实验（加权图）

下面是.cpp文件及.h文件

/*    本实验是加权图，要求实现的功能是：    1.建立一个无向有权图    2.求图的路径矩阵（即求任意两个点之间的最短路径长度，Floyd算法）    3.测试图是否正确着色（任何邻接点不能涂一样的颜色，所有点扫一遍即可）    4.测试是否每个点的度数都是偶数（如果每个点的度数都是偶数，并且是连通图，    那么，删除任意一条边之后还是连通图）    本程序示例图采用重定向读入，示例图如下粗略给出，相信聪明的读者很容易明白!    A--(1)--B                    |(2)    |(3)    D--(4)--C*/#include"标头.h"int main(){    //freopen("in.txt", "r", stdin);    go();    return 0;}

#pragma once#include<iostream>#include<string>#include<map>#include<algorithm>using namespace std;const int vertex_max = 100;//节点的最大数目const int inf = (int)1e7;//假设的无穷大typedef struct {    char name;//结点的名字    int num;//结点的编号    string color;//结点的颜色}point;typedef struct {    point P[vertex_max];//图的顶点集合    int w[vertex_max][vertex_max];//图的邻接矩阵，边权    int path[vertex_max][vertex_max];//图的路径矩阵    int vertex_num;//顶点个数    int edge_num;//边数    map<char, int>mp;}graph;void graph_create(graph &G);//创建一个图void graph_path_matrix(graph &G);//求图的路径矩阵bool graph_color_right(graph G);//测试图是否正确着色bool graph_all_even(graph G);//测试是否每个点的度数都是偶数void go();//本实验大门控制函数//实验之门开启函数void go() {    graph G;    graph_create(G);    cout << endl << endl;    cout << "针对该图，我们可以得出以下结论!!!!!!!!!!!!!!!!!" << endl;    cout << "该图的邻接矩阵如下：" << endl;    for (int i = 1; i <= G.vertex_num; i++) {        for (int j = 1; j <= G.vertex_num; j++) {            if (G.w[i][j] == inf) cout << "-" << " ";            else cout << G.w[i][j] << " ";        }        cout << endl;    }    cout << endl;    graph_path_matrix(G);    cout << "该图的路径矩阵如下： " << endl;    for (int i = 1; i <= G.vertex_num; i++) {        for (int j = 1; j <= G.vertex_num; j++) {            if (G.path[i][j] >= inf) cout << "-" << " ";            else cout << G.path[i][j] << " ";        }        cout << endl;    }    cout << endl;    bool flag1 = graph_color_right(G);    if (flag1) cout << "该图着色正确" << endl;    else cout << "该图着色错误" << endl;    cout << endl;    bool flag2 = graph_all_even(G);    if (flag2) cout << "该图所有结点的度数是偶数" << endl;    else cout << "该图并非每个结点的度数都是偶数" << endl;    cout << endl;    cout << "Congratulations!" << endl;    cout << "到此，本实验效果已经全部实现，期待对此实验新的改进与探讨" << endl;}//创建一个图void graph_create(graph &G) {    int v_num, e_num;//顶点个数，边数    cout << "请根据如下提示，创建你想要的图！" << endl;    cout << "请输入要创建的图的结点个数： "; cin >> v_num;    cout << "请输入要创建的图的边的条数： "; cin >> e_num;    G.vertex_num = v_num;    G.edge_num = e_num;    //初始化边权矩阵    for (int i = 1; i <= G.vertex_num; i++) {        for (int j = 1; j <= G.vertex_num; j++)            G.path[i][j]=G.w[i][j] = inf;    }    for (int i = 1; i <= G.vertex_num; i++) G.path[i][i]=G.w[i][i] = 0;    cout << "=========顶点信息========="<<endl;    for (int i = 1; i <= v_num; i++) {        G.P[i].num = i;        cout << "------第" << i << "个结点------" << endl;        cout << "结点名称： "; cin >> G.P[i].name; G.mp[G.P[i].name] = i;        cout << "结点颜色： "; cin >> G.P[i].color;    }    cout << "=========边权信息=========" << endl;    char v1, v2;    int weight;    for (int i = 1; i <= e_num; i++) {        cout << "------第" << i << "条边的边权及相连的两结点： " ;        cin >> weight>>v1>>v2;        int x = G.mp[v1], y = G.mp[v2];        G.w[x][y] = G.w[y][x] = weight;        G.path[x][y] = G.path[y][x] = weight;    }    cout << "************************图已经创建完毕************************" << endl;}//求图的路径矩阵(floyd算法)void graph_path_matrix(graph &G) {    fill(G.path[0], G.path[0] + (G.vertex_num+1)*(G.vertex_num+1), inf);    for (int i = 1; i <= G.vertex_num; i++) G.path[i][i] = 0;    for (int k = 1; k <= G.vertex_num; k++)        for (int i = 1; i <= G.vertex_num; i++)            for (int j = 1; j <= G.vertex_num; j++)                if (G.path[i][k] + G.path[k][j] < G.path[i][j])                    G.path[i][j] = G.path[i][k] + G.path[k][j];}//测试图是否正确着色bool graph_color_right(graph G) {    for (int i = 1; i <=G.vertex_num; i++) {        for (int j = i + 1; j <= G.vertex_num; j++) {            if (G.w[i][j] != inf && G.P[i].color == G.P[j].color)                return false;        }    }    return true;}//测试是否每个点的度数都是偶数bool graph_all_even(graph G) {    for (int i = 1; i <= G.vertex_num; i++) {        int cnt = 0;        for (int j = 1; j <= G.vertex_num; j++) {            if (G.w[i][j] != inf && i!=j) cnt++;        }        if (cnt % 2) return false;    }    return true;}