最小路径问题 | Dijkstra算法详解（附代码）

#include"Dijkstra.h"
//构造函数Graph_DG::Graph_DG(int vexnum, int edge) {    //初始化顶点数和边数    this->vexnum = vexnum;    this->edge = edge;    //为邻接矩阵开辟空间和赋初值    arc = new int*[this->vexnum];    dis = new Dis[this->vexnum];    for (int i = 0; i < this->vexnum; i++) {        arc[i] = new int[this->vexnum];        for (int k = 0; k < this->vexnum; k++) {            //邻接矩阵初始化为无穷大                arc[i][k] = INT_MAX;        }    }}//析构函数Graph_DG::~Graph_DG() {    delete[] dis;    for (int i = 0; i < this->vexnum; i++) {        delete this->arc[i];    }    delete arc;}
// 判断我们每次输入的的边的信息是否合法//顶点从1开始编号bool Graph_DG::check_edge_value(int start, int end, int weight) {    if (start<1 || end<1 || start>vexnum || end>vexnum || weight < 0) {        return false;    }    return true;}
void Graph_DG::createGraph() {    cout << "请输入每条边的起点和终点（顶点编号从1开始）以及其权重" << endl;    int start;    int end;    int weight;    int count = 0;    while (count != this->edge) {        cin >> start >> end >> weight;        //首先判断边的信息是否合法        while (!this->check_edge_value(start, end, weight)) {            cout << "输入的边的信息不合法，请重新输入" << endl;            cin >> start >> end >> weight;        }        //对邻接矩阵对应上的点赋值        arc[start - 1][end - 1] = weight;        //无向图添加上这行代码        //arc[end - 1][start - 1] = weight;        ++count;    }}
void Graph_DG::print() {    cout << "图的邻接矩阵为：" << endl;    int count_row = 0; //打印行的标签    int count_col = 0; //打印列的标签    //开始打印    while (count_row != this->vexnum) {        count_col = 0;        while (count_col != this->vexnum) {            if (arc[count_row][count_col] == INT_MAX)                cout << "∞" << " ";            else            cout << arc[count_row][count_col] << " ";            ++count_col;        }        cout << endl;        ++count_row;    }}void Graph_DG::Dijkstra(int begin){    //首先初始化我们的dis数组    int i;    for (i = 0; i < this->vexnum; i++) {        //设置当前的路径        dis[i].path = "v" + to_string(begin) + "-->v" + to_string(i + 1);        dis[i].value = arc[begin - 1][i];    }    //设置起点的到起点的路径为0    dis[begin - 1].value = 0;    dis[begin - 1].visit = true;
    int count = 1;    //计算剩余的顶点的最短路径（剩余this->vexnum-1个顶点）    while (count != this->vexnum) {        //temp用于保存当前dis数组中最小的那个下标        //min记录的当前的最小值        int temp=0;        int min = INT_MAX;        for (i = 0; i < this->vexnum; i++) {            if (!dis[i].visit && dis[i].value                min = dis[i].value;                temp = i;            }        }        //cout << temp + 1 << "  "<        //把temp对应的顶点加入到已经找到的最短路径的集合中        dis[temp].visit = true;        ++count;        for (i = 0; i < this->vexnum; i++) {            //注意这里的条件arc[temp][i]!=INT_MAX必须加，不然会出现溢出，从而造成程序异常            if (!dis[i].visit && arc[temp][i]!=INT_MAX && (dis[temp].value + arc[temp][i]) < dis[i].value) {                //如果新得到的边可以影响其他为访问的顶点，那就就更新它的最短路径和长度                dis[i].value = dis[temp].value + arc[temp][i];                dis[i].path = dis[temp].path + "-->v" + to_string(i + 1);            }        }    }
}void Graph_DG::print_path(int begin) {    string str;    str = "v" + to_string(begin);    cout << "以"<"为起点的图的最短路径为：" << endl;    for (int i = 0; i != this->vexnum; i++) {        if(dis[i].value!=INT_MAX)        cout << dis[i].path << "=" << dis[i].value << endl;        else {            cout << dis[i].path << "是无最短路径的" << endl;        }    }}

#include"Dijkstra.h"
//检验输入边数和顶点数的值是否有效，可以自己推算为啥：//顶点数和边数的关系是：((Vexnum*(Vexnum - 1)) / 2) < edgebool check(int Vexnum, int edge) {    if (Vexnum <= 0 || edge <= 0 || ((Vexnum*(Vexnum - 1)) / 2) < edge)        return false;    return true;}int main() {    int vexnum; int edge;
    cout << "输入图的顶点个数和边的条数：" << endl;    cin >> vexnum >> edge;    while (!check(vexnum, edge)) {        cout << "输入的数值不合法，请重新输入" << endl;        cin >> vexnum >> edge;    }    Graph_DG graph(vexnum, edge);    graph.createGraph();    graph.print();    graph.Dijkstra(1);    graph.print_path(1);    system("pause");    return 0;}