邻接矩阵ｃ源码（构造邻接矩阵，深度优先遍历，广度优先遍历，最小生成树prim,kruskal算法）

matrix.c

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <limits.h>

#include "aqueue.h"

#define MAX_VALUE INT_MAX
#define MAX_NUM 100

typedef char node_type;

typedef struct matrix
{
    node_type vertex[MAX_NUM];//节点信息
    int arcs[MAX_NUM][MAX_NUM];//矩阵
    int vertexs, brim;//节点数,边数
} Graph;

void g_create(Graph * graph)
{
    int num;
    int i, j, k;
    char c;

    printf("输入节点个数:");
    scanf("%d", &graph->vertexs);
    getchar();//接受回车键

    printf("输入节点信息:");
    for ( i = 0; i < graph->vertexs; i++ )
    {
        scanf("%c", &graph->vertex[i]);
        getchar();
    }

    for ( i = 0; i < graph->vertexs; i++ )//初始化矩阵
        for ( j = 0; j < graph->vertexs; j++ )
            graph->arcs[i][j] = MAX_VALUE;
    graph->brim = 0;//初始化边数

    // i 代表行数, j 是用来循环的, k 代表列数
    for ( i = 0; i < graph->vertexs; i++ )
    {
        printf("输入与%c节点相邻的节点与权值,输入#号键结束\n", graph->vertex[i]);
        for ( j = 0; j < graph->vertexs; j++ )
        {
            scanf("%c", &c);
            if ( c == ‘#‘ )
            {
                getchar();
                break;
            }
            scanf("%d", &num);
            for ( k = 0; k < graph->vertexs; k++ )
            {
                if ( graph->vertex[k] != c )
                    continue;
                graph->arcs[i][k] = num;
                graph->brim++;
            }
            getchar();
        }
    }
    graph->brim /= 2;
}

void g_printMatrix(Graph * graph)//打印矩阵状态
{
    int i, j;

    printf("brim = %d\n", graph->brim);
    for ( i = 0; i < graph->vertexs; i++ )
    {
        for ( j = 0; j < graph->vertexs; j++ )
        {
            printf("%-10d ", graph->arcs[i][j]);
        }
        printf("\n");
    }
}

//深度优先遍历
static void dfs_graph(Graph * graph, bool visited[], const int i);
void g_depth_first_search(Graph * graph)
{
    bool visited[graph->vertexs];
    int i;
    for ( i = 0; i < graph->vertexs; i++ )
        visited[i] = false;
    visited[0] = true;
    dfs_graph(graph, visited, 0);
    printf("\n");
}

static void dfs_graph(Graph * graph, bool visited[], const int i)
{
    int j;
    printf("%c\t", graph->vertex[i]);
    for ( j = 0; j < graph->vertexs; j++ )//依次检查矩阵
    {
        if ( graph->arcs[i][j] != MAX_VALUE && !visited[j] )//i 代表矩阵的行, j 代表矩阵的列
        {
            visited[j] = true;
            dfs_graph(graph, visited, j);
        }
    }
}

//广度优先遍历
void g_breadth_first_search(Graph * graph)
{
    Queue queue;//队列存储的是节点数组的下标(int)
    bool visited[graph->vertexs];
    int i, pos;

    q_init(&queue);
    for ( i = 0; i < graph->vertexs; i++ )
        visited[i] = false;

    visited[0] = true;
    q_push(&queue, 0);
    while ( !q_empty(&queue) )
    {
        pos = q_front(&queue);
        printf("%c\t", graph->vertex[pos]);
        for ( i = 0; i < graph->vertexs; i++ )//把队头元素的邻接点入队
        {
            if ( !visited[i] && graph->arcs[pos][i] != MAX_VALUE )
            {
                visited[i] = true;
                q_push(&queue, i);
            }
        }
        q_pop(&queue);
    }
    printf("\n");
}

//最小生成树prim算法
static void init_prim(Graph * graph, Graph * prim_tree);
void Prim(Graph * graph, Graph * prim_tree)
{
    bool visited[graph->vertexs];
    int i, j, k, h;
    int power, power_j, power_k;

    for ( i = 0; i < graph->vertexs; i++ )
        visited[i] = false;
    init_prim(graph, prim_tree);

    visited[0] = true;
    for ( i = 0; i < graph->vertexs; i++ )
    {
        power = MAX_VALUE;
        for ( j = 0; j < graph->vertexs; j++ )
        {
            if ( visited[j] )
            {
                for ( k = 0; k < graph->vertexs; k++ )
                {
                    if ( power > graph->arcs[j][k] && !visited[k] )
                    {
                        power = graph->arcs[j][k];
                        power_j = j;
                        power_k = k;
                    }
                }
            }
        }
        //min power
        if ( !visited[power_k] )
        {
            visited[power_k] = true;
            prim_tree->arcs[power_j][power_k] = power;
        }
    }
}

static void init_prim(Graph * graph, Graph * prim_tree)
{
    int i, j;

    prim_tree->vertexs = graph->vertexs;
    for ( i = 0; i < prim_tree->vertexs; i++ )//初始化节点
        prim_tree->vertex[i] = graph->vertex[i];
    for ( i = 0 ; i < prim_tree->vertexs; i++ )//初始化矩阵
    {
        for ( j = 0; j < prim_tree->vertexs; j++ )
        {
            prim_tree->arcs[i][j] = MAX_VALUE;
        }
    }
}

//最小生成树kruskal算法
typedef struct
{
    int head;//边的始点下标
    int tail;//边的终点下标
    int power;//边的权值
} Edge;

static void init_kruskal(Graph * graph, Graph * kruskal_tree);
static void my_sort(Edge * arr, int size);
void kruskal(Graph * graph, Graph * kruskal_tree)
{
    int visited[graph->vertexs];
    Edge edge[graph->brim];
    int i, j, k;
    int v1, v2, vs1, vs2;

    for ( i = 0; i < graph->vertexs; i++ )
        visited[i] = i;

    k = 0;
    for ( i = 0; i < graph->vertexs; i++ )
    {
        for ( j = i + 1; j < graph->vertexs; j++ )
        {
            if ( graph->arcs[i][j] != MAX_VALUE )
            {
                edge[k].head = i;
                edge[k].tail = j;
                edge[k].power = graph->arcs[i][j];
                k++;
            }
        }
    }

    init_kruskal(graph, kruskal_tree);
    my_sort(edge, graph->brim);

    for ( i = 0; i < graph->brim; i++ )
    {
        v1 = edge[i].head;
        v2 = edge[i].tail;
        vs1 = visited[v1];
        vs2 = visited[v2];
        if ( vs1  != vs2 )
        {
            kruskal_tree->arcs[v1][v2] = graph->arcs[v1][v2];
            for ( j = 0; j < graph->vertexs; j++ )
            {
                if ( visited[j] == vs2 )
                    visited[j] = vs1;
            }
        }
    }
}

static void init_kruskal(Graph * graph, Graph * kruskal_tree)
{
    int i, j;

    kruskal_tree->vertexs = graph->vertexs;
    kruskal_tree->brim = graph->brim;

    for ( i = 0; i < graph->vertexs; i++ )
        kruskal_tree->vertex[i] = graph->vertex[i];

    for ( i = 0; i < graph->vertexs; i++ )
        for ( j = 0; j < graph->vertexs; j++ )
            kruskal_tree->arcs[i][j] = MAX_VALUE;
}

static void my_sort(Edge * arr, int size)
{
    int i, j;
    Edge tmp;

    for ( i = 0; i < size - 1; i++ )
    {
        for ( j = i + 1; j < size; j++ )
        {
            if ( arr[i].power > arr[j].power )
            {
                tmp.head = arr[i].head;
                tmp.tail = arr[i].tail;
                tmp.power = arr[i].power;

                arr[i].head = arr[j].head;
                arr[i].tail = arr[j].tail;
                arr[i].power = arr[j].power;

                arr[j].head = tmp.head;
                arr[j].tail = tmp.tail;
                arr[j].power = tmp.power;
            }
        }
    }
}

int main(void)
{
    Graph graph;
    Graph prim_tree;
    Graph kruskal_tree;

    g_create(&graph);
    g_printMatrix(&graph);
//    printf("\n");
//    g_depth_first_search(&graph);
//    g_breadth_first_search(&graph);
//
//    Prim(&graph, &prim_tree);
//    g_printMatrix(&prim_tree);
//    g_depth_first_search(&prim_tree);
//    g_breadth_first_search(&prim_tree);

    kruskal(&graph, &kruskal_tree);
    g_printMatrix(&kruskal_tree);

    return 0;
}

aqueue.h

#ifndef _QUEUE_H
#define _QUEUE_H

#define MAXSIZE 10

typedef struct queue
{
    int * arr;
    int front;
    int rear;
} Queue;

void q_init(Queue * queue);//初始化
void q_push(Queue * queue, const int data);//入队
void q_pop(Queue * queue);//出队
bool q_empty(Queue * queue);//为空
bool q_full(Queue * queue);//为满
int q_size(Queue * queue);//队大小
int q_front(Queue * queue);//队头元素
int q_back(Queue * queue);//队尾元素
void q_destroy(Queue * queue);//销毁

#endif //_QUEUE_h

aqueue.c

#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <stdbool.h>

#include "aqueue.h"

void q_init(Queue * queue)
{
    queue->arr = (int *)malloc( sizeof(int) * MAXSIZE );//初始化数组
    assert(queue->arr != NULL);
    queue->front = 0;
    queue->rear = 0;
}

void q_push(Queue * queue, const int data)
{
    if ( q_full(queue) )
        return;
    queue->arr[queue->rear++] = data;//入队，队尾+1
    queue->rear = queue->rear % MAXSIZE;//如果队尾
}

void q_pop(Queue * queue)
{
    if ( q_empty(queue) )
        return;
    queue->front = ++queue->front % MAXSIZE;//front+1，对MAXSIZE取余
}

bool q_empty(Queue * queue)
{
    return queue->front == queue->rear;
}

bool q_full(Queue * queue)
{
    return queue->front == (queue->rear + 1) % MAXSIZE;
}

int q_size(Queue * queue)
{
    return (queue->rear - queue->front) % MAXSIZE;
}

int q_front(Queue * queue)
{
    assert( !q_empty(queue) );
    return queue->arr[queue->front];
}

int q_back(Queue * queue)
{
    assert( !q_empty(queue) );
    return queue->arr[queue->rear - 1];
}

void q_destroy(Queue * queue)
{
    free(queue->arr);
}