Test

图/main.cpp

+// graphics_judge.cpp : 此文件包含 "main" 函数。程序执行将在此处开始并结束。
+//
+
+#include <iostream>
+#include <stdio.h>
+#include <string.h>
+using namespace std;
+#define MAX 100
+
+//邻接矩阵的变量
+int vernum; //节点个数
+int graphic[MAX][MAX];
+int rech_matrix[MAX][MAX]; //可达矩阵
+
+/*初始化矩阵*/
+void init_graphic();
+/*输出有序顶点对，以及每个顶点的入度和出度*/
+void display_degree();
+/*矩阵乘法*/
+void matrix_multi(int A[][MAX], int B[][MAX]);
+/*求可达矩阵*/
+void rechable_matrix();
+/*判断强连通或则若连通：通过可达矩阵判断,强连通返回0，单向连通返回1，否则返回-1*/
+int judge_connected_graph();
+/*判断是否是弱连通*/
+void judge_connected_weakgraph();
+
+int main()
+{
+    init_graphic();
+    display_degree();
+    rechable_matrix();
+    int flag = judge_connected_graph();
+    if (flag == 0)
+    {
+        cout << "输入的图是强连通图" << endl;
+    }
+    else
+    {
+        if (flag == 1)
+            cout << "输入的图是单向连通图" << endl;
+        judge_connected_weakgraph();
+    }
+    return 0;
+}
+
+/*初始化矩阵*/
+void init_graphic()
+{
+    cout << "请输入图的节点个数：";
+    cin >> vernum;
+    cout << "请输入一个为" << vernum << "的0,1方正：" << endl;
+    for (int i = 0; i < vernum; i++)
+    {
+        for (int j = 0; j < vernum; j++)
+        {
+            cin >> graphic[i][j];
+            if (i == j)
+                graphic[i][j] = 1;
+        }
+    }
+}
+
+/*输出有序顶点对，以及每个顶点的入度和出度*/
+void display_degree()
+{
+    cout << "输出有序顶点对:" << endl;
+    for (int i = 0; i < vernum; i++)
+    {
+        for (int j = 0; j < vernum; j++)
+        {
+            if (graphic[i][j] != 0)
+            {
+                cout << "<" << i << "," << j << ">"
+                     << "\t";
+            }
+        }
+    }
+    cout << "\n每个顶点的入度和出度如下：" << endl;
+    for (int i = 0; i < vernum; i++)
+    {
+        cout << "第" << i << "个顶点的入度和出度:";
+        int intoDegree = 0; //入度
+        int outDegree = 0;  //出度
+        for (int j = 0; j < vernum; j++)
+        {
+            if (graphic[j][i] != 0 && i != j)
+                intoDegree++;
+            if (graphic[i][j] != 0 && i != j)
+                outDegree++;
+        }
+        cout << intoDegree << "\t" << outDegree << endl;
+    }
+}
+
+/*矩阵乘法*/
+void matrix_multi(int A[][MAX], int B[][MAX])
+{
+    //乘法的最后结果保存再A矩阵中
+    int result[MAX][MAX];
+    memset(result, 0, sizeof(result));
+    for (int i = 0; i < vernum; i++)
+    {
+        for (int j = 0; j < vernum; j++)
+        {
+            for (int v = 0; v < vernum; v++)
+            {
+                result[i][j] += A[i][v] * B[v][j];
+            }
+        }
+    }
+    //拷贝到A中
+    for (int i = 0; i < vernum; i++)
+    {
+        for (int j = 0; j < vernum; j++)
+        {
+            A[i][j] = result[i][j];
+        }
+    }
+}
+
+/*求可达矩阵*/
+void rechable_matrix()
+{
+    int tmp_matrix[MAX][MAX];        //可到达矩阵的每一项比如A^i
+    for (int i = 0; i < vernum; i++) //主对角线设置为1
+        graphic[i][i] = 1;
+    for (int i = 0; i < vernum; i++)
+    {
+        for (int j = 0; j < vernum; j++)
+        {
+            tmp_matrix[i][j] = graphic[i][j];
+            rech_matrix[i][j] = graphic[i][j];
+        }
+    }
+    for (int i = 1; i < vernum; i++)
+    {
+        for (int j = 0; j < i; j++)
+        {
+            matrix_multi(tmp_matrix, graphic);
+        }
+        //相加
+        for (int m = 0; m < vernum; m++)
+        {
+            for (int n = 0; n < vernum; n++)
+            {
+                rech_matrix[m][n] = rech_matrix[m][n] + tmp_matrix[m][n];
+            }
+        }
+    }
+    cout << "可达矩阵为：" << endl;
+    for (int i = 0; i < vernum; i++)
+    {
+        for (int j = 0; j < vernum; j++)
+        {
+            if (rech_matrix[i][j] != 0)
+                cout << "1"
+                     << "\t";
+            else
+                cout << "0"
+                     << "\t";
+        }
+        cout << endl;
+    }
+}
+
+int judge_connected_graph()
+{
+    int flag_connected = 0; //强连通为0，单向连通为1，否则为-1
+    /*判断强连通和单向连通*/
+    for (int i = 0; i < vernum; i++)
+    {
+        for (int j = 0; j < vernum; j++)
+        {
+            if (rech_matrix[i][j] == 0)
+                flag_connected = 1;
+        }
+    }
+    if (flag_connected == 0)
+        return 0;
+
+    for (int i = 0; i < vernum; i++)
+    {
+        for (int j = 0; j < vernum; j++)
+        {
+            if (rech_matrix[i][j] == 0 && rech_matrix[j][i] == 0)
+                return -1;
+        }
+    }
+    return 1;
+}
+
+/*判断是否是弱连通*/
+void judge_connected_weakgraph()
+{
+    for (int i = 0; i < vernum; i++)
+    {
+        for (int j = 0; j < vernum; j++)
+        {
+            if (graphic[i][j] != 0)
+            {
+                graphic[j][i] = graphic[i][j];
+            }
+        }
+    }
+    cout << "转化成无向图后的可达矩阵为：" << endl;
+    rechable_matrix();
+    if (judge_connected_graph() == 0)
+        cout << "可以发现原图是个弱连通图" << endl;
+    else
+        cout << "可以发现原图不是一个弱连通图" << endl;
+}
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