實現Prim算法

#include<stdio.h>

#include<stdlib.h>

#define Max 10

typedef char elementType;

//定義圖頂點相關的內容

typedef struct Graph_g {

elementType peek[Max];

int number_vertex;//定義頂點個數

int nubmer_edge;//定義邊的個數

int G[Max][Max];//定義臨接矩陣

bool c[Max];

}Graph, *Graph_matrax;

//對圖進行初始化

Graph_matrax init() {

Graph_matrax  graph = (Graph_matrax)malloc(sizeof(Graph));

int vertex;

printf("請輸入頂點的個數\n");

scanf("%d", &vertex);

graph->number_vertex = vertex;

graph->nubmer_edge = 0;

int i;

//對頂點的信息進行賦值

for (i = 0; i < vertex; i++)
{
	getchar();
	
	char c;
	
	printf("請輸入%d個頂點的信息：", i + 1);
	
	scanf("%c", &c);
	
	graph->peek[i] = c;
	
}


//臨接矩陣的對腳線賦值爲0,其餘的初始化爲最大值，假設全都不連通

for (int i = 0; i < graph->number_vertex; i++) {

	for (int j = 0; j < graph->number_vertex; j++)
	
	{
		if (i == j)
		
			graph->G[i][j] = 0;
			
		else
			graph->G[i][j] = 8888;
	}
}

int edge = 0;

int v1, v2, w;

printf("請輸入邊的數目:");

scanf("%d", &edge);

for (i = 0; i < edge; i++) {

	printf("請輸入i,j,w，有關頂點的到頂點的邊的相關信息:");
	
	scanf("%d%d%d", &v1, &v2, &w);
	
	graph->G[v1 - 1][v2 - 1] = w;
	
	graph->G[v2 - 1][v1 - 1] = w;
	
}

return graph;

}

void display(Graph_matrax g) {

printf("輸出臨接矩陣:\n");

for (int i = 0; i < g->number_vertex; i++) {

	for (int j = 0; j < g->number_vertex; j++)

	{
		printf("%8d", g->G[i][j]);

	}
	printf("\n");


}

}

void Prim(Graph_matrax g, int v) {

//lowcost存儲爲放到集合到已經放到集合的最小值，lowcost[i]=0表示該i節點己經放到集合中了，也能夠做爲後面判斷有環的條件

int lowcost[Max];

int close[Max];//存儲誰指向本身的節點，也就是該節點的父親

int i;

//初始化，第一個放入的節點

for (i = 0; i < g->number_vertex; i++) {

	lowcost[i] = g->G[v][i];
	
	close[i] = v;
}

int min;

int k=0;

int j;

//把另外的n-1元素作相同的操做

for (i = 1; i < g->number_vertex; i++) {

	min = 8888888;
	
	//找到還未放到集合到集合某個節點的最小權值的節點
	
	for (j = 0; j < g->number_vertex; j++) 
	
		if (lowcost[j] != 0 && min >lowcost[j]) {
		
			min = lowcost[j];
			
			k = j;
		}
	
	printf("%d->%d  權重爲%d ",close[k], k,lowcost[k]);
	
	//放入到集合的元素要把權值放置爲0
	
	lowcost[k] = 0;
	
	//在剛找的節點的臨接點中的最小權值，與lowcost[]中的比較，小就更新
	
	for (j = 0; j < g->number_vertex; j++) {
	
		if (g->G[k][j] != 0 && g->G[k][j] < lowcost[j]) {
		
			lowcost[j] = g->G[k][j];
			
			//把父親節點存入進去
			
			close[j] = k;
		}
	}
	printf("\n");

}

}

int main() {

Graph_g *g = init();

printf("%d\n", g->number_vertex);

display(g);

printf("\n");

//爲了不出現錯誤，把c[]所有設爲false

Prim(g, 0);

printf("\n");

system("pause");
return 0;

}