演算法篇-用棧來求解漢諾塔問題

閱讀了java版的《程式設計師程式碼面試指南 IT名企演算法與資料結構題目最優解》後，用c++以自己的想法完成了這道題

完整題目

在漢諾塔規則的基礎上，限制不能從最左的塔移動到最右的塔上，必須經過中間的塔，移動的跨度只能是一個塔。當塔有N層的時候，列印最優移動過程和最優移動步數。
看到原題我實際上並不能理解這道題，百度後才理解
相傳在古印度聖廟中，有一種被稱為漢諾塔(Hanoi)的遊戲。該遊戲是在一塊銅板裝置上，有三根杆(編號A、B、C)，在A杆自下而上、由大到小按順序放置64個金盤(如下圖)。遊戲的目標：把A杆上的金盤全部移到C杆上，並仍保持原有順序疊好。操作規則：每次只能移動一個盤子，並且在移動過程中三根杆上都始終保持大盤在下，小盤在上，操作過程中盤子可以置於A、B、C任一杆上。

題目限制：

1.一次只能移動一個數字
2.大的數字不能出現在小的盤子（數字）的上方（棧頂）
3.左右兩棧盤子（數字）移動必須經過中間的塔

遞迴實現
遞迴實現基本依照書本實現思路

int minstep;//步數
//遞迴

void move(int num, string from, string to)
{
    if (num == 1)
    {
        if (from=="mid" || to == "mid")
        {
            cout << "Move " << num << " from "
 
 << from << " to " << to << endl;
            minstep+=1;
        }
        else {
            cout << "Move " << num << " from " << from << " to " << "mid" << endl;
            cout << "Move " << num << " from " << "mid"
 
 << " to " << to << endl;
            minstep += 2;
        }
    }
    else {
        if (from=="mid" || to == "mid")
        {
            string another = (from._Equal("left") || to._Equal("left")) ? "right" : "left";
            move(num - 1, from, another);
            cout << "Move " << num << " from " << from << " to " << to << endl;
            minstep += 1; 
            move(num - 1, another, to);
        }
        else {
            move(num-1, from, to);
            cout << "Move " << num << " from " << from << " to " << "mid" << endl;
            minstep += 1;
            move(num - 1, to, from);
            cout << "Move " << num << " from " << "mid" << " to " << to << endl;
            minstep += 1;
            move(num - 1, from, to);

        }
    }



}

 void HanoiProblemnBydfd(int num)
{
    if (num <= 0) return;
    minstep  = 0; 

    move(num, "left", "right");
 }

測試

int main()
{
    HanoiProblemnBydfd(3);
    cout << minstep << endl;

    return 0;
}

棧模擬
棧模擬實現和書本略有不同，由於每次移動只能出現一種方式，所以把所有盤子的移動判斷完全由程式判斷

#include <stack>
#include <iostream>
#include <string>
using namespace std;
long minstep = 0;//最小步數
//非遞迴，用棧模擬
class HanoiStack {
private:
    stack<int> LeftP;
    stack<int> MidP;
    stack<int> RightP;
    int n;
    string lastfrom;
    string lastto;
    void Move(string from,string to)
    {
        if (from== lastto&&to== lastfrom) return;

        int fromVal=0;
        if (from == "left"&&!LeftP.empty())
        {
            fromVal = LeftP.top();
            //LeftP.pop();
        }
        else if (from == "mid" && !MidP.empty())
        {
            fromVal = MidP.top();
            //MidP.pop();
        }
        else if (from == "right" && !RightP.empty())
        {
            fromVal = RightP.top();
            //RightP.pop();
        }
        if (fromVal == 0) return;
        if (to == "left")
        {
            if(LeftP.empty()) LeftP.push(fromVal);
            else if(fromVal<LeftP.top()) LeftP.push(fromVal);
            else return;
        }
        else if(to=="mid") 
        {
            if (MidP.empty()) MidP.push(fromVal);
            else if (fromVal<MidP.top()) MidP.push(fromVal);
            else return;
        }
        else if (to == "right")
        {
            if (RightP.empty()) RightP.push(fromVal);
            else if (fromVal<RightP.top()) RightP.push(fromVal); 
            else return;
        }
        Pop(from);
        lastto = to;
        lastfrom = from;
        cout << "Move " << fromVal << " from " << from << " to " << to << endl;
        minstep += 1;
    }
    void Pop(string from)
    {
        if (from == "left" && !LeftP.empty())
        {

            LeftP.pop();
        }
        else if (from == "mid" && !MidP.empty())
        {

            MidP.pop();
        }
        else if (from == "right" && !RightP.empty())
        {

            RightP.pop();
        }
    }
public:
    HanoiStack(int n)
    {
        for (int i = n; i >0; i--)
        {
            LeftP.push(i);
        }
        this->n = n;
        minstep = 0;
    }
    void HanoiProblem()
    {
        while (RightP.size() != n)
        {
            Move("left", "mid");
            Move("mid", "left");
            Move("mid", "right");           
            Move("right", "mid");               
        }
        cout << minstep << endl;
    }

};

測試

int main()
{
    /*HanoiProblemnBydfd(3);
    cout << minstep << endl;*/
    HanoiStack  test = HanoiStack(3);
    test.HanoiProblem();
    return 0;
}