Pascalsches Dreieck, Pascalsche Pyramide, Pascalsches Pentatop
Mein erstes Programm, das ich auf meiner Webseite vorstelle ist ein Programm, mit dem man verschiedene Pascalsche Simplizes erstellen lassen kann. Was ein Pascalsches Dreieck ist, weiß wohl jeder. Eine Pascalsche Pyramide ist eingentlich das gleiche wie ein Pascalsches Dreieck nur dreidimensional. Ein Pascalsches Penatatop ist ein vierdimensionales Gebilde.
pascal.cpp
/* * Pascal - a program to draw Pascal's simplices * Copyright (C) 2005 Nicolas Bellm * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or (at * your option) any later version. * * This program is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * General Public License for more details. * * g++ pascal.cpp * */ #include "pascal.h" void Triangle::resize(int size) { m_size = size; m_triangle.resize(m_size); for (int i=0; i<m_size; i++) { m_triangle[i].resize(i+1); } } void Triangle::center(int c) { if (c >= 1000000) printf("%d ", c); else if (c >= 100000) printf(" %d ", c); else if (c >= 10000) printf(" %d ", c); else if (c >= 1000) printf(" %d ", c); else if (c >= 100) printf(" %d ", c); else if (c >= 10) printf(" %d ", c); else printf(" %d ", c); } void Triangle::draw(int space=0) { for (int i=0; i<m_size; i++) { for (int j=0; j<(m_size-i-1+space); j++) { printf(" "); } for (int j=0; j<=i; j++) { center(m_triangle[i][j]); } printf("\n"); } } void Tetrahedron::resize(int size) { m_size = size; m_tetrahedron.resize(m_size); for (int i=0; i<m_size; i++) { m_tetrahedron[i].resize(i+1); } } void Tetrahedron::draw(int space=0) { for (int i=0; i<m_size; i++) { m_tetrahedron[i].draw(m_size-i-1+space); if (i<m_size-1) printf("\n"); } } void Pentatope::resize(int size) { m_size = size; m_pentatope.resize(m_size); for (int i=0; i<m_size; i++) { m_pentatope[i].resize(i+1); } } void Pentatope::draw() { for (int i=0; i<m_size; i++) { m_pentatope[i].draw(m_size-i-1); if (i<m_size-1) printf("-------------------------\n"); } } //----- Calc functions ----- void PTriangle::calc() { (*this)[0][0] = 1; for (int i=1; i < size(); i++) { (*this)[i][0] = (*this)[i][i] = 1; for (int j=1; j<i; j++) { (*this)[i][j] = (*this)[i-1][j-1] + (*this)[i-1][j]; } } } void PTetrahedron::calc() { PTriangle p(size()); for (int i=0; i<size(); i++) { for (int j=0; j<=i; j++) { for (int k=0; k<=j; k++) { (*this)[i][j][k] = p[i][j]*p[j][k]; } } } } void PPentatope::calc() { PTriangle p(size()); for (int i=0; i<size(); i++) { for (int j=0; j<=i; j++) { for (int k=0; k<=j; k++) { for (int l=0; l<=k; l++) { (*this)[i][j][k][l] = p[i][j]*p[j][k]*p[k][l]; } } } } } int main() { int simplex, size; while(true) { printf("Welches Pascalsche Simplex soll gezeichniet werden?\n\ [2] Pascalsches Dreieck\n\ [3] Pascalscher Tetraeder\n\ [4] Pascalsches Pentatop\n\ [5] Beenden\n\ Auswahl: "); scanf("%d", &simplex); PTriangle p; PTetrahedron q; PPentatope r; switch(simplex) { case 2: printf("Bis zur wievielten Zeile soll das Pascalsche Dreieck gezeichnet werden? "); scanf("%d", &size); p.resize(size); p.draw(); break; case 3: printf("Bis zur wievielten Ebene soll der Pascalsche Tetraeder gezeichnet werden? "); scanf("%d", &size); q.resize(size); q.draw(); break; case 4: printf("Bis zum wievielten Tetraeder soll der Pascalsche Pentatop gezeichnet werden? "); scanf("%d", &size); r.resize(size); r.draw(); break; case 5: return 0; default: printf("Fehlerhafte Eingabe!\n"); } } }
pascal.h
/* * Pascal - a program to draw Pascal's simplices * Copyright (C) 2005 Nicolas Bellm * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or (at * your option) any later version. * * This program is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * General Public License for more details. * */ #include <vector> using namespace std; class Triangle { public: Triangle() {} Triangle(int size) { resize(size); } void resize(int size); void draw(int space); int size() { return m_size; } vector<int>& operator[](int i) { return m_triangle[i]; } private: void center(int c); int m_size; vector<vector<int> > m_triangle; }; class Tetrahedron { public: Tetrahedron() {} Tetrahedron(int size) { resize(size); } void resize(int size); void draw(int space); int size() { return m_size; } Triangle& operator[](int i) { return m_tetrahedron[i]; } private: int m_size; vector<Triangle> m_tetrahedron; }; class Pentatope { public: Pentatope() {} Pentatope(int size) { resize(size); } void resize(int size); void draw(); int size() { return m_size; } Tetrahedron& operator[](int i) { return m_pentatope[i]; } private: int m_size; vector<Tetrahedron> m_pentatope; }; class PTriangle : public Triangle { public: PTriangle() {} PTriangle(int size) : Triangle(size) { calc(); } void resize(int size) { Triangle::resize(size); calc(); } private: void calc(); }; class PTetrahedron : public Tetrahedron { public: PTetrahedron() {} PTetrahedron(int size) : Tetrahedron(size) { calc(); } void resize(int size) { Tetrahedron::resize(size); calc(); } private: void calc(); }; class PPentatope : public Pentatope { public: PPentatope() {} PPentatope(int size) : Pentatope(size) { calc(); } void resize(int size) { Pentatope::resize(size); calc(); } private: void calc(); };