首页 > ACM题库 > HDU-杭电 > HDU 1025 Constructing Roads In JGShining’s Kingdom-计算几何-[解题报告] C++
2013
11-26

HDU 1025 Constructing Roads In JGShining’s Kingdom-计算几何-[解题报告] C++

Constructing Roads In JGShining’s Kingdom

问题描述 :

JGShining’s kingdom consists of 2n(n is no more than 500,000) small cities which are located in two parallel lines.

Half of these cities are rich in resource (we call them rich cities) while the others are short of resource (we call them poor cities). Each poor city is short of exactly one kind of resource and also each rich city is rich in exactly one kind of resource. You may assume no two poor cities are short of one same kind of resource and no two rich cities are rich in one same kind of resource.

With the development of industry, poor cities wanna import resource from rich ones. The roads existed are so small that they’re unable to ensure the heavy trucks, so new roads should be built. The poor cities strongly BS each other, so are the rich ones. Poor cities don’t wanna build a road with other poor ones, and rich ones also can’t abide sharing an end of road with other rich ones. Because of economic benefit, any rich city will be willing to export resource to any poor one.

Rich citis marked from 1 to n are located in Line I and poor ones marked from 1 to n are located in Line II.

The location of Rich City 1 is on the left of all other cities, Rich City 2 is on the left of all other cities excluding Rich City 1, Rich City 3 is on the right of Rich City 1 and Rich City 2 but on the left of all other cities … And so as the poor ones.

But as you know, two crossed roads may cause a lot of traffic accident so JGShining has established a law to forbid constructing crossed roads.

For example, the roads in Figure I are forbidden.

In order to build as many roads as possible, the young and handsome king of the kingdom – JGShining needs your help, please help him. ^_^

输入:

Each test case will begin with a line containing an integer n(1 ≤ n ≤ 500,000). Then n lines follow. Each line contains two integers p and r which represents that Poor City p needs to import resources from Rich City r. Process to the end of file.

输出:

For each test case, output the result in the form of sample.
You should tell JGShining what’s the maximal number of road(s) can be built.

样例输入:

2
1 2
2 1
3
1 2
2 3
3 1

样例输出:

Case 1:
My king, at most 1 road can be built.

Case 2:
My king, at most 2 roads can be built.

Hint
Huge input, scanf is recommended.

题意: 给你两条街,上面的街编号从 1-n 下面的也是,然后告诉你他们的一些边,

    让你从中尽可能选出多的边,使他们两两之间没有交点。

分析: LIS 的变形,把一条街看成有序的,求令一条街的最长递增子序列,

    因为当 上面 i < j 时 有 f[i]<f[j]。

#include<stdio.h>
#include<string.h>
int d[500005];
int l[500005];
int bis(int len,int x)
{
    int low=0,high=len-1,mid;
    while(low<=high)
    {
        mid=(low+high)>>1;
        if(d[mid]>x)
            high=mid-1;
        else if(d[mid]<x)
            low=mid+1;
        else return mid;
    }
    return low;
}
int main()
{
    int ca=1,len,i,n,a,b,x,pos;
    while(scanf("%d",&n)!=EOF)
    {
        d[0]=5000006;
        len=1;
        for(i=1;i<=n;i++)
        {
            scanf("%d%d",&a,&b);
            l[a]=b;
        }
        for(i=1;i<=n;i++)
        {
            x=l[i];
            if(x>d[len-1])
                d[len++]=x;
            else
            {
                pos=bis(len,x);
                d[pos]=x;
            }
        }
        printf("Case %d:\nMy king, at most %d %s can be built.\n\n",ca++,len,len>1?"roads":"road");
    }
    return 0;
}

 


  1. 一开始就规定不相邻节点颜色相同,可能得不到最优解。我想个类似的算法,也不确定是否总能得到最优解:先着一个点,随机挑一个相邻点,着第二色,继续随机选一个点,但必须至少有一个边和已着点相邻,着上不同色,当然尽量不增加新色,直到完成。我还找不到反例验证他的错误。。希望LZ也帮想想, 有想法欢迎来邮件。谢谢