大话数据结构之图-邻接矩阵最小生成树Kruskal算法（C++）

大话数据结构

Unit6 图

邻接矩阵的最小生成树Kruskal算法

代码

#include 
typedef char VertexType;
typedef int EdgeType;
#define MAXVEX 100
#define MAXEDGE 10
#define INFINITY 65535
using namespace std;
int visited[100];


//构建顶点表
typedef struct {
	VertexType vexs[MAXVEX];        //顶点数组
	EdgeType arc[MAXVEX][MAXVEX];   //边的矩阵表示
	int numVertexes, numEdges;      //图中当前的顶点数和边数
}MGraph;


//创建邻接矩阵
MGraph* CreatMgraph(MGraph* G) {
	int i, j, k, w;
	cout << "输入顶点数和边数:" << endl;
	cin >> G->numVertexes >> G->numEdges;


	for (i = 0;i < G->numVertexes;i++) {
		cout << "请输入顶点名:" << endl;
		cin >> G->vexs[i];
	}
	//初始化邻接矩阵
	for (i = 0;i < G->numVertexes;i++) {
		for (j = 0;j < G->numVertexes;j++) {
			G->arc[i][j] = INFINITY;
		}
	}
	//构建邻接矩阵
	for (k = 0;k < G->numEdges;k++) {
		cout << "输入边（vi,vj）上的下标i,下标j和权w:" << endl;
		cin >> i >> j >> w;
		G->arc[i][j] = w;
		G->arc[j][i] = G->arc[i][j];
	}
	return G;
}



//对边集数组结构的定义
typedef struct
{
	int begin;
	int end;
	int weight;
}Edge;

void swap(Edge e[],int  i,int j ) {
	Edge temp;
	temp.begin = e[i].begin;
	temp.end = e[i].end;
	temp.weight = e[i].weight;
	e[i].begin = e[j].begin;
	e[i].end = e[j].end;
	e[i].weight = e[j].weight;
	e[j].begin = temp.begin;
	e[j].end = temp.end;
	e[j].weight = temp.weight;
}


void printf_edge(Edge* E) {
	for (int i = 0;i < 5;i++) {
		cout << E[i].begin << " " << E[i].end << " " << E[i].weight << endl;
	}

}


int Find(int* parent, int f) {//查找连线顶点的尾部下标
	while (parent[f] > 0) {
		f = parent[f];
		return f;
	}
}


Edge* sort(MGraph G) {
	static Edge edges[5];
	int i, j,k = 0;
	for (int i = 0;i < G.numVertexes;i++) {
		for (int j = i;j < G.numVertexes;j++) {
			if (G.arc[i][j] != 0 && G.arc[i][j] != 65535) {
				edges[k].begin = i;
				edges[k].end = j;
				edges[k].weight = G.arc[i][j];
				++k;
				//cout << edges[i].begin << " " + edges[i].end << " " + edges[i].weight << endl;
			}
		}
	}
	//排序
	for (i = 0;i < G.numVertexes;i++) {
		for (j = i+1;j< G.numVertexes;j++) {
			if (edges[j].weight < edges[i].weight)
			{
				swap(edges, i, j);

			}
		}
		
	}
	//printf_edge(edges);
	return edges;
}





//Kruskal算法生成最小生成树
void MiniDpanTree_Kruskal(MGraph G) {
	int i, n, m;
	//Edge edges[MAXEDGE];//定义边集数组
	int parent[MAXVEX];//定义一组数来判断边与边是否形成回路
	//此处省略将邻接矩阵G转化为边集数组edges并按权重由小到大排序的代码
	Edge *edges = sort(G);
	cout << "边集数组为" << endl;
	printf_edge(edges);
	for (i = 0;i < G.numVertexes;i++) {
		parent[i] = 0;//初始化数组值为0

	}

	//循环每一条边
	cout << "最小生成树为" << endl;
	for (i = 0;i < G.numEdges;i++) {
		n = Find(parent, edges[i].begin);
		m = Find(parent, edges[i].end);
		if (n != m) {//若m!=n说明未形成回路
			parent[n] = m;//将此边的结尾点放入下标为顶点的parent中，表示此顶点已经在生成树中
			
			cout << edges[i].begin<<" "<";

		}
	}
}





int main() {
	MGraph* grap = (MGraph*)malloc(sizeof(MGraph));
	MGraph* G = CreatMgraph(grap);
	//sort(*G);
	MiniDpanTree_Kruskal(*grap);
	//printf_edge(edges);
	free(grap);
	grap = NULL;
	return 0;
}

运行结果