The Towers of Hanoi recursion 汉诺塔 C++

What is Towers of Hanoi ?

Figure1 shows an tower of hanoi setup with three discs on the first pole. Note that all the discs are a different size. The a < b < c.

The Rules

The goal is move all discs from first pole to the last pole. There are three rules:

1. A large disc can never be placed on top of a small disc.

2. You can only move one disc at a time

3. You can move discs on first pole  to third pole with one movement.

Solving the Puzzle

1. Move a to 3.
2. Move b to 2.
3. Move a to 2.
4. Move c to 3.
5. Move a to 1.
6. Move b to 3.
7. Move a to 3.

Solving the Puzzle with a Computer

Look at Figure2. To solve the Towers of Hani with four discs.

Step1. Move 3 discs to the second pole.

Step2. Move biggest disc to the third pole.

Step3. Move 3 discs to the third pole.

How to Move 3 discs to the second pole?

Step1. Move 2 discs to the third pole.

Step2. Move biggest disc to the second pole.

Step3. Move 2 discs to the second pole.

So if you want to move n discs:

Step1. Move the top n - 1 discs to the pole 2          (Move top n - 1 discs From beginning pole to empty)

Step2. Move the nthdisc to the pole 3                    (Move the nth  From beginning pole to destination)

step3. Move the n -1 discs from the pole 2 to 3.     (Move the n - 1 discs From empty pole to destination)

int findEmpty(int from, int destination){
    if((from == 1 && destination == 2) || (from == 2 && destination == 1))
		return 3;
	else if((from == 2 && destination == 3) || (from == 3 && destination == 2))
	    return 1;
	else if((from == 1 && destination == 3) || (from == 3 && destination == 1))
	    return 2;
}

void moveTown(int totalNum, int beginning, int destination){

	
		if(totalNum == 1){
			cout << "move "<< totalNum << " from " << beginning << " to " << destination << endl;
		}else{
			int empty = findEmpty(beginning, destination);
			moveTown(totalNum - 1, beginning, empty);
			cout << "move "<< totalNum << " from " << beginning << " to " << destination << endl;
			moveTown(totalNum - 1, empty, destination);
		}
}

For example, If you want computer to solve the 3 discs tower.

just call

moveTown(3, 1, 3);

Look At moveTown function. Every time we need findEmpty function to find the empty pole. There are only 3 poles. So  we can tell the function what the empty pole is.

void Hanoi(const int& n,const int& beginning,const int& destination,const int& empty )
{
	if( n > 0 )
	{
		Hanoi( n-1, beginning, empty, destination );
		cout << "Moving " << n << " from " << beginning << " to " << destination << endl;
		Hanoi( n-1, empty, destination, beginning );
	}
}

The whole Code

// Hanoi.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include <iostream>

using namespace std;


int findEmpty(int from, int destination){
    if((from == 1 && destination == 2) || (from == 2 && destination == 1))
		return 3;
	else if((from == 2 && destination == 3) || (from == 3 && destination == 2))
	    return 1;
	else if((from == 1 && destination == 3) || (from == 3 && destination == 1))
	    return 2;
}
//slow one
void moveTown(int totalNum, int beginning, int destination){

	
		if(totalNum == 1){
			cout << "move "<< totalNum << " from " << beginning << " to " << destination << endl;
		}else{
			int empty = findEmpty(beginning, destination);
			moveTown(totalNum - 1, beginning, empty);
			cout << "move "<< totalNum << " from " << beginning << " to " << destination << endl;
			moveTown(totalNum - 1, empty, destination);
		}
}

//better one
void Hanoi(const int& n,const int& beginning,const int& destination,const int& empty )
{
	if( n > 0 )
	{
		Hanoi( n-1, beginning, empty, destination );
		cout << "Moving " << n << " from " << beginning << " to " << destination << endl;
		Hanoi( n-1, empty, destination, beginning );
	}
}


int main(int argc, char* argv[])
{
	//moveTown(3, 1, 3);

	cout << endl;

	Hanoi(3, 1, 3, 2);
	return 0;
}

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