POJ1751Highways

Posted 2020-12-27 lif323

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;
}

如有错误，恳请指正