用Qt设计一款聊天软件，聊天室人数上限20人的代码。

以下是一个简单的Qt聊天室软件的代码示例，聊天室人数上限为20人：

mainwindow.h

#ifndef MAINWINDOW_H
#define MAINWINDOW_H

#include <QMainWindow>
#include <QTcpSocket>
#include <QTcpServer>
#include <QList>

QT_BEGIN_NAMESPACE
namespace Ui { class MainWindow; }
QT_END_NAMESPACE

class MainWindow : public QMainWindow
{
    Q_OBJECT

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

private slots:
    void on_sendButton_clicked();
    void newConnection();
    void readMessage();
    void displayError(QAbstractSocket::SocketError socketError);

private:
    Ui::MainWindow *ui;
    QTcpServer *tcpServer;
    QTcpSocket *tcpSocket;
    QList<QTcpSocket*> clients;
};

#endif // MAINWINDOW_H

mainwindow.cpp

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

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

    tcpServer = new QTcpServer(this);
    tcpSocket = new QTcpSocket(this);

    if (!tcpServer->listen(QHostAddress::Any, 8888))
    {
        QMessageBox::critical(this, tr("Error"), tr("Unable to start the server: %1.").arg(tcpServer->errorString()));
        close();
    }

    connect(tcpServer, SIGNAL(newConnection()), this, SLOT(newConnection()));
}

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

void MainWindow::on_sendButton_clicked()
{
    QString message = ui->messageEdit->toPlainText();
    if (message.isEmpty())
        return;

    QByteArray block;
    QDataStream out(&block, QIODevice::WriteOnly);
    out.setVersion(QDataStream::Qt_5_15);
    out << message;

    for (int i = 0; i < clients.size(); i++)
    {
        clients[i]->write(block);
    }

    ui->messageEdit->clear();
}

void MainWindow::newConnection()
{
    tcpSocket = tcpServer->nextPendingConnection();

    if (clients.size() >= 20)
    {
        tcpSocket->close();
        return;
    }

    clients.append(tcpSocket);

    connect(tcpSocket, SIGNAL(readyRead()), this, SLOT(readMessage()));
    connect(tcpSocket, SIGNAL(error(QAbstractSocket::SocketError)), this, SLOT(displayError(QAbstractSocket::SocketError)));
}

void MainWindow::readMessage()
{
    for (int i = 0; i < clients.size(); i++)
    {
        QByteArray buffer = clients[i]->readAll();
        QString message = QString::fromUtf8(buffer.data(), buffer.size());

        ui->chatEdit->append(message);
    }
}

void MainWindow::displayError(QAbstractSocket::SocketError socketError)
{
    if (socketError == QTcpSocket::RemoteHostClosedError)
        return;

    QTcpSocket *socket = qobject_cast<QTcpSocket*>(sender());
    QMessageBox::critical(this, tr("Error"), tr("Socket error: %1").arg(socket->errorString()));

    clients.removeAll(socket);
    socket->deleteLater();
}

在这个示例中，我们使用了QTcpServer和QTcpSocket来处理连接和通信。当新的连接建立时，我们将客户端的QTcpSocket对象添加到一个QTcpSocket列表中。如果客户端数量超过20个，我们将关闭新连接并不接受它。当客户端发送消息时，我们将消息广播给所有其他客户端。如果有任何错误，我们将从客户端列表中删除QTcpSocket对象。

请注意，这只是一个简单的示例，并且需要进行更多的测试和改进才能用于实际应用程序。