POJ1751

题目链接

参考博客:
https://blog.csdn.net/qq_32680617/article/details/51537339
https://blog.csdn.net/u013480600/article/details/37969655

TLE代码

#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <cmath>
#include <algorithm>
using namespace std;
#define INF 0x7fffffff
#define N 755
struct P
{
	int x;
	int y;
	P():x(0),y(0){}
};
struct Edge
{
	int u,v;
	double w;
	Edge():u(0),v(0),w(0){}
	bool operator < (const Edge&e)const
	{
		return w < e.w;
	}
};
int a[N];
int rk[N];
int n;
int num;
P nod[N];
Edge edge[N * N];
double getDis(int i,int j)
{
	double xd = double(nod[i].x - nod[j].x);
	double yd = double(nod[i].y - nod[j].y);
	return sqrt(xd * xd + yd * yd);
};
void init_edge()
{
	int id = 0;
	int e = n * n;
	for(int i = 0; i <= e; ++i)
	{
		edge[i].w = INF;
	}
	for(int i = 1; i <= n; ++i)
	{
		for(int j = 1; j <= n; ++j)
		{
			id = (i - 1)* n +j;
			
			edge[id].u = i;
			edge[id].v = j;
			edge[id].w = getDis(i,j);
			if(i == j) edge[id].w = INF;
		}
	}
}
void init_set()
{
	for(int i = 1; i <= n; ++i)
	{
		a[i] = i;
		rk[i] = 0;
	}
}
int find_set(int x)
{
	int p = x;
	while(a[p] != p)
	{
		p = a[p];
	}
	int tmp;
	int now = x;
	while(now != p)
	{
		tmp = a[now];
		a[now] = p;
		now = tmp;
	}
	return p;
}
void union_set(int x,int y)
{
	if(rk[x] < rk[y])
	{
		a[x] = y;
	}
	else
	{
		a[y] = x;
		if(rk[x] == rk[y])
		{
			++rk[x];
		}
	}
}


void kruskal()
{
	int e = n * n;
	sort(edge,edge + e + 1);
	int u,v;
	for(int i = 0; i <= e; ++i)
	{
		if(num == 1) break;
		u = edge[i].u;
		v = edge[i].v;
		u = find_set(u);
		v = find_set(v);
		if(u != v)
		{
			union_set(u,v);
			--num;
			printf("%d %d
",edge[i].u,edge[i].v);
		}
	}
}
int main()
{
	scanf("%d",&n);
	num = n;
	int x,y;
	for(int i = 1; i <= n; ++i)
	{
		scanf("%d%d",&x,&y);
		nod[i].x = x;
		nod[i].y = y;
	}
	init_edge();
	int m;
	scanf("%d",&m);
	init_set();
	for(int i = 1; i <= m; ++i)
	{
		scanf("%d%d",&x,&y);
		x = find_set(x);
		y = find_set(y);
		if(x != y)
		{
			union_set(x,y);
			--num;
		}
	}
	kruskal();
	return 0;
}

超时的原因主要是：
1.不必要计算出double类型的距离，只需计算x^2 + y^2，达到边之间的比较效果即可，并且数据的约束不会超出int范围 。
2.n个点需要记录的边数为(n ( imes) (n-1)) (div) 2,而不是n ( imes) n，这样记录边，时间耗费减少一半。

AC代码

#include <cstdio>
#include <iostream>
#include <cstdlib>
#include <cmath>
#include <algorithm>
using namespace std;
#define INF 0x7fffffff
#define N 755
struct P
{
	int x;
	int y;
	P():x(0),y(0){}
};
struct Edge
{
	int u,v;
	int w;
	Edge():u(0),v(0),w(0){}
	bool operator < (const Edge&e)const
	{
		return w < e.w;
	}
};
int a[N];
int rk[N];
int n;
int num;
int edge_num;
P nod[N];
Edge edge[N * N];
int getDis(int i,int j)
{
	int xd = (nod[i].x - nod[j].x);
	int yd = (nod[i].y - nod[j].y);
	return xd * xd + yd * yd;
};
void init_edge()
{
	int id = 0;
	int e = n * n;
	edge_num = 0;
	for(int i = 1; i <= n; ++i)
	{
		for(int j = i + 1; j <= n; ++j)
		{
			edge[edge_num].u = i;
			edge[edge_num].v = j;
			edge[edge_num].w = getDis(i,j);
			++edge_num;
		}
	}
}
void init_set()
{
	for(int i = 1; i <= n; ++i)
	{
		a[i] = i;
		rk[i] = 0;
	}
}
int find_set(int x)
{
	int p = x;
	while(a[p] != p)
	{
		p = a[p];
	}
	int tmp;
	int now = x;
	while(now != p)
	{
		tmp = a[now];
		a[now] = p;
		now = tmp;
	}
	return p;
}
void union_set(int x,int y)
{
	if(rk[x] < rk[y])
	{
		a[x] = y;
	}
	else
	{
		a[y] = x;
		if(rk[x] == rk[y])
		{
			++rk[x];
		}
	}
}


void kruskal()
{
	int e = n * n;
	sort(edge,edge + edge_num);
	int u,v;
	for(int i = 0; i < edge_num; ++i)
	{
		if(num == 1) break;
		u = edge[i].u;
		v = edge[i].v;
		u = find_set(u);
		v = find_set(v);
		if(u != v)
		{
			union_set(u,v);
			--num;
			printf("%d %d
",edge[i].u,edge[i].v);
		}
	}
}
int main()
{
	scanf("%d",&n);
	num = n;
	int x,y;
	for(int i = 1; i <= n; ++i)
	{
		scanf("%d%d",&x,&y);
		nod[i].x = x;
		nod[i].y = y;
	}
	init_edge();
	int m;
	scanf("%d",&m);
	init_set();
	for(int i = 1; i <= m; ++i)
	{
		scanf("%d%d",&x,&y);
		x = find_set(x);
		y = find_set(y);
		if(x != y)
		{
			union_set(x,y);
			--num;
		}
	}
	kruskal();
	return 0;
}