UVA_10034_Freckles-优快云博客

本文链接：https://blog.youkuaiyun.com/cxy7tv/article/details/51090342

本文介绍了一种使用克鲁斯卡尔算法求解最小生成树问题的方法，并通过具体的C++实现展示了如何构建顶点间距离计算、边权重比较、并查集等关键组件。该算法适用于解决网络设计中的问题。

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#include<iostream>  
#include<sstream>  
#include<string>  
#include<vector>  
#include<list>  
#include<set>  
#include<map>  
#include<stack>  
#include<queue>  
#include<algorithm>  
#include<cmath>  
#pragma warning(disable:4996)  
using std::cin;
using std::cout;
using std::endl;
using std::stringstream;
using std::string;
using std::vector;
using std::list;
using std::pair;
using std::set;
using std::multiset;
using std::map;
using std::multimap;
using std::stack;
using std::queue;
using std::sort;
class DisjoinSet
{
private:
	vector<int>represent, rank;
public:
	DisjoinSet(const int &n) :represent(n), rank(n)
	{
		for (int i = 0; i < n; i++)
		{
			represent[i] = i;
		}
	}
	int find(int i)
	{
		return represent[i] = represent[i] == i ? i : find(represent[i]);
	}
	void merge(const int &x, const int &y)
	{
		auto a = find(x); auto b = find(y);
		if (rank[a] < rank[b])
		{
			represent[a] = b;
		}
		else
		{
			represent[b] = a;
			if (rank[b] == rank[a])
			{
				rank[a]++;
			}
		}
	}
};
class Edge
{
public:
	pair<int,int>vertex;
	double weight;
	Edge(const pair<int, int>&v, const double &w)
	{
		vertex = v;
		weight = w;
	}
};
bool compare(const Edge&a, const Edge&b)
{
	if (a.weight != b.weight)
	{
		return a.weight < b.weight;
	}
	if (a.vertex.first != b.vertex.first)
	{
		return a.vertex.first < b.vertex.first;
	}
	return a.vertex.second < b.vertex.second;
}
vector<Edge>getEdge()
{
	int n; cin >> n;
	vector<pair<double, double>>vertex(n);
	map<pair<double, double>, int>Map;
	for (int i = 0; i < n; i++)
	{
		cin >> vertex[i].first >> vertex[i].second;
		Map.insert({ { vertex[i].first, vertex[i].second },0 });
	}
	int i = 0;
	for (auto iter = Map.begin(); iter != Map.end(); iter++)
	{
		iter->second = i++;
	}
	vector<Edge>edge;
	for (size_t i = 0; i < n; i++)
	{
		for (size_t j = i + 1; j < n; j++)
		{
			edge.push_back({ {Map[vertex[i]],Map[vertex[j]] }, sqrt(pow(vertex[i].first - vertex[j].first,2) + pow(vertex[i].second - vertex[j].second, 2)) });
		}
	}
	sort(edge.begin(), edge.end(), compare);
	return edge;
}
double kruscal(const vector<Edge>&edge)
{
	DisjoinSet union_set((int)sqrt(edge.size()*2)+1);
	double sum = 0;
	int block = (int)sqrt(edge.size() * 2) + 1;
	for (size_t i = 0; i < edge.size(); i++)
	{
		if (union_set.find(edge[i].vertex.first) != union_set.find(edge[i].vertex.second))
		{
			union_set.merge(edge[i].vertex.first, edge[i].vertex.second);
			sum += edge[i].weight;
			block--;
			if (block == 1)
			{
				return sum;
			}
		}
	}
	return 0;
}
int main()
{
	//freopen("input.txt","r",stdin);  
	//freopen("output.txt","w",stdout);
	int T; cin >> T;
	while (T--)
	{
		auto edge=getEdge();
		printf("%.2lf\n", kruscal(edge));
		if (T)
		{
			cout << endl;
		}
	}
	return 0;
}