2021秋季《数据结构》_ EOJ 1096.Building Roads

题目

Farmer John had just acquired several new farms! He wants to connect the farms with roads so that he can travel from any farm to any other farm via a sequence of roads; roads already connect some of the farms.

思路

将已经连接上的点放进同一个并查集中，再用kruskal生成MST，判断条件由一般kruskal的edgeSelected<n-1调整为到图连通为止。

• 能用double就不用float，否则造成精度丢失
• 放进同一个并查集的时候用root[find(a)]=find(b)，而不是简单的root[a]=b]，因为不能确保已知的每条边都连两个新的独立顶点

代码

#include<bits/stdc++.h>
using namespace std;
#define MAXN 1001
#define INF 999999999
//int cost[MAXN][MAXN];

typedef struct ms
{
	double x, y;
}point;

typedef struct ed
{
	int u, v;
	double w;
}edge;

point cord[MAXN];
int root[MAXN] = { 0 };
vector<edge> Edges;


double compDis(point a, point b)
{
	double dx = a.x - b.x;
	double dy = a.y - b.y;
	return sqrt(dx * dx + dy * dy);
}

bool cmp(edge a, edge b)
{
	return a.w < b.w;
}

int find(int x)
{
	int tmp = x;
	while (root[tmp] != tmp)
	{
		tmp = root[tmp];
	}

	int k = x;
	while (k != tmp)
	{
		int j = root[k];
		root[k] = tmp;
		k = j;
	}

	return tmp;
}

void join(int x, int y)
{
	int rootx = find(x);
	int rooty = find(y);
	if (rootx != rooty)
	{
		root[rootx] = rooty;
	}
}

bool isConnect(int root[], int n)
{
	int cnt = 0;
	for (int i = 1; i <= n; i++)
	{
		if (root[i] == i)
		{
			cnt++;
		}
	}
	if (cnt != 1) return false;
	return true;
}

int main()
{
	int n, m; cin >> n >> m;
	for (int i = 1; i <= n; i++)
	{
		double x, y; cin >> x >> y;
		cord[i] = point{ x,y };
	}

	for (int i = 1; i <= n; i++)
	{
		root[i] = i;
	}

	for (int i = 0; i < m; i++)
	{
		int a, b; cin >> a >> b;
		join(find(a), find(b));
	}

	for (int i = 1; i < n; i++)
	{
		for (int j = i + 1; j <= n; j++)
		{
			double w = compDis(cord[i], cord[j]);
			Edges.push_back(edge{ i,j,w });
		}
	}
	sort(Edges.begin(), Edges.end(), cmp);

	int i = 0;
	double res = 0;
	while (!isConnect(root,n))
	{
		if (find(Edges[i].u) != find(Edges[i].v))
		{
			// cout << Edges[i].u << ' ' << Edges[i].v << ' ' << Edges[i].w << endl;
			join(find(Edges[i].u), find(Edges[i].v));
			res += Edges[i].w;
		}
		i++;
	}

	cout.setf(ios::fixed);
	cout << setprecision(2) << res << endl;

	return 0;
}

标签：Building,tmp,1096,int,EOJ,Edges,double,root,find
来源： https://blog.csdn.net/rd142857/article/details/122050982