl;
	
		resultsTable[i][k] = (newton(resultsTable, tabX, tabY, k - 1, i + 1) - newton(resultsTable, tabX, tabY, k - 1, i)) / (tabX[i + k] - tabX[i]);
		return(newton(resultsTable, tabX, tabY, k - 1, i + 1) - newton(resultsTable, tabX, tabY, k - 1, i)) / (tabX[i + k] - tabX[i]);
	}
	else return resultsTable[i][k];
	
}


int main() {
	int wynik;
	int tabX[] = { 0,2,3,5,6 };
	int tabY[] = { 0,8,27,125,216 };
	int pointsQuantity = 5;
	double result = 0;
	double tmp = 0;
	
	int ** resultsTable = new int*[pointsQuantity];
	for (int i = 0; i < pointsQuantity; i++) {
		resultsTable[i] = new int[pointsQuantity];
		for(int j = 0; j < pointsQuantity; j++){
			resultsTable[i][j] = NULL;
		}
	}

	
	
	//tabela 1
	for (double x=0; x < 6.5; x += 0.5) {
		result =tabY[0];
		for (int i = 0; i < pointsQuantity; i++)
		{
			tmp = 0;
			for (int j = 0; j < i; j++)
			{
				if (j == 0)tmp = x - tabX[0];
				else tmp *= x - tabX[j];
			}
			result += tmp*newton(resultsTable,tabX, tabY, i, 0);
		}
		cout <<"Wynik dla x="<<x<<" to "<< result<<endl;
	}

	//tabela 2
	int tab2X[] = { 0,2,4};
	int tab2Y[] = { 1,5,17 };
	pointsQuantity = 3;
	for (int i = 0; i < pointsQuantity; i++) {
		for (int j = 0; j < pointsQuantity; j++) {
			resultsTable[i][j] = NULL;
		}
	}

	cout << "Tabela 2:#######################################################";
	for (double x = 0; x < 6.5; x += 0.5) {
		result = tab2Y[0];
		for (int i = 0; i < pointsQuantity; i++)
		{
			tmp = 0;
			for (int j = 0; j < i; j++)
			{
				if (j == 0)tmp = x - tab2X[0];
				else tmp *= x - tab2X[j];
			}
			result += tmp*newton(resultsTable, tab2X, tab2Y, i, 0);
		}
		cout << "Wynik dla x=" << x << " to " << result << endl;
	}

	system("pause");
}