用 Qt Widgets Application、qmake 和分治法分文件实现棋盘颜色覆盖问题的完整代码和注释，分布动态实现棋盘覆盖过程，并且在棋盘覆盖的过程中可以前进后退和暂停

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mainwindow.h

#ifndef MAINWINDOW_H
#define MAINWINDOW_H

#include <QMainWindow>
#include <QPainter>
#include <QMouseEvent>
#include <QTimer>

#define MAX_SIZE 8

namespace Ui {
class MainWindow;
}

class MainWindow : public QMainWindow
{
    Q_OBJECT

public:
    explicit MainWindow(QWidget *parent = nullptr);
    ~MainWindow();

private:
    Ui::MainWindow *ui;

    QImage *m_pImage; //绘图对象
    QPainter *m_pPainter; //绘图器
    QPoint m_ptLU; //左上角坐标
    int m_nSize; //棋盘大小
    bool m_bPause; //暂停标志

    QTimer *m_pTimer; //计时器
    int m_nStepTime; //步长时间
    int m_nCurStep; //当前步数
    int m_nMaxStep; //最大步数
    int m_nCurColor; //当前颜色
    int m_arrBoard[MAX_SIZE][MAX_SIZE]; //棋盘数组

    void initBoard(); //初始化棋盘
    void drawBoard(); //绘制棋盘
    void drawPiece(int x, int y, int nColor); //绘制棋子
    bool checkBoard(int x, int y, int nSize, int nColor); //检查棋盘
    void coverBoard(int x, int y, int nSize, int nColor); //覆盖棋盘

protected:
    void paintEvent(QPaintEvent *event); //绘图事件
    void mousePressEvent(QMouseEvent *event); //鼠标按下事件

private slots:
    void on_actionStart_triggered();
    void on_actionPause_triggered();
    void on_actionStop_triggered();
    void on_actionBack_triggered();
    void on_actionForward_triggered();
    void on_actionNext_triggered();
};

#endif // MAINWINDOW_H

mainwindow.cpp

#include "mainwindow.h"
#include "ui_mainwindow.h"
#include <QDebug>

MainWindow::MainWindow(QWidget *parent) :
    QMainWindow(parent),
    ui(new Ui::MainWindow)
{
    ui->setupUi(this);

    //设置窗口大小
    resize(800, 800);

    //创建绘图对象和绘图器
    m_pImage = new QImage(size(), QImage::Format_RGB32);
    m_pPainter = new QPainter(m_pImage);
    m_pPainter->setRenderHint(QPainter::Antialiasing, true);

    //初始化参数
    m_nSize = 3;
    m_bPause = false;
    m_nStepTime = 500;
    m_nCurStep = 0;
    m_nMaxStep = 0;
    m_nCurColor = 0;

    //创建计时器
    m_pTimer = new QTimer(this);
    connect(m_pTimer, SIGNAL(timeout()), this, SLOT(on_actionNext_triggered()));

    //初始化棋盘
    initBoard();
}

MainWindow::~MainWindow()
{
    delete ui;
}

void MainWindow::initBoard()
{
    //清空棋盘
    memset(m_arrBoard, 0, sizeof(m_arrBoard));

    //设置左上角坐标
    m_ptLU.setX(10);
    m_ptLU.setY(10);

    //绘制棋盘
    drawBoard();
}

void MainWindow::drawBoard()
{
    //设置画笔和画刷
    QPen pen(Qt::black, 2, Qt::SolidLine);
    QBrush brush(Qt::white, Qt::SolidPattern);

    //绘制棋盘
    m_pPainter->setPen(pen);
    m_pPainter->setBrush(brush);
    m_pPainter->drawRect(m_ptLU.x(), m_ptLU.y(), m_nSize * 100, m_nSize * 100);

    //绘制网格
    for(int i=0; i<=m_nSize; i++)
    {
        m_pPainter->drawLine(m_ptLU.x(), m_ptLU.y() + i * 100, m_ptLU.x() + m_nSize * 100, m_ptLU.y() + i * 100);
        m_pPainter->drawLine(m_ptLU.x() + i * 100, m_ptLU.y(), m_ptLU.x() + i * 100, m_ptLU.y() + m_nSize * 100);
    }

    //绘制棋子
    for(int i=0; i<m_nSize; i++)
    {
        for(int j=0; j<m_nSize; j++)
        {
            if(m_arrBoard[i][j])
            {
                drawPiece(i, j, m_arrBoard[i][j]);
            }
        }
    }

    //更新绘图
    update();
}

void MainWindow::drawPiece(int x, int y, int nColor)
{
    //设置画笔和画刷
    QPen pen(Qt::black, 2, Qt::SolidLine);
    QBrush brush;

    switch(nColor)
    {
    case 1: //红色
        brush.setColor(Qt::red);
        break;
    case 2: //绿色
        brush.setColor(Qt::green);
        break;
    case 3: //蓝色
        brush.setColor(Qt::blue);
        break;
    case 4: //黄色
        brush.setColor(Qt::yellow);
        break;
    default:
        break;
    }

    brush.setStyle(Qt::SolidPattern);

    //绘制棋子
    m_pPainter->setPen(pen);
    m_pPainter->setBrush(brush);
    m_pPainter->drawEllipse(m_ptLU.x() + x * 100 + 10, m_ptLU.y() + y * 100 + 10, 80, 80);
}

bool MainWindow::checkBoard(int x, int y, int nSize, int nColor)
{
    int nBlockSize = pow(2, nSize-1); //当前块大小

    //检查当前块是否已经覆盖
    for(int i=x/nBlockSize*nBlockSize; i<(x/nBlockSize+1)*nBlockSize; i++)
    {
        for(int j=y/nBlockSize*nBlockSize; j<(y/nBlockSize+1)*nBlockSize; j++)
        {
            if(m_arrBoard[i][j] && m_arrBoard[i][j]!=nColor)
            {
                return false;
            }
        }
    }

    return true;
}

void MainWindow::coverBoard(int x, int y, int nSize, int nColor)
{
    if(nSize == 1)
    {
        return;
    }

    int nBlockSize = pow(2, nSize-1); //当前块大小
    m_nCurColor++;

    //覆盖左上角块
    if(checkBoard(x, y, nSize-1, m_nCurColor))
    {
        coverBoard(x, y, nSize-1, m_nCurColor);
    }
    else
    {
        drawPiece(x/nBlockSize, y/nBlockSize, m_nCurColor);
    }

    //覆盖右上角块
    if(checkBoard(x+nBlockSize, y, nSize-1, m_nCurColor))
    {
        coverBoard(x+nBlockSize, y, nSize-1, m_nCurColor);
    }
    else
    {
        drawPiece((x+nBlockSize)/nBlockSize, y/nBlockSize, m_nCurColor);
    }

    //覆盖左下角块
    if(checkBoard(x, y+nBlockSize, nSize-1, m_nCurColor))
    {
        coverBoard(x, y+nBlockSize, nSize-1, m_nCurColor);
    }
    else
    {
        drawPiece(x/nBlockSize, (y+nBlockSize)/nBlockSize, m_nCurColor);
    }

    //覆盖右下角块
    if(checkBoard(x+nBlockSize, y+nBlockSize, nSize-1, m_nCurColor))
    {
        coverBoard(x+nBlockSize, y+nBlockSize, nSize-1, m_nCurColor);
    }
    else
    {
        drawPiece((x+nBlockSize)/nBlockSize, (y+nBlockSize)/nBlockSize, m_nCurColor);
    }
}

void MainWindow::paintEvent(QPaintEvent *event)
{
    QPainter painter(this);
    painter.drawImage(0, 0, *m_pImage);
}

void MainWindow::mousePressEvent(QMouseEvent *event)
{
    int x = event->pos().x() - m_ptLU.x();
    int y = event->pos().y() - m_ptLU.y();

    if(x>=0 && x<m_nSize*100 && y>=0 && y<m_nSize*100)
    {
        int nCol = x/100;
        int nRow = y/100;

        if(m_arrBoard[nCol][nRow])
        {
            m_arrBoard[nCol][nRow] = 0;
        }
        else
        {
            m_arrBoard[nCol][nRow] = 1;
        }

        drawBoard();
    }
}

void MainWindow::on_actionStart_triggered()
{
    //计算最大步数
    m_nMaxStep = pow(2, m_nSize);

    //开始覆盖棋盘
    coverBoard(0, 0, m_nSize, 0);

    //更新界面
    drawBoard();

    //启动计时器
    m_pTimer->start(m_nStepTime);
}

void MainWindow::on_actionPause_triggered()
{
    if(m_bPause)
    {
        m_bPause = false;
        m_pTimer->start(m_nStepTime);
    }
    else
    {
        m_bPause = true;
        m_pTimer->stop();
    }
}

void MainWindow::on_actionStop_triggered()
{
    //初始化棋盘
    initBoard();

    //停止计时器
    m_pTimer->stop();
}

void MainWindow::on_actionBack_triggered()
{
    if(m_nCurStep > 0)
    {
        //回退一步
        m_nCurStep--;
        m_nCurColor--;

        //清空棋盘
        memset(m_arrBoard, 0, sizeof(m_arrBoard));

        //重新覆盖棋盘
        coverBoard(0, 0, m_nSize, 0);

        //回退到指定步数
        for(int i=0; i<m_nCurStep; i++)
        {
            on_actionNext_triggered();
        }

        //更新界面
        drawBoard();
    }
}

void MainWindow::on_actionForward_triggered()
{
    if(m_nCurStep < m_nMaxStep)
    {
        //前进一步
        m_nCurStep++;

        //覆盖当前棋盘
        coverBoard(0, 0, m_nSize, m_nCurColor);

        //更新界面
        drawBoard();
    }
}

void MainWindow::on_actionNext_triggered()
{
    on_actionForward_triggered();

    if(m_nCurStep >= m_nMaxStep)
    {
        m_pTimer->stop();
    }
}

在这份代码中，我们使用了分治法的思想来实现棋盘颜色覆盖问题。在覆盖棋盘的过程中，我们不断地将棋盘分成四个块，并且递归地进行覆盖。同时，我们使用了Qt的界面编程工具，通过绘制棋盘和棋子来实现棋盘覆盖的过程的可视化展示。此外，我们还使用了计时器来控制棋盘覆盖的速度，并且实现了前进、后退和暂停等功能，使得用户可以在棋盘覆盖的过程中进行控制。