给定一个加权无向连通图G 生成图g的最小生成树,你需要回答不同选择边的方法的数量。 当且仅当存在一条边,一种方法选择它,而另一种方法不选择它,两种方法被认为是不同的。 图的序号从1开始输出对1000000007进行mod即可 用java输出这个程序
时间: 2024-04-16 11:24:10 浏览: 32
以下是用Java编写的程序,用于计算生成图的最小生成树的不同选择边的方法的数量:
```java
import java.util.*;
class Edge implements Comparable<Edge> {
int src, dest, weight;
public int compareTo(Edge edge) {
return this.weight - edge.weight;
}
}
class Subset {
int parent, rank;
}
class Graph {
int V, E;
Edge[] edges;
Graph(int v, int e) {
V = v;
E = e;
edges = new Edge[E];
for (int i = 0; i < e; ++i)
edges[i] = new Edge();
}
int find(Subset[] subsets, int i) {
if (subsets[i].parent != i)
subsets[i].parent = find(subsets, subsets[i].parent);
return subsets[i].parent;
}
void union(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++;
}
}
long countDifferentChoices() {
Edge[] result = new Edge[V];
int e = 0;
int i = 0;
for (i = 0; i < V; ++i)
result[i] = new Edge();
Arrays.sort(edges);
Subset[] subsets = new Subset[V];
for (i = 0; i < V; ++i)
subsets[i] = new Subset();
for (int v = 0; v < V; ++v) {
subsets[v].parent = v;
subsets[v].rank = 0;
}
i = 0;
while (e < V - 1) {
Edge next_edge = edges[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);
}
}
long choices = 1;
for (i = 0; i < e; ++i) {
choices *= result[i].weight;
choices %= 1000000007;
}
return choices;
}
}
public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
int V = scanner.nextInt();
int E = scanner.nextInt();
Graph graph = new Graph(V, E);
for (int i = 0; i < E; ++i) {
graph.edges[i].src = scanner.nextInt();
graph.edges[i].dest = scanner.nextInt();
graph.edges[i].weight = scanner.nextInt();
}
long choices = graph.countDifferentChoices();
System.out.println(choices);
scanner.close();
}
}
```
你可以将该程序保存为`Main.java`,然后使用Java编译器编译并运行它。程序将从标准输入读取图的输入,并输出不同选择边的方法的数量。