【图】最小生成树Prim算法和Kruskal算法

最新推荐文章于 2025-05-23 19:51:01 发布

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本文介绍并实现了两种经典的最小生成树算法：Prim算法和Kruskal算法。通过C++代码展示了如何寻找带权图的最小生成树，适用于解决网络设计等问题。

一、Prim算法

#include<iostream>
using namespace std;

const int max = 10000;
class Hdu1233{
public:
	void initial(int n);
	void read_case();
	void prim();
	void print_result();
private:
	int path[101][101];
	int distance[101];
	bool visited[101];
	int village_num;
	int min_sum;
};
void Hdu1233::initial(int n){
	village_num = n;
	min_sum = 0;
	for (int i = 0; i < 101; i++){
		for (int j = 0; j < 101; j++){
			path[i][j] = max;
		}
		distance[i] = max;
	}
	memset(visited, false, sizeof(visited));
}
void Hdu1233::read_case(){
	int v1, v2, w;
	int num = village_num*(village_num - 1) / 2;
	for (int i = 0; i < num; i++){
		cin >> v1 >> v2 >> w;
		path[v1][v2] = path[v2][v1] = w;
	}
}
void Hdu1233::prim(){
	int min;
	int i, j, k;
	visited[1] = true;//把节点1添加到最小生成树中  
	for (i = 1; i <= village_num; i++){
		distance[i] = path[1][i];
	}
	for (i = 2; i <= village_num; i++){
		min = max;
		for (j = 1; j <= village_num; j++){//在剩余节点中，选择离最小生成树中节点距离最近的点
			if (min > distance[j] && !visited[j]){
				min = distance[j];
				k = j;
			}
		}
		min_sum += min;
		visited[k] = true;//把节点k添加到最小生成树中  
		for (j = 1; j <= village_num; j++){
			if (distance[j] > path[k][j] && !visited[j])
				distance[j] = path[k][j];//更新distance
		}
	}
}

void Hdu1233::print_result(){
	cout << min_sum << endl;
}

int main(){
	int n;
	Hdu1233 x;
	while (cin >> n&&n){
		x.initial(n);
		x.read_case();
		x.prim();
		x.print_result();
	}
	return 0;
}

二、Kruskal算法

#include<iostream>
using namespace std;

const int max = 10000;
//边的定义
struct Edge{
	int begin;
	int end;
	int weight;
};
class Hdu1233{
public:
	void initial(int n);
	void read_case();
	int find(int n);
	void kruskal();
	void print_result();
private:
	Edge edge[5000];
	int father[101];//用来判断边与边是否形成环路 
	int edge_num;
	int min_sum;
};
void Hdu1233::initial(int n){
	edge_num = n*(n - 1) / 2;
	min_sum = 0;
	int i;
	for (i = 0; i < 5000; i++){
		edge[i].begin = 0;
		edge[i].end = 0;
		edge[i].weight = max;
	}
	for (i = 0; i < 101; i++)
		father[i] = i;
}
int cmp(const void* a, const void* b){
	Edge e1 = *(Edge*)a;
	Edge e2 = *(Edge*)b;
	return e1.weight - e2.weight;
}
void Hdu1233::read_case(){
	int v1, v2, w;
	for (int i = 0; i < edge_num; i++){
		cin >> v1 >> v2 >> w;
		edge[i].begin = v1;
		edge[i].end = v2;
		edge[i].weight = w;
	}
	qsort(edge, edge_num, sizeof(Edge), cmp);//按边的权值从小到大排序
}
int Hdu1233::find(int n){
	int k = n;
	while (k != father[k]){
		k = father[k];
	}
	int t = n;
	int temp;
	while (t != k){//剪枝，减小深度
		temp = father[t];
		father[t] = k;
		t = temp;
	}
	return k;
}
void Hdu1233::kruskal(){
	int a, b;
	for (int i = 0; i < edge_num; i++){
		a = find(edge[i].begin);
		b = find(edge[i].end);
		if (a != b){//没有形成环时加入最小生成树
			father[a] = b;
			min_sum += edge[i].weight;
		}
	}
}

void Hdu1233::print_result(){
	cout << min_sum << endl;
}

int main(){
	int n;
	Hdu1233 x;
	while (cin >> n&&n){
		x.initial(n);
		x.read_case();
		x.kruskal();
		x.print_result();
	}
	return 0;
}