用c语言实现Prim算法和Kruskal算法

Prim算法和Kruskal算法都是用来解决最小生成树问题的算法。下面是用C语言实现Prim算法和Kruskal算法的示例代码。

## Prim算法

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

#define V 5

int minKey(int key[], int mstSet[])
{
   int min = INT_MAX, min_index;

   for (int v = 0; v < V; v++)
     if (mstSet[v] == 0 && key[v] < min)
         min = key[v], min_index = v;

   return min_index;
}

int printMST(int parent[], int n, int graph[V][V])
{
   printf("Edge \tWeight\n");
   for (int i = 1; i < V; i++)
      printf("%d - %d \t%d \n", parent[i], i, graph[i][parent[i]]);
}

void primMST(int graph[V][V])
{
     int parent[V];
     int key[V];
     int mstSet[V];

     for (int i = 0; i < V; i++)
        key[i] = INT_MAX, mstSet[i] = 0;

     key[0] = 0;
     parent[0] = -1;

     for (int count = 0; count < V-1; count++)
     {
        int u = minKey(key, mstSet);

        mstSet[u] = 1;

        for (int v = 0; v < V; v++)
          if (graph[u][v] && mstSet[v] == 0 && graph[u][v] <  key[v])
             parent[v]  = u, key[v] = graph[u][v];
     }

     printMST(parent, V, graph);
}

int main()
{
   int graph[V][V] = {{0, 2, 0, 6, 0},
                      {2, 0, 3, 8, 5},
                      {0, 3, 0, 0, 7},
                      {6, 8, 0, 0, 9},
                      {0, 5, 7, 9, 0},
                     };

    primMST(graph);

    return 0;
}

## Kruskal算法

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define V 5
#define E 9

struct Edge
{
    int src, dest, weight;
};

struct Graph
{
    int V, E;
    struct Edge* edge;
};

struct Graph* createGraph(int V, int E)
{
    struct Graph* graph = (struct Graph*) malloc( sizeof(struct Graph) );
    graph->V = V;
    graph->E = E;

    graph->edge = (struct Edge*) malloc( graph->E * sizeof( struct Edge ) );

    return graph;
}

struct subset
{
    int parent;
    int rank;
};

int find(struct subset subsets[], int i)
{
    if (subsets[i].parent != i)
        subsets[i].parent = find(subsets, subsets[i].parent);

    return subsets[i].parent;
}

void Union(struct subset subsets[], int x, int y)
{
    int xroot = find(subsets, x);
    int yroot = find(subsets, y);

    if (subsets[xroot].rank < subsets[yroot].rank)
        subsets[xroot].parent = yroot;
    else if (subsets[xroot].rank > subsets[yroot].rank)
        subsets[yroot].parent = xroot;
    else
    {
        subsets[yroot].parent = xroot;
        subsets[xroot].rank++;
    }
}

int myComp(const void* a, const void* b)
{
    struct Edge* a1 = (struct Edge*)a;
    struct Edge* b1 = (struct Edge*)b;
    return a1->weight > b1->weight;
}

void KruskalMST(struct Graph* graph)
{
    int V = graph->V;
    struct Edge result[V];
    int e = 0;
    int i = 0;

    qsort(graph->edge, graph->E, sizeof(graph->edge[0]), myComp);

    struct subset *subsets =
        (struct subset*) malloc( V * sizeof(struct subset) );

    for (int v = 0; v < V; ++v)
    {
        subsets[v].parent = v;
        subsets[v].rank = 0;
    }

    while (e < V - 1 && i < graph->E)
    {
        struct Edge next_edge = graph->edge[i++];

        int x = find(subsets, next_edge.src);
        int y = find(subsets, next_edge.dest);

        if (x != y)
        {
            result[e++] = next_edge;
            Union(subsets, x, y);
        }
    }

    printf("Following are the edges in the constructed MST\n");
    for (i = 0; i < e; ++i)
        printf("%d -- %d == %d\n", result[i].src, result[i].dest,
                                                 result[i].weight);
    return;
}

int main()
{
    int V = 5; // Number of vertices in graph
    int E = 9; // Number of edges in graph
    struct Graph* graph = createGraph(V, E);

    // add edge 0-1
    graph->edge[0].src = 0;
    graph->edge[0].dest = 1;
    graph->edge[0].weight = 4;

    // add edge 0-2
    graph->edge[1].src = 0;
    graph->edge[1].dest = 2;
    graph->edge[1].weight = 4;

    // add edge 1-2
    graph->edge[2].src = 1;
    graph->edge[2].dest = 2;
    graph->edge[2].weight = 2;

    // add edge 2-3
    graph->edge[3].src = 2;
    graph->edge[3].dest = 3;
    graph->edge[3].weight = 3;

    // add edge 2-4
    graph->edge[4].src = 2;
    graph->edge[4].dest = 4;
    graph->edge[4].weight = 1;

    // add edge 3-4
    graph->edge[5].src = 3;
    graph->edge[5].dest = 4;
    graph->edge[5].weight = 2;

    // add edge 1-4
    graph->edge[6].src = 1;
    graph->edge[6].dest = 4;
    graph->edge[6].weight = 5;

    // add edge 1-3
    graph->edge[7].src = 1;
    graph->edge[7].dest = 3;
    graph->edge[7].weight = 6;

    // add edge 0-3
    graph->edge[8].src = 0;
    graph->edge[8].dest = 3;
    graph->edge[8].weight = 5;

    KruskalMST(graph);

    return 0;
}