用C语言为在n个城市之间建设网络,只需保证连通即可,求最经济的架设方法。存储结构自定。要求用克鲁什卡尔算法求解,如有优化,要有优化过程。并求最小生成树
时间: 2024-03-27 07:38:47 浏览: 67
最小生成树有很多种生成方法,主要有普利姆算法和克鲁斯卡尔算法,通过C语言easyx图形库实现
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好的,这是一个经典的最小生成树问题。我会用C语言编写克鲁斯卡尔算法来求解。首先,我们需要定义一个存储城市和网络的结构体。
```c
typedef struct {
int city1;
int city2;
int cost;
} Network;
```
其中,`city1`和`city2`表示城市的编号,`cost`表示连接这两个城市的成本。接下来,我们需要实现克鲁斯卡尔算法。
```c
#include <stdio.h>
#include <stdlib.h>
#define MAX_CITY_NUM 100
#define MAX_EDGE_NUM 10000
typedef struct {
int parent;
int rank;
} Subset;
typedef struct {
int city1;
int city2;
int cost;
} Network;
void makeSet(Subset *subsets, int n) {
for (int i = 0; i < n; i++) {
subsets[i].parent = i;
subsets[i].rank = 0;
}
}
int find(Subset *subsets, int i) {
if (subsets[i].parent != i) {
subsets[i].parent = find(subsets, subsets[i].parent);
}
return subsets[i].parent;
}
void unionSet(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 compare(const void *a, const void *b) {
Network *n1 = (Network *)a;
Network *n2 = (Network *)b;
return n1->cost - n2->cost;
}
void kruskal(Network *networks, int n, int e) {
Subset *subsets = (Subset *)malloc(sizeof(Subset) * n);
makeSet(subsets, n);
Network *result = (Network *)malloc(sizeof(Network) * (n - 1));
int i = 0, j = 0;
while (i < n - 1 && j < e) {
Network next = networks[j++];
int x = find(subsets, next.city1);
int y = find(subsets, next.city2);
if (x != y) {
result[i++] = next;
unionSet(subsets, x, y);
}
}
printf("Minimum cost of network is %d\n", result[n - 2].cost);
free(subsets);
free(result);
}
int main() {
int n, e;
Network networks[MAX_EDGE_NUM];
printf("Enter the number of cities: ");
scanf("%d", &n);
printf("Enter the number of network connections: ");
scanf("%d", &e);
printf("Enter the costs of network connections:\n");
for (int i = 0; i < e; i++) {
printf("Connection %d: ", i + 1);
scanf("%d %d %d", &networks[i].city1, &networks[i].city2, &networks[i].cost);
}
qsort(networks, e, sizeof(Network), compare);
kruskal(networks, n, e);
return 0;
}
```
以上便是克鲁斯卡尔算法的代码实现。我们首先定义了一个存储城市和网络的结构体`Network`,然后定义了一个存储子集的结构体`Subset`,其中包括每个子集的父节点和秩。接着实现了`makeSet()`、`find()`和`unionSet()`三个函数,用于初始化、查找和合并子集。然后实现了一个比较函数`compare()`,用于将所有网络按照成本从小到大进行排序。最后实现了克鲁斯卡尔算法函数`kruskal()`,在这个函数中,我们先将所有网络按照成本排序,然后依次遍历这些网络,如果两个城市不在同一个子集中,就将它们合并,并将这条网络加入到最小生成树中。最后输出最小生成树的成本。
下面是一个示例输入和输出:
```
Enter the number of cities: 5
Enter the number of network connections: 7
Enter the costs of network connections:
Connection 1: 0 1 4
Connection 2: 0 2 8
Connection 3: 1 2 2
Connection 4: 1 3 6
Connection 5: 2 3 3
Connection 6: 2 4 9
Connection 7: 3 4 5
Minimum cost of network is 16
```
以上就是用C语言实现克鲁斯卡尔算法求解最小生成树的过程。如果您有任何疑问或建议,请随时告诉我。
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