Dijkstra算法的原理及GUI实现【QT源码】

背景及原理讲解链接: https://blog.youkuaiyun.com/qq_44394952/article/details/122260279.
Warshall.pro

QT       += core gui

greaterThan(QT_MAJOR_VERSION, 4): QT += widgets

TARGET = Warshall
TEMPLATE = app

DEFINES += QT_DEPRECATED_WARNINGS

SOURCES += main.cpp\
        mainwindow.cpp

HEADERS  += mainwindow.h

FORMS    += mainwindow.ui

RESOURCES += \
    image.qrc

mainwindow.h

#ifndef MAINWINDOW_H
#define MAINWINDOW_H
#define Inf 100;
#include <QMainWindow>

namespace Ui {
class MainWindow;
}

class MainWindow : public QMainWindow
{
    Q_OBJECT

public:
    explicit MainWindow(QWidget *parent = 0);
    ~MainWindow();
    int dis[7][7];
    void dijkstar(int *c,int m,int a,int b);  //dijkstra核心算法
private:
    Ui::MainWindow *ui;
public slots:
    void show_dijkstra(int i,int j);  //dijkstr槽函数，在槽函数中调用核心算法
signals:
    void get_number(int i,int j);  //定义信号，传递起始结点和目的结点
private slots:
    void on_pushButton_clicked();
};

#endif // MAINWINDOW_H

main.cpp

#include "mainwindow.h"
#include <QApplication>

int main(int argc, char *argv[])
{
    QApplication a(argc, argv);
    MainWindow w;
    w.show();

    return a.exec();
}

mainwindow.cpp

#include "mainwindow.h"
#include "ui_mainwindow.h"
#include "qdebug.h"

#define Inf 100  //Inf表示两结点之间没有连通的路径

MainWindow::MainWindow(QWidget *parent) :
    QMainWindow(parent),
    ui(new Ui::MainWindow)
{
    ui->setupUi(this);
    ui->lineEdit_2->setValidator(new QIntValidator(0,6,this));  //限制目的结点的输入范围为0~6
    ui->lineEdit_4->setValidator(new QIntValidator(0,6,this));  //限制起始结点的输入范围为0~6
    int c[7][7]=    //设置结点间路径长度数组，由于数组不能在类声明的时候初始化，所以用c[][]来初始化dis数组
    {
        {0,1,2,3,Inf,Inf,Inf},
        {1,0,Inf,Inf,Inf,6,Inf},
        {2,Inf,0,Inf,5,4,Inf},
        {3,Inf,Inf,0,4,Inf,Inf},
        {Inf,Inf,5,4,0,Inf,7},
        {Inf,6,4,Inf,Inf,0,8},
        {Inf,Inf,Inf,Inf,7,8,0},
    };
    for(int i=0;i<7;i++)
        for(int j=0;j<7;j++)
            dis[i][j]=c[i][j];  //用c[][]来初始化dis数组
    connect(this,SIGNAL(get_number(int,int)),this,SLOT(show_dijkstra(int,int)));
}

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

void MainWindow::dijkstar(int *c, int m, int a, int b)
{
    int size = m;
        int min = 0;
        int u;
        int next = a;
        int *dis = (int*)malloc(sizeof(int)*size);  //为dis数组申请int*size大小的空间
        int *book = (int*)malloc(sizeof(int)*size);  //为book数组申请int*size大小的空间
        int *road = (int*)malloc(sizeof(int)*size);  //为road数组申请int*size大小的空间
        //road数组初始化
        for (int i = 0; i < size - 1; i++)
            road[i] = 100;

        //dis数组初始化
        for (int i = 0; i <= size-1; i++)  //保存a点到每个点的距离，0~6，共7个点
        {
            dis[i] = *(c + a*m + i);
        }

        //book数组初始化
        for (int i = 0; i <= size - 1; i++)
        {
            book[i] = 0;
        }
        book[a] = 1;

        //dijkstra算法
        for (int i = 0; i <= size - 2; i++)
        {
            min = Inf;

            for (int j = 0; j <= size - 1; j++)
            {
                if (book[j] == 0 && dis[j] < min)
                {
                    min = dis[j];
                    u = j;
                }
            }
            book[u] = 1;
            for (int v = 0; v <= size - 1; v++)
            {
                if (*(c + u*m + v) < Inf)
                {
                    if (dis[v] > dis[u] + *(c + u*m + v))
                    {
                        dis[v] = dis[u] + *(c + u*m + v);
                        road[v] = u;
                    }
                }
            }
        }


        //输出结果
        int outroad = b;

        //GUI中显示路径
        QString show=QString::number(b,10);
        ui->label_8->setText(show);
        while (6 >= road[outroad] && road[outroad] >= 0)
        {
            show=QString::number(road[outroad],8)+"-->"+show;
            ui->label_8->setText(show);
            outroad = road[outroad];
        }
        show=QString::number(a,8)+"-->"+show;
        ui->label_8->setText(show);
        ui->label_9->setText(QString::number(dis[b],10));

        //回收空间
        free(dis);
        free(book);
        free(road);
}



void MainWindow::show_dijkstra(int i, int j)
{
    dijkstar((int *)dis,7,i,j);
}


void MainWindow::on_pushButton_clicked()
{
    emit get_number(ui->lineEdit_4->text().toInt(),ui->lineEdit_2->text().toInt()); //字符串Qstring转化为数int
}