(数据结构)图的应用,一个简单的学校地图.包含的内容:图的最短路径算法 和 图的深度优先遍历算法

数据结构,图的应用实例,一个简单的学校地图.

其中包含的内容:图的最短路径算法(迪杰斯特拉算法) 和 图的深度优先遍历算法

其中程序功能: 1.存储简单的学校地图并显示; 2.给出一个点,能够输出从此点到其他顶点的最短路径及最短距离; 3.给出两个顶点,能够输出次两点之间所有路径及距离 和 最短路径及距离

学校地图:(建立图的基础,看着这个图会容易理解一点)

程序运行结果截图:

废话不说,直接上程序源码. 自己需要的地方可以看一下源码,找一下自己需要的地方

我写的代码是用C++干着面向过程的勾当...真心觉得自己能力不咋滴...贴出代码, 大家有需要的函数可以参考一下原理.

程序源码:

main.cpp#include "GraphList.h"int main(){    GraphList graphList;//图    int choice;//存放用户的选择    char element_1, element_2;    int locate_1, locate_2;    int Path[MAX_VERTEX_NUM], Dest[MAX_VERTEX_NUM];    bool DIJFlag = false;//标记是否进行过了DIJ算法    createGraph(graphList);    cout << "A.学校正门, B.研究院, C.校训石, D.体育场, E.M楼, F.G楼, G.主楼, H.C楼, I.教师公寓, J.食堂, K.N楼\n"         << "\n--The output formate: (Source,Destination,Value)"         << "\n------------------------------------------------------------------------"         << "\n--The Graph have been created:";    printGraph(graphList);    cout << "\n------------------------------------------------------------------------"         << "\n--Program Menu:"         << "\n--1.shortest path between source to other vertex(Dijkstra Algorithm)."         << "\n--2.all path and shortest path between two vertexs(Floyd Algorithm)."         << "\n--0.exit."         << "\n\n-------------------------------------------"         << "\n--Please enter your choice(0/1/2): ";    cin >> choice;    while(choice != 0)    {        switch(choice)        {        case 1:            cout << "\n--Please enter one vertex: ";            cin >> element_1;            if((locate_1=findNode(graphList, element_1)) == -1) return 0;            if(!DIJFlag)//如果没有进行了DIJ算法查找最短路径            {                shortestPath_DIJ(graphList, locate_1, Path, Dest);                DIJFlag = true;            }            printShortestPath_DIJ(graphList, locate_1, Path, Dest);            break;        case 2:            cout << "\n--Please enter two vertexs(e.g.: A B): ";            cin >> element_1 >> element_2;            locate_1 = findNode(graphList, element_1);            locate_2 = findNode(graphList, element_2);            if((locate_1==-1) || (locate_2==-1)) return 0;            if(!DIJFlag)//如果没有进行了DIJ算法查找最短路径            {                shortestPath_DIJ(graphList, locate_1, Path, Dest);                DIJFlag = true;            }            cout << "All Path  Between " << element_1 << " and " << element_2 << ":";            allPath_2Vexs(graphList, locate_1, locate_2);//输出所有路径            cout << "\n--------------------------------------";            printShortestPath_2Vexs(graphList, locate_1, locate_2, Path, Dest);            break;        default:            cout << "--Your input unavailable!\n";            return 0;        }        cout << "\n\n-------------------------------------------"             << "\n--Please enter your choice(0/1/2): ";        cin >> choice;    }    deleteGraph(graphList);//删除图,防止内存泄露    return 0;}

GraphList.h#ifndef GRAPHLIST_H_INCLUDED#define GRAPHLIST_H_INCLUDED#include <iostream>#include <string>#include <cstdlib>#include <stack>#include <vector>using namespace std;#define MAX_VERTEX_NUM 11//最大支持的节点数#define INFINITY 1000//表示无穷大typedef int EdgeValueType;//定义边权重类型typedef char VertexType;//定义顶点表顶点的内容类型typedef struct EdgeNode//边表节点{    int adjvexLocate;//该弧所指向的顶点在定点表中的位置    EdgeValueType value;//权重    EdgeNode *next;//指向下一个节点} EdgeNode;typedef struct VertexNode//顶点表{    VertexType data;//顶点名称    EdgeNode *firstarc;//指向第一条依附顶点的指针} VertexNode, VertexList[MAX_VERTEX_NUM]; //顶点节点,顶点表typedef struct GraphList{    VertexList vertexList;//建立顶点表    int vertexNum, edgeNum;//整个图中存放顶点、边的个数} GraphList;//函数声明int findNode(GraphList &graphList, char element);bool createGraph(GraphList &graphList);bool printGraph(GraphList &graphList);void shortestPath_DIJ(GraphList &graphList, int vex, int P[], int D[]);//单源最短路径算法void printShortestPath_DIJ(GraphList &graphList, int vex, int Path[], int Dest[]);//打印出生成的单源最短路径void printShortestPath_2Vexs(GraphList &graphList, int vex1, int vex2, int Path[], int Dest[]);//打印两点之间最短路径及距离void allPath_2Vexs(GraphList &graphList, int startVex, int endVex);//任意两点之间的所有路径void visit(GraphList &graphList, int vex, int endVex, bool status[], vector<int> &pathStack, int length);bool deleteGraph(GraphList &graphList);//销毁图,防止内存泄露#endif // GRAPHLIST_H_INCLUDED

GraphList.cpp#include "GraphList.h"int findNode(GraphList &graphList, char element)//查找顶点,工具方法{    int i;    for(i=0; i<graphList.vertexNum; i++)    {        if(element == graphList.vertexList[i].data)        {            break;        }    }    if(i >= graphList.vertexNum)    {        cout << "The element not find\n";        return -1;    }    return i;}bool createGraph(GraphList &graphList)//创建图,并执行初始化{    //为了方便,所有顶点以及边都已经在程序内部定义好了    //初始化定点表    graphList.vertexNum = 0;//顶点数    graphList.edgeNum = 0;//边数    int value = 0;//暂时存放从邻接矩阵中读取的数值    char vexArray[MAX_VERTEX_NUM] = {'A','B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K'};    for(int v=0; v<MAX_VERTEX_NUM; v++)//建立顶点表    {        if(vexArray[v] != '\0') graphList.vertexNum++;        graphList.vertexList[v].data = vexArray[v];        graphList.vertexList[v].firstarc = NULL;    }    //初始化边表    int edgeArray[MAX_VERTEX_NUM][MAX_VERTEX_NUM] = {//初始化邻接矩阵    //   0,1,2,3,4,5,6,7,8,9,10        {0,70,40,100,0,0,0,0,0,0,0},//0        {70,0,50,0,0,0,0,60,0,0,0},//1        {40,0,0,0,0,100,50,0,0,0,0},//2        {100,0,0,0,70,65,0,0,0,0,0},//3        {0,0,0,70,0,40,0,0,0,0,130},//4        {0,0,100,65,40,0,40,0,0,150,140},//5        {0,0,50,0,0,40,0,115,0,0,0},//6        {0,60,0,0,0,0,115,0,105,0,0},//7        {0,0,0,0,0,0,0,105,0,110,0},//8        {0,0,0,0,0,150,0,0,110,0,55},//9        {0,0,0,0,130,140,0,0,0,55,0}//10    };    for(int i=0; i<graphList.vertexNum; i++)    {        EdgeNode *temp = NULL;        EdgeNode *Node = NULL;//存放新生成的节点        for(int j=0; j<graphList.vertexNum; j++)        {            if((value = edgeArray[i][j]) != 0)//有边            {                if(!(Node = new EdgeNode))                {                    cerr << "No Enough Memory!";                    exit(1);                }                Node->adjvexLocate = j;                Node->value = value;                Node->next = NULL;//生成节点                graphList.edgeNum++;                if(graphList.vertexList[i].firstarc == NULL)//第一个节点                {                    graphList.vertexList[i].firstarc = Node;                    temp = Node;                }                else                {                    temp->next = Node;                    temp = Node;                }            }        }    }    return true;}bool printGraph(GraphList &graphList)//输出图{    EdgeNode *temp = NULL;    //if(!&graphList) return false;    for(int i=0; i<graphList.vertexNum; i++)    {        cout << "\n" << graphList.vertexList[i].data << ": ";        temp = graphList.vertexList[i].firstarc;        while(temp)        {            cout << " (" << graphList.vertexList[i].data << "," << graphList.vertexList[temp->adjvexLocate].data << ","                 << temp->value << ") ";            temp = temp->next;        }    }    return true;}void shortestPath_DIJ(GraphList &graphList, int vex, int Path[], int Dest[])///单源最短路径算法{    bool finalShortest[MAX_VERTEX_NUM];    EdgeNode *temp = NULL;    int minValue = INFINITY;//用作寻找最小的路径权值    int v = 0;//记录每一次寻找的最小路径终点的位置    for(int i=0; i<graphList.vertexNum; i++)//第一步初始化    {        finalShortest[i] = false;        Path[i] = -1;//没有前驱,即没有路径        Dest[i] = INFINITY;//存放vi与给出的源点之间的最短路径    }    finalShortest[vex] = true;    Dest[vex] = 0;//修改源点的值    Path[vex] = -1;    temp = graphList.vertexList[vex].firstarc;    while(temp)    {        Dest[temp->adjvexLocate] = temp->value;        Path[temp->adjvexLocate] = vex;//前驱        temp = temp->next;    }//初始化完成    for(int i=1; i<graphList.vertexNum; i++)//执行n-1次循环,对剩余的n-1个顶点操作    {        minValue = INFINITY;        for(int j=0; j<graphList.vertexNum; j++)        {            if(!finalShortest[j])//还没有求出最短路径            {                if(Dest[j] < minValue)                {                    v = j;                    minValue = Dest[j];                }//if(Dest[j] < minValue)            }//if(!finalShortest[j])        }//for        finalShortest[v] = true;//将此终点加入已求出最短路径的集合        //更新参数        //temp = graphList.vertexList[v].firstarc;        for(int j=0; j<graphList.vertexNum; j++)        {            int vValue = INFINITY;//存放v 与 j之间的权重            temp = graphList.vertexList[v].firstarc;//一句话如果放错位置就会出现无法预料的错误!            while(temp)            {                if(temp->adjvexLocate == j)                {                    vValue = temp->value;                    break;                }                temp = temp->next;            }            if(!finalShortest[j] && (minValue+vValue<Dest[j]))            {                Dest[j] = minValue + vValue;//更新为更小的权重                Path[j] = v;//更新前驱节点            }//if(!finalShortest[j] && minValue+vValue<Dest[j])        }//for(int j=0; j<graphList.vertexNum; j++)    }//for(int i=1; i<graphList.vertexNum; i++)}void printShortestPath_DIJ(GraphList &graphList, int vex, int Path[], int Dest[]){    int pre = 0;    cout << "The Shortest Path From "<< graphList.vertexList[vex].data << " to Other Vertexs:";    for(int i=0; i<graphList.vertexNum; i++)    {        if(Dest[i] >= INFINITY || i == vex) continue;        cout << "\n\t(" << graphList.vertexList[vex].data << "->" << graphList.vertexList[i].data             << "):  Length = " << Dest[i] << ";  Path: " << graphList.vertexList[i].data;        pre = Path[i];        while(pre != -1)        {            cout << " " << graphList.vertexList[pre].data;            pre = Path[pre];        }    }}//打印两点之间最短路径及距离void printShortestPath_2Vexs(GraphList &graphList, int vex1, int vex2, int Path[], int Dest[]){    int pre = 0;    cout << "\nThe Shortest Path Between " << graphList.vertexList[vex1].data << " to "         << graphList.vertexList[vex2].data << " :";    for(int i=0; i<graphList.vertexNum; i++)    {        if(i == vex2)        {            cout << "\n\t(" << graphList.vertexList[vex1].data << "->" << graphList.vertexList[vex2].data                 << "):  Length = " << Dest[i] << "\tPath: " << graphList.vertexList[i].data;            pre = Path[i];            while(pre != -1)            {                cout << " " << graphList.vertexList[pre].data;                pre = Path[pre];            }            return;        }    }}bool deleteGraph(GraphList &graphList)//销毁图{    if(graphList.vertexNum == 0) return false;    EdgeNode *temp = NULL;    for(int i=0; i<graphList.vertexNum; i++)//定点表中每个顶点    {        if((temp = graphList.vertexList[i].firstarc) == NULL) continue;        while(temp)        {            graphList.vertexList[i].firstarc = temp->next;            delete temp;            temp = graphList.vertexList[i].firstarc;        }    }    return true;}void allPath_2Vexs(GraphList &graphList, int startVex, int endVex){    if(startVex == endVex)    {        return;    }    bool status[MAX_VERTEX_NUM] = {false};//标记点被访问的状态    vector<int> pathStack;//记录访问到节点的位置    int length = 0;    visit(graphList, startVex, endVex, status, pathStack, length);}//递归访问每个元素void visit(GraphList &graphList, int vex, int endVex, bool status[], vector<int> &pathStack, int length)//对vex点进行访问{    if(vex == endVex)//找到了终点    {        //cout << "\n\tLength=" << pathStack.size()+1 << "\tPath: ";        cout << "\n\tLength=" << length << "\tPath: ";        for(unsigned int i=0; i<pathStack.size(); i++)        {            cout << " " << graphList.vertexList[pathStack[i]].data;            //length += graphList.vertexL        }        cout << " " << graphList.vertexList[endVex].data;        return;    }    status[vex] = true;    pathStack.push_back(vex);    EdgeNode *current = NULL;    for(current=graphList.vertexList[vex].firstarc; current!=NULL; current = current->next)    {        if(!status[current->adjvexLocate])        {            length += current->value;            visit(graphList, current->adjvexLocate, endVex, status, pathStack, length);        }    }    status[vex] = false;//修改标志    pathStack.pop_back();//回溯}