实验要求

变量定义

因为如果我们使用局部变量，每一个函数都会使用这些变量，会让函数的参数越变越多。所以我们定义全局变量，这样就不用在参数中调用了。

#define MAX  100
int arrMap[MAX][MAX] = { 0 };//图的矩阵
int degree[MAX] = { 0 };//节点的度
int visit[MAX] = { 0 };//记录是否被访问
int euler[MAX] = { -1 };
int ans[MAX];     //欧拉路
int c[MAX][MAX];    //判断该边是否已经走过
int m = 0;//结点个数
int n = 0;//边数

根据边来生成图函数

//随机生成边
void creatSide()
{int count = 0;while (count < n){int x = rand() % m;int y = rand() % m;while (x == y)x = rand() % m;if (!arrMap[x][y]){arrMap[x][y] = arrMap[y][x] = 1;count++;degree[x]++;degree[y]++;}}for (int i = 0; i < m; i++){for (int j = 0; j < m; j++){printf("%d ", arrMap[i][j]);}printf("\n");}
}

判断联通函数

DFS通过递归的方式，从给定的起始顶点开始，沿着一条路径一直走到底，然后回退到上一个节点，再选择另一条路径继续走下去。当所有路径都被探索完毕时，如果所有的节点都被访问到，则图是连通的

//深度优先搜索判断是否为连通图
void DFS(int x)
{visit[x] = 1;for (int i = 0; i < m; i++){if (!visit[i] && arrMap[x][i]){DFS(i);}}
}
//判断联通是返回1不是返回0
int judgeConnect()
{DFS(0);for (int i = 0; i < m; i++){if (!visit[i]){return 0;}}return 1;
}

判断是否有欧拉路

有0个或2个奇数度结点的有欧拉路。

//判断是否是（半）欧拉图
void judgeEuler()
{int first = 0;int num = 0;//奇数结点个数for (int i = 0; i < m; i++){if (degree[i] % 2 != 0){first = i;num++;}}if (num == 1 || num > 2){printf("不是欧拉图或半欧拉图\n");}else{euler[0]= first;trav(first, 1);if (num == 0){printf("随机生成的图是欧拉图\n");printf("该欧拉图的一条欧拉路是\n");}else{printf("随机生成的图是半欧拉图\n");printf("该半欧拉图的一条欧拉路是\n");}for (int i = 0; i < n; i++){printf("%d->", ans[i]);}printf("%d\n", ans[n]);}
}

生成欧拉路

如果图满足所有顶点的度数都是偶数，可以从任意顶点开始，任意顺序遍历边，直到回到起始顶点，这样就能生成一条欧拉路。
如果图中仅有两个顶点的度数为奇数，首先找到这两个奇数度顶点，然后从其中一个奇数度顶点开始，遍历所有边直到另一个奇数度顶点，这样也能生成一条欧拉路。

//找欧拉路
void trav(int p, int q)
{int flag = 1;if (euler[n] != -1){if(flag == 1){for (int i = 0; i <= n; i++){ans[i] = euler[i];}flag = 0;}}for (int i = 0; i < m; i++){if (arrMap[p][i] && !c[p][i]){euler[q] = i;c[p][i] = c[i][p] = 1;trav(i, q + 1);if (!flag)return;else c[p][i] = c[i][p] = 0;}}
}

源码

# define _CRT_SECURE_NO_WARNINGS 1；
#include<stdio.h>
#include<time.h>
#include<stdlib.h>
#define MAX  100
int arrMap[MAX][MAX] = { 0 };//图的矩阵
int degree[MAX] = { 0 };//节点的度
int visit[MAX] = { 0 };//记录是否被访问
int euler[MAX] = { -1 };
int ans[MAX];     //欧拉路
int c[MAX][MAX];    //判断该边是否已经走过
int m = 0;//结点个数
int n = 0;//边数
//随机生成边
void creatSide()
{int count = 0;while (count < n){int x = rand() % m;int y = rand() % m;while (x == y)x = rand() % m;if (!arrMap[x][y]){arrMap[x][y] = arrMap[y][x] = 1;count++;degree[x]++;degree[y]++;}}for (int i = 0; i < m; i++){for (int j = 0; j < m; j++){printf("%d ", arrMap[i][j]);}printf("\n");}
}
//深度优先搜索判断是否为连通图
void DFS(int x)
{visit[x] = 1;for (int i = 0; i < m; i++){if (!visit[i] && arrMap[x][i]){DFS(i);}}
}
//判断联通是返回1不是返回0
int judgeConnect()
{DFS(0);for (int i = 0; i < m; i++){if (!visit[i]){return 0;}}return 1;
}
//找欧拉路
void trav(int p, int q)
{int flag = 1;if (euler[n] != -1){if(flag == 1){for (int i = 0; i <= n; i++){ans[i] = euler[i];}flag = 0;}}for (int i = 0; i < m; i++){if (arrMap[p][i] && !c[p][i]){euler[q] = i;c[p][i] = c[i][p] = 1;trav(i, q + 1);if (!flag)return;else c[p][i] = c[i][p] = 0;}}
}
//判断是否是（半）欧拉图
void judgeEuler()
{int first = 0;int num = 0;//奇数结点个数for (int i = 0; i < m; i++){if (degree[i] % 2 != 0){first = i;num++;}}if (num == 1 || num > 2){printf("不是欧拉图或半欧拉图\n");}else{euler[0]= first;trav(first, 1);if (num == 0){printf("随机生成的图是欧拉图\n");printf("该欧拉图的一条欧拉路是\n");}else{printf("随机生成的图是半欧拉图\n");printf("该半欧拉图的一条欧拉路是\n");}for (int i = 0; i < n; i++){printf("%d->", ans[i]);}printf("%d\n", ans[n]);}
}int main()
{srand((unsigned int)time(NULL));printf("请输入结点个数：");scanf("%d", &m);printf("请输入边数，需小于等于%d：", m * (m - 1) / 2);scanf("%d", &n);back:creatSide();int ret = judgeConnect();if (ret == 0){printf("该图不是连通图,结点度为\n");for (int i = 0; i < m; i++){printf("%d ", degree[i]);}printf("\n");goto back;}else {judgeEuler();}return 0;
}