最小生成树算法，分别用C语言，C++,java,python编写出来

最小生成树问题，简称MST，指给定一个带权的无向连通图，如果选取一棵生成树，使树上所有边上权的总和为最小，这叫最小生成树。

图有N个顶点，就一定有N-1条边，且必须包含所有顶点，所有边都在图中。解决最小生成树问题的算法主要有普利姆算法和克鲁斯卡尔算法。

最小生成树算法，分别用C语言，C++,java,python编写出来
当涉及最小生成树算法时，可以使用多种编程语言来实现。以下是使用C语言、C++、Java和Python编写最小生成树算法的示例：
1.**C语言示例：**

#include <stdio.h>
#include <stdbool.h>
#include <limits.h>
#define V 5
int minKey(int key[], bool mstSet[]) {
int min = INT_MAX, min_index;
for (int v = 0; v < V; v++) {
if (mstSet[v] == false && key[v] < min) {
min = key[v];
min_index = v;
}
}
return min_index;
}
void printMST(int parent[], 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];
bool mstSet[V];
for (int i = 0; i < V; i++) {
key[i] = INT_MAX;
mstSet[i] = false;
}
key[0] = 0;
parent[0] = -1;
for (int count = 0; count < V – 1; count++) {
int u = minKey(key, mstSet);
mstSet[u] = true;
for (int v = 0; v < V; v++) {
if (graph[u][v] && mstSet[v] == false && graph[u][v] < key[v]) {
parent[v] = u;
key[v] = graph[u][v];
}
}
}
printMST(parent, graph);
}

2.**C++示例：**

#include <iostream>
#include <climits>
using namespace std;
#define V 5
int minKey(int key[], bool mstSet[]) {
int min = INT_MAX, min_index;
for (int v = 0; v < V; v++) {
if (mstSet[v] == false && key[v] < min) {
min = key[v];
min_index = v;
}
}
return min_index;
}
void printMST(int parent[], int graph[V][V]) {
cout << “Edge \tWeight\n”;
for (int i = 1; i < V; i++) {
cout << parent[i] << ” – ” << i << “\t” << graph[i][parent[i]] << endl;
}
}
void primMST(int graph[V][V]) {
int parent[V];
int key[V];
bool mstSet[V];
for (int i = 0; i < V; i++) {
key[i] = INT_MAX;
mstSet[i] = false;
}
key[0] = 0;
parent[0] = -1;
for (int count = 0; count < V – 1; count++) {
int u = minKey(key, mstSet);
mstSet[u] = true;
for (int v = 0; v < V; v++) {
if (graph[u][v] && mstSet[v] == false && graph[u][v] < key[v]) {
parent[v] = u;
key[v] = graph[u][v];
}
}
}
printMST(parent, graph);
}

3.**Java示例：**

import java.util.Arrays;
class MST {
private static final int V = 5;
int minKey(int key[], Boolean mstSet[]) {
int min = Integer.MAX_VALUE, min_index = -1;
for (int v = 0; v < V; v++) {
if (mstSet[v] == false && key[v] < min) {
min = key[v];
min_index = v;
}
}
return min_index;
}
void printMST(int parent[], int graph[][]) {
System.out.println(“Edge \tWeight”);
for (int i = 1; i < V; i++) {
System.out.println(parent[i] + ” – ” + i + “\t” + graph[i][parent[i]]);
}
}
void primMST(int graph[][]) {
int parent[] = new int[V];
int key[] = new int[V];
Boolean mstSet[] = new Boolean[V];
Arrays.fill(key, Integer.MAX_VALUE);
Arrays.fill(mstSet, false);
key[0] = 0;
parent[0] = -1;
for (int count = 0; count < V – 1; count++) {
int u = minKey(key, mstSet);
mstSet[u] = true;
for (int v = 0; v < V; v++) {
if (graph[u][v] != 0 && mstSet[v] == false && graph[u][v] < key[v]) {
parent[v] = u;
key[v] = graph[u][v];
}
}
}
printMST(parent, graph);
}

}

4.**Python示例：**

class MST:
def __init__(self, vertices):
self.V = vertices
self.graph = [[0 for _ in range(vertices)] for _ in range(vertices)]
def minKey(self, key, mstSet):
min = float(“inf”)
min_index = -1
for v in range(self.V):
if key[v] < min and mstSet[v] == False:
min = key[v]
min_index = v
return min_index
def printMST(self, parent):
print(“Edge \tWeight”)
for i in range(1, self.V):
print(parent[i], “-“, i, “\t”, self.graph[i][parent[i]])
def primMST(self):
key = [float(“inf”)] * self.V
parent = [None] * self.V
mstSet = [False] * self.V
key[0] = 0
parent[0] = -1
for _ in range(self.V – 1):
u = self.minKey(key, mstSet)
mstSet[u] = True
for v in range(self.V):
if (
self.graph[u][v] > 0
and mstSet[v] == False
and key[v] > self.graph[u][v]
):
key[v] = self.graph[u][v]
parent[v] = u
self.printMST(parent)

这些示例展示了使用不同编程语言实现最小生成树算法。每个示例都使用了类似的思路，通过选择最小权重的边来构建最小生成树。您可以根据需要修改算法和输入图形。请注意，这只是最小生成树算法的简单示例，实际应用中可能会有更复杂的问题和算法。

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