数据结构系列23 - 最小生成树kruskal算法 - C语言实现

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

#define MAX 32767

typedef struct Graph {
    char* vexs;
    int** arcs;
    int vexNum;
    int arcNum;
}Graph;

typedef struct Edge {
    int start;
    int end;
    int weight;
}Edge;

Edge* initEdge(Graph* G) {
    int index = 0;
    Edge* edge = (Edge*)malloc(sizeof(Edge) * G -> arcNum);
    for (int i = 0; i < G -> vexNum; i++) {
        for (int j = i + 1; j < G -> vexNum; j++) {
            if (G -> arcs[i][j] != MAX) {
                edge[index].start = i;
                edge[index].end = j;
                edge[index].weight = G -> arcs[i][j];
                index++;
            }
        }
    }
    return edge;
}

void sortEdge(Edge* edge, Graph* G) {
    Edge temp;
    for (int i = 0; i < G -> arcNum - 1; i++) {
        for (int j = 0; j < G -> arcNum - i - 1; j++) {
            if (edge[j].weight > edge[j + 1].weight) {
                temp = edge[j];
                edge[j] = edge[j + 1];
                edge[j + 1] = temp;
            }
        }
    }
}

void kruskal(Graph* G) {
    int* connected = (int*)malloc(sizeof(int) * G -> vexNum);
    for (int i = 0 ; i < G -> vexNum; i++) {
        connected[i] = i;
    }
    Edge* edge = initEdge(G);
    sortEdge(edge, G);
    for (int i = 0; i < G -> arcNum; i++) {
        int start = connected[edge[i].start];
        int end = connected[edge[i].end];
        if (start != end) {
            printf("v%c --> v%c weight = %d\n", G -> vexs[edge[i].start], G -> vexs[edge[i].end], edge[i].weight);
            for (int j = 0; j < G -> vexNum; j++) {
                if (connected[j] == end) {
                    connected[j] = start;
                }
            }
        }
    }
}

Graph* initGraph(int vexNum) {
    Graph* G = (Graph*)malloc(sizeof(Graph));
    G -> vexs = (char*)malloc(sizeof(char) * vexNum);
    G -> arcs = (int**)malloc(sizeof(int*) * vexNum);
    for (int i = 0 ; i < vexNum; i++) {
        G -> arcs[i] = (int*)malloc(sizeof(int) * vexNum);
    }
    G -> vexNum = vexNum;
    G -> arcNum = 0;
    return G;
}

void createGraph(Graph* G, char* vexs, int* arcs) {
    for (int i = 0 ; i < G -> vexNum; i++) {
        G -> vexs[i] = vexs[i];
        for (int j = 0; j < G -> vexNum; j++) {
            G -> arcs[i][j] = *(arcs + i * G -> vexNum + j);
            if (G -> arcs[i][j] != 0 && G -> arcs[i][j] != MAX)
                G -> arcNum ++;
        }
    }
    G -> arcNum /= 2;
}

void DFS(Graph* G, int* visited, int index) {
    printf("%c\t", G -> vexs[index]);
    visited[index] = 1;
    for (int i = 0; i < G ->vexNum; i++) {
        if (G -> arcs[index][i] > 0 && G -> arcs[index][i] != MAX && !visited[i]) {
            DFS(G, visited, i);
        }
    }
}

int main() {
    Graph* G = initGraph(6);
    int* visited = (int*)malloc(sizeof(int) * G -> vexNum);
    for (int i = 0; i < G -> vexNum; i++)
        visited[i] = 0;
    int arcs[6][6] = {
        0, 6, 1, 5, MAX, MAX,
        6, 0, 5, MAX, 3, MAX,
        1, 5, 0, 5, 6, 4,
        5, MAX, 5, 0, MAX, 2,
        MAX, 3, 6, MAX, 0, 6,
        MAX, MAX, 4, 2, 6, 0
    };
    createGraph(G, "123456", (int*)arcs);
    DFS(G, visited, 0);
    printf("\n");
    kruskal(G);
    return 0;
}