Qt C++春晚刘谦魔术约瑟夫环问题的模拟程序

什么是约瑟夫环问题？

约瑟夫问题是个有名的问题：N个人围成一圈，从第一个开始报数，第M个将被杀掉，最后剩下一个，其余人都将被杀掉。例如N=6，M=5，被杀掉的顺序是：5，4，6，2，3。
分析：
（1）由于对于每个人只有死和活两种状态，因此可以用布尔型数组标记每个人的状态，可用true表示死，false表示活。
（2）开始时每个人都是活的，所以数组初值全部赋为false。
（3）模拟杀人过程，直到所有人都被杀死为止。

魔术

1、4张牌对折后撕开，就是8张，叠放在一起就是ABCDABCD。注意，ABCD四个数字是完全等价的。
2、根据名字字数，把顶上的牌放到下面，但怎么放都不会改变循环序列的相对位置。譬如2次，最后变成CDABCDAB；譬如3次，最后换成DABCDABC。但无论怎么操作，第4张和第8张牌都是一样的。
3、把顶上3张插到中间任意位置。这一步非常重要！因为操作完之后必然出现第1张和第8张牌是一样的！以名字两个字为例，可以写成BxxxxxxB（这里的x是其他和B不同的牌）。
4、拿掉顶上的牌放到一边，记为B。剩下的序列是xxxxxxB，一共7张牌。
5、南方人/北方人/不确定，分别拿顶上的1/2/3张牌插到中间，但是不会改变剩下7张牌是xxxxxxB的结果。
6、男生拿掉1张，女生拿掉2张。也就是男生剩下6张，女生剩下5张。分别是xxxxxB和xxxxB。
7、把最顶上的放到最底下，循环7次，男生和女生分别会是xxxxBx和xxBxx。
8、最后执行约瑟夫环过程！操作到最后只剩下1张。当牌数为6时（男生），剩下的就是第5张牌；当牌数为5时（女生），剩下的就是第3张牌。就是第4步拿掉的那张牌！

.h

#ifndefWIDGET_H#defineWIDGET_H#include<QWidget>#include<vector>#include"brand.h"#include<QPushButton>#include<QRadioButton>#include<QLineEdit>#include<QLayout>#include<QStackedWidget>#include<QSplitter>#include<QButtonGroup>classStep:publicQWidget{public:Step(QWidget *parent =0):QWidget(parent){
        QVBoxLayout* vbox =newQVBoxLayout(this);
        QHBoxLayout* hboxLabel =new QHBoxLayout;
        hboxChoose =new QHBoxLayout;
        QHBoxLayout* hboxBtn =new QHBoxLayout;
        label =newQLabel(this);
        hboxLabel->addStretch();
        hboxLabel->addWidget(label);
        hboxLabel->addStretch();
        hboxBtn->addStretch();
        vbox->addLayout(hboxLabel);
        vbox->addLayout(hboxChoose);
        vbox->addLayout(hboxBtn);}voidSetText(QString text){
        label->setText(text);}

    QHBoxLayout*GetChooseLayout(){return hboxChoose;}virtualboolCheck(){returntrue;}private:
    QLabel* label;
    QHBoxLayout* hboxChoose;};classStart:publicStep{public:Start(QWidget *parent =0):Step(parent){SetText("请输入四个数字、字母或汉字");
        edit =newQLineEdit(this);
        edit->setPlaceholderText("请输入四个数字、字母或汉字");GetChooseLayout()->addWidget(edit);}
    QString GetStr(){return edit->text();}boolCheck(){return edit->text().size()==4;}private:
    QLineEdit* edit;};classFirst:publicStep{public:First(QWidget *parent =0):Step(parent){SetText("4张牌对折后撕开");}};classSecond:publicStep{public:Second(QWidget *parent =0):Step(parent){SetText("请输入您的名字");
        edit =newQLineEdit(this);
        edit->setPlaceholderText("请输入您的名字");GetChooseLayout()->addWidget(edit);}intGetNumber(){return edit->text().size();}boolCheck(){return edit->text().size()>0;}private:
    QLineEdit* edit;};classThird:publicStep{public:Third(QWidget *parent =0):Step(parent){SetText("把顶上3张插到中间任意位置");
        radio =newQRadioButton("第一张后面",this);
        radio1 =newQRadioButton("第二张后面",this);
        radio2 =newQRadioButton("第三张后面",this);
        radio3 =newQRadioButton("第四张后面",this);GetChooseLayout()->addWidget(radio);GetChooseLayout()->addWidget(radio1);GetChooseLayout()->addWidget(radio2);GetChooseLayout()->addWidget(radio3);
        radio->setChecked(true);}intGetChoose(){if(radio->isChecked())return1;if(radio1->isChecked())return2;if(radio2->isChecked())return3;if(radio3->isChecked())return4;return1;}private:
    QRadioButton* radio;
    QRadioButton* radio1;
    QRadioButton* radio2;
    QRadioButton* radio3;};classFour:publicStep{public:Four(QWidget *parent =0):Step(parent){SetText("拿掉顶上的牌放到一边");}};classFive:publicStep{public:Five(QWidget *parent =0):Step(parent){SetText("南方人/北方人/不确定，分别拿顶上的1/2/3张牌插到中间");
        QVBoxLayout* vbox =new QVBoxLayout;
        QHBoxLayout* hbox =new QHBoxLayout;
        QHBoxLayout* hbox1 =new QHBoxLayout;
        QButtonGroup* group =newQButtonGroup(this);
        QButtonGroup* group1 =newQButtonGroup(this);
        radio =newQRadioButton("南方人",this);
        radio1 =newQRadioButton("北方人",this);
        radio2 =newQRadioButton("不确定",this);
        radio3 =newQRadioButton("第一张后面",this);
        radio4 =newQRadioButton("第二张后面",this);
        radio5 =newQRadioButton("第三张后面",this);
        hbox->addWidget(radio);
        hbox->addWidget(radio1);
        hbox->addWidget(radio2);
        hbox1->addWidget(radio3);
        hbox1->addWidget(radio4);
        hbox1->addWidget(radio5);
        group->addButton(radio);
        group->addButton(radio1);
        group->addButton(radio2);
        group1->addButton(radio3);
        group1->addButton(radio4);
        group1->addButton(radio5);
        vbox->addLayout(hbox);
        vbox->addLayout(hbox1);GetChooseLayout()->addLayout(vbox);
        radio2->setChecked(true);
        radio3->setChecked(true);}intGetChoose(){if(radio->isChecked())return1;elseif(radio1->isChecked())return2;elseif(radio2->isChecked())return3;return1;}intGetChoose1(){if(radio3->isChecked())return1;elseif(radio4->isChecked())return2;elseif(radio5->isChecked())return3;return1;}private:
    QRadioButton* radio;
    QRadioButton* radio1;
    QRadioButton* radio2;
    QRadioButton* radio3;
    QRadioButton* radio4;
    QRadioButton* radio5;};classSix:publicStep{public:Six(QWidget *parent =0):Step(parent){SetText("男生拿掉1张，女生拿掉2张");
        radio =newQRadioButton("男生",this);
        radio1 =newQRadioButton("女生",this);GetChooseLayout()->addWidget(radio);GetChooseLayout()->addWidget(radio1);
        radio->setChecked(true);}intGetChoose(){if(radio->isChecked())return1;if(radio1->isChecked())return2;return1;}private:
    QRadioButton* radio;
    QRadioButton* radio1;};classSeven:publicStep{public:Seven(QWidget *parent =0):Step(parent){SetText("把最顶上的放到最底下,循环7次");}};classLast:publicStep{public:Last(QWidget *parent =0):Step(parent){SetText("好运留下来");
        flag =1;}voidInit(){SetText("好运留下来");
        flag =1;}voidChangeText(){switch(flag){case0:
                flag =1;SetText("好运留下来");break;case1:
                flag =0;SetText("烦恼都丢掉");break;default:break;}}intGetFlag(){return flag;}private:int flag;};classWidget:publicQSplitter{
    Q_OBJECT

public:Widget(QWidget *parent =0);~Widget();private:voidStartGetData();voidFirstStep();voidSecondStep();voidThridStep();voidFourStep();voidFiveStep();voidSixStep();voidSevenStep();voidLastStep();voidUpdateData();protected slots:voidOnClicked(bool);private:
    std::vector<Brand*> m_vecBrand;
    QString m_firstCard;

    QLabel* label;
    QPushButton* btn;
    QStackedWidget* m_stackedWidget;bool bOver;};#endif// WIDGET_H

.cpp

#pragmaexecution_character_set("utf-8")#include"widget.h"#include<QDebug>Widget::Widget(QWidget *parent):QSplitter(parent){setOrientation(Qt::Vertical);
    label =newQLabel("qweqwe",this);
    QWidget* widget =newQWidget(this);
    m_stackedWidget =newQStackedWidget(this);addWidget(label);addWidget(widget);setStretchFactor(1,2);

    m_stackedWidget->addWidget(new Start);
    m_stackedWidget->addWidget(new First);
    m_stackedWidget->addWidget(new Second);
    m_stackedWidget->addWidget(new Third);
    m_stackedWidget->addWidget(new Four);
    m_stackedWidget->addWidget(new Five);
    m_stackedWidget->addWidget(new Six);
    m_stackedWidget->addWidget(new Seven);
    m_stackedWidget->addWidget(new Last);

    QHBoxLayout* hbox =new QHBoxLayout;
    QVBoxLayout* vbox =new QVBoxLayout;
    btn =newQPushButton("下一步",this);
    hbox->addStretch();
    hbox->addWidget(btn);
    vbox->addWidget(m_stackedWidget);
    vbox->addLayout(hbox);
    widget->setLayout(vbox);connect(btn,SIGNAL(clicked(bool)),this,SLOT(OnClicked(bool)));

    bOver =false;}Widget::~Widget(){}voidWidget::StartGetData(){
    Start* start =(Start*)m_stackedWidget->widget(0);
    QString str = start->GetStr();for(int i=0; i<str.length(); i++){
        Brand* brand =newBrand(QString(str[i]));
        m_vecBrand.push_back(brand);}}voidWidget::FirstStep(){
    Start* start =(Start*)m_stackedWidget->widget(0);
    QString str = start->GetStr();for(int i=0; i<str.length(); i++){
        Brand* brand =newBrand(QString(str[i]));
        m_vecBrand.push_back(brand);}}voidWidget::SecondStep(){
    Second* second =(Second*)m_stackedWidget->widget(2);int number = second->GetNumber();for(int i=0; i<number; i++){
        Brand* brand = m_vecBrand[0];
        m_vecBrand.erase(m_vecBrand.begin());
        m_vecBrand.push_back(brand);}}voidWidget::ThridStep(){
    Third* third =(Third*)m_stackedWidget->widget(3);int number = third->GetChoose();

    Brand* brand = m_vecBrand[0];
    Brand* brand1 = m_vecBrand[1];
    Brand* brand2 = m_vecBrand[2];

    m_vecBrand.erase(m_vecBrand.begin());
    m_vecBrand.erase(m_vecBrand.begin());
    m_vecBrand.erase(m_vecBrand.begin());

    std::vector<Brand*> vecBrand;for(int i=0; i<m_vecBrand.size(); i++){
        vecBrand.push_back(m_vecBrand[i]);if(number == i +1){
            vecBrand.push_back(brand);
            vecBrand.push_back(brand1);
            vecBrand.push_back(brand2);}}
    m_vecBrand = vecBrand;}voidWidget::FourStep(){
    m_firstCard = m_vecBrand[0]->GetStr();setWindowTitle("当前选择牌为："+ m_firstCard);
    m_vecBrand.erase(m_vecBrand.begin());}voidWidget::FiveStep(){
    Five* five =(Five*)m_stackedWidget->widget(5);int number = five->GetChoose();int number1 = five->GetChoose1();

    std::vector<Brand*> vecBrand;switch(number){case1:
        vecBrand.push_back(m_vecBrand[0]);
        m_vecBrand.erase(m_vecBrand.begin());break;case2:
        vecBrand.push_back(m_vecBrand[0]);
        vecBrand.push_back(m_vecBrand[1]);
        m_vecBrand.erase(m_vecBrand.begin());
        m_vecBrand.erase(m_vecBrand.begin());break;case3:
        vecBrand.push_back(m_vecBrand[0]);
        vecBrand.push_back(m_vecBrand[1]);
        vecBrand.push_back(m_vecBrand[2]);
        m_vecBrand.erase(m_vecBrand.begin());
        m_vecBrand.erase(m_vecBrand.begin());
        m_vecBrand.erase(m_vecBrand.begin());break;default:break;}

    std::vector<Brand*> vecBrand1;for(int i=0; i<m_vecBrand.size(); i++){
        vecBrand1.push_back(m_vecBrand[i]);if(number1 == i +1){
            vecBrand1.insert(vecBrand1.end(), vecBrand.begin(), vecBrand.end());}}
    m_vecBrand = vecBrand1;}voidWidget::SixStep(){
    Six* six =(Six*)m_stackedWidget->widget(5);int number = six->GetChoose();switch(number){case1:
        m_vecBrand.erase(m_vecBrand.begin());break;case2:
        m_vecBrand.erase(m_vecBrand.begin());
        m_vecBrand.erase(m_vecBrand.begin());break;default:break;}}voidWidget::SevenStep(){for(int i=0; i<7; i++){
        Brand* brand = m_vecBrand[0];
        m_vecBrand.erase(m_vecBrand.begin());
        m_vecBrand.push_back(brand);}}voidWidget::LastStep(){
    Last* last =(Last*)m_stackedWidget->widget(8);int flag = last->GetFlag();switch(flag){case0:
        m_vecBrand.erase(m_vecBrand.begin());break;case1:
        Brand* brand = m_vecBrand[0];
        m_vecBrand.erase(m_vecBrand.begin());
        m_vecBrand.push_back(brand);break;}

    last->ChangeText();}voidWidget::UpdateData(){
    QString str;for(int i=0; i<m_vecBrand.size(); i++){
        str+= m_vecBrand[i]->GetStr();}
    label->setText(str);}voidWidget::OnClicked(bool){if(bOver){setWindowTitle("magic");
        Last* last =(Last*)m_stackedWidget->widget(8);
        last->Init();
        bOver =false;
        btn->setText("下一步");
        m_stackedWidget->setCurrentIndex(0);return;}

    Step* step =(Step*)m_stackedWidget->currentWidget();if(!step->Check())return;if(m_vecBrand.size()==1){
        m_vecBrand.clear();
        Last* last =(Last*)m_stackedWidget->widget(8);
        last->SetText("之前的牌为："+ m_firstCard+" 对上否？");
        bOver =true;
        btn->setText("重新开始");return;}switch(m_stackedWidget->currentIndex()){case0://4张牌StartGetData();break;case1://对折撕开FirstStep();break;case2://根据名字字数，把顶上的牌放到下面SecondStep();break;case3://把顶上3张插到中间任意位置ThridStep();break;case4://拿掉顶上的牌放到一边FourStep();break;case5://南方人/北方人/不确定，分别拿顶上的1/2/3张牌插到中间FiveStep();break;case6://男生拿掉1张，女生拿掉2张SixStep();break;case7://把最顶上的放到最底下,循环7次SevenStep();break;case8://好运留下来 烦恼都丢掉LastStep();break;default:break;}UpdateData();if(m_stackedWidget->currentIndex()+1< m_stackedWidget->count())
        m_stackedWidget->setCurrentIndex(m_stackedWidget->currentIndex()+1);}