模擬行星轉動，求終止步數

world.h

// world.h
#ifndef WORLD_H_
#define WORLD_H_
#define WIDTH 7
#define BALL 3

enum World {space, centre, surround};

class Galaxy {
private:
	int steps;
	int centre_xy;
	struct Coord {
		int x;
		int y;
	};
	char Map[WIDTH][WIDTH];
	Coord Ball[BALL];
public:
	Galaxy();
	~Galaxy();
	void Show();
	void Update();
	bool Judge();
};

#endif

world.cpp

// world.cpp
#include <iostream>
#include "world.h"

int main() {
	Galaxy solay;

	for (;;) {
		solay.Show();
		solay.Update();

		if (solay.Judge()) {
			solay.Show();
			break;
		}
	}
	return 0;
}

sola.cpp

// sola.cpp
#include <iostream>
#include "world.h"

Galaxy::Galaxy() {
	for (int i = 0; i < WIDTH; i++)
		memset(Map[i], space, sizeof(Map[i]));
	steps = 0;
	centre_xy = (WIDTH - 1) / 2;
	Map[centre_xy][centre_xy] = centre;

	int ball_x = centre_xy;
	int ball_y = centre_xy - 1;

	for (int i = 0; i < BALL; i++) {
		Ball[i].x = ball_x;
		Ball[i].y = ball_y;
		Map[ball_x][ball_y--] = surround;
	}
}

Galaxy::~Galaxy() {
	using std::cout;

	cout << "Step: " << steps << '\n';
	cout << "See the world\n";
}

void Galaxy::Show() {
	using std::cout;
        system("CLS");

	for (int i = 0; i < WIDTH; i++) {
		for (int j = 0; j < WIDTH; j++) {
			switch (Map[i][j]) {
			case space: cout << "."; 
				break;
			case centre: cout << "*";
				break;
			case surround: cout << "o";
				break;
			}
		}
		cout << '\n';
	}
}

void Galaxy::Update() {
	for (int i = 0; i < BALL; i++) {
		if (Ball[i].x == centre_xy &&
			Ball[i].y < centre_xy) {
			Map[Ball[i].x++][Ball[i].y++] = space;
			Map[Ball[i].x][Ball[i].y] = surround;
		}
		else if (Ball[i].x == centre_xy &&
			Ball[i].y > centre_xy) {
			Map[Ball[i].x--][Ball[i].y--] = space;
			Map[Ball[i].x][Ball[i].y] = surround;
		}
		else if (Ball[i].x < centre_xy &&
			Ball[i].y == centre_xy) {
			Map[Ball[i].x++][Ball[i].y--] = space;
			Map[Ball[i].x][Ball[i].y] = surround;
		}
		else if (Ball[i].x > centre_xy &&
			Ball[i].y == centre_xy) {
			Map[Ball[i].x--][Ball[i].y++] = space;
			Map[Ball[i].x][Ball[i].y] = surround;
		}
		else if (Ball[i].x < centre_xy &&
			Ball[i].y < centre_xy) {
			Map[Ball[i].x++][Ball[i].y--] = space;
			Map[Ball[i].x][Ball[i].y] = surround;
		}
		else if (Ball[i].x > centre_xy &&
			Ball[i].y < centre_xy) {
			Map[Ball[i].x++][Ball[i].y++] = space;
			Map[Ball[i].x][Ball[i].y] = surround;
		}
		else if (Ball[i].x > centre_xy &&
			Ball[i].y > centre_xy) {
			Map[Ball[i].x--][Ball[i].y++] = space;
			Map[Ball[i].x][Ball[i].y] = surround;
		}
		else if (Ball[i].x < centre_xy &&
			Ball[i].y > centre_xy) {
			Map[Ball[i].x--][Ball[i].y--] = space;
			Map[Ball[i].x][Ball[i].y] = surround;
		}
	}
	++steps;
}

bool Galaxy::Judge() {
	int ball_x = centre_xy;
	int ball_y = centre_xy - 1;

	for (int i = 0; i < BALL; i++, ball_y--) {
		if (Ball[i].x != ball_x ||
			Ball[i].y != ball_y)
			return false;
	}
	return true;
}

實驗數據如下：

n=1	m=4
n=2	m=8
n=3	m=24
n=4	m=48
n=5	m=240
n=6	m=240
n=7	m=1680
n=8	m=3360
n=9	m=10080
n=10	m=10080
-	-
-	-

實驗之前，我認爲球的個數應和步數大小成正比關係，但是其中發現了意想不到的事，即當 n = 5 和 n = 6 時，步數爲一樣多；當 n = 9 和 n = 10 時，步數爲一樣多。